hepss09 proceedings v7 - PPD · IPPP Durham RAL HEP Summer School 7.9.-18.9.2009 F. Krauss IPPP...

PHENOMENOLOGY

By Dr F Krauss University of Durham

Lecture presented at the School for Experimental High Energy Physics Students Somerville College, Oxford, September 2009

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Contents

Part 1: QCD............................................................................................................ 215 Introduction....................................................................................................... 216 Hard processes & PDFs ................................................................................... 220 QCD radiation................................................................................................... 239 Hard QCD processes: Jets................................................................................ 245 Summary............................................................................................................ 268

Part 2: SM measurements.................................................................................... 270 Interpretations................................................................................................... 271 Gauge sector of the SM .................................................................................... 273 Flavor physics ................................................................................................... 285 Top physics........................................................................................................ 289 Summary............................................................................................................ 299

Part 3: The Higgs boson ...................................................................................... 300 Higgs mechanism ............................................................................................. 301 SM Higgs boson searches ................................................................................ 305 SM Higgs boson properties............................................................................. 317 More Higgs bosons........................................................................................... 321

Part 4: BSM physics.............................................................................................. 327 BSM motivation ................................................................................................ 328 Supersymmetry................................................................................................. 329 Other models..................................................................................................... 334

Part 5: MC generators .......................................................................................... 337 Orientation......................................................................................................... 328 MC integration.................................................................................................. 338 Reminder: ME’s ................................................................................................ 342 Reminder: QCD showers................................................................................. 346 Hadronization ................................................................................................... 350 Underlying Event ............................................................................................. 355 Upshot ................................................................................................................ 360

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�

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Introduction Hard processes & PDFs QCD radiation Hard QCD processes: Jets Summary

Phenomenologyat collider experiments

[Part 1: QCD]

Frank Krauss

IPPP Durham

RAL HEP Summer School 7.9.-18.9.2009

F. Krauss IPPP

Phenomenology at collider experiments [Part 1: QCD]


Outline

1 Introductory remarksStatus of particle physicsDesign considerations for LHC

2 Cross section calculations at hadron collidersMatrix elements at leading and next-to leading orderPDFs and factorisation

3 QCD radiationPattern of QCD radiation: Infrared region rulesParton showers: Simulating QCD radiation

4 Hard QCD processes: JetsBasic considerations: Definitions and IR safetyModern jet definitions

5 Summary

F. Krauss IPPP


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Status of particle physics

Chasing the energy frontier

View of the 1990’s . . .10,000

1000

100

10

1

1960 1970 1980 1990 2000Year of First Physics

Con

stitu

ent C

ente

r-of

-Mas

s E

nerg

y

(GeV

)

ISR

PRIN-STAN, VEPP II, ACO

ADONESPEAR, DORIS

SPEAR IIVEPP IVCESR

PETRA, PEP

TRISTAN

SLC, LEP

LHC

NLC

Tevatron

SppS

2-96 8047A363

Hadron Colliders

e+e– Colliders

THE ENERGY FRONTIER

Completed

Under Construction

In Planning Stages

LEP II

F. Krauss IPPP




Phenomenology at colliders

The past up to LEP and Tevatron

1950’s: The particle zooDiscovery of hadrons, but no order criterion

1960’s: Strong interactions before QCDSymmetry: Chaos to order

1970’s: The making of the Standard Model:Gauge symmetries, renormalisability, asymptotic freedomAlso: November revolution and third generation

1980’s: Finding the gauge bosonsNon-Abelian gauge theories are real!

1990’s: The triumph of the Standard Model at LEP and TevatronPrecision tests for precision physics

F. Krauss IPPP


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The present: LHC

Historical trend: Hadron colliders for discovery physicsLepton colliders for precision physics.

Historical trend: Shape your searches - know what you’re looking for.This has never been truer.

In last decades: Theory triggers, experiment executes.Also true for the LHC?!

F. Krauss IPPP




Setting the scene

Reminder: The Standard Model3 generations of matter fields:left-handed doublets, right-handed singlets

Quarks Leptons

„u

d

«L

„c

s

«L

„t

b

«L

„νee

«L

„νμμ

«L

„νττ

«L

uRdR

cRsR

tRbR eR μR τR

(Broken) gauge group: SU(3)× SU(2)× U(1) → SU(3)× U(1):8 gluons, 3 (massive) weak gauge bosons, 1 photon

Electroweak symmetry breaking (EWSB) by introducing a complexscalar doublet (Higgs doublet) with a vacuum expectation value(vev) =⇒ 1 physical Higgs scalar

F. Krauss IPPP


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How we know what we know (examples)

Generations

0

10

20

30

86 88 90 92 94Ecm [GeV]

�ha

d [n

b]

3�

2�

4�

average measurements,error bars increased by factor 10

ALEPHDELPHIL3OPAL

EW precision data

Measurement Fit |Omeas�Ofit|/�meas

0 1 2 3

0 1 2 3

��had(mZ)��(5) 0.02758 ± 0.00035 0.02767

mZ [GeV]mZ [GeV] 91.1875 ± 0.0021 91.1874

Z [GeV]Z [GeV] 2.4952 ± 0.0023 2.4959

�had [nb]�0 41.540 ± 0.037 41.478

RlRl 20.767 ± 0.025 20.742

AfbA0,l 0.01714 ± 0.00095 0.01643

Al(P)Al(P) 0.1465 ± 0.0032 0.1480

RbRb 0.21629 ± 0.00066 0.21579

RcRc 0.1721 ± 0.0030 0.1723

AfbA0,b 0.0992 ± 0.0016 0.1038

AfbA0,c 0.0707 ± 0.0035 0.0742

AbAb 0.923 ± 0.020 0.935

AcAc 0.670 ± 0.027 0.668

Al(SLD)Al(SLD) 0.1513 ± 0.0021 0.1480

sin2�effsin2�

lept(Qfb) 0.2324 ± 0.0012 0.2314

mW [GeV]mW [GeV] 80.399 ± 0.025 80.378

W [GeV]W [GeV] 2.098 ± 0.048 2.092

mt [GeV]mt [GeV] 173.1 ± 1.3 173.2

March 2009

(from LEP EWWG public page, winter 2009

plot)

F. Krauss IPPP




Open questions (private preference)

True mechanism of EWSB: Higgs mechanism in its minimal or anextended version or something different?

Generations: Three or more?

More symmetry: Is there low-scale Supersymmetry?

Space-time: How many dimensions? Four or more?

Cosmology: Any candidates for dark matter?

F. Krauss IPPP


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LHC design

LHC - The energy frontier

Design defines difficulty

Design paradigm for LHC:1 Build a hadron collider2 Build it in the existing LEP tunnel3 Build it as competitor to the 40 TeV SSC

Consequence:1 LHC is a pp collider2 LHC operates at 10-14 TeV c.m.-energy3 LHC is a high-luminosity collider: 100 fb−1/y

Trade energy vs. lumi, thus pp

Physics:1 Check the EWSB scenario & search for more2 Fight with overwhelming backgrounds, QCD always a stake-holder3 Consider niceties such as pile-up, underlying event etc..

F. Krauss IPPP



LHC design

Some example cross sectionsOr: Yesterdays signals = todays backgrounds

Process Evts/sec.Jet, E⊥ > 100 GeV 103

Jet, E⊥ > 1 TeV 1.5 · 10−2

bb 5 · 105tt 1

Z → �� 2W → �ν 20

WW → �ν�ν 6 · 10−3

Rates at “low” luminosity, L = 1033/cm2s = 10−1fb−1/y, and s = 14 TeV.

F. Krauss IPPP


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Cross sections at hadron colliders

Master formulaProduction cross section for final state Φ in AB collisions:

σAB→Φ+X =∑ab

1∫0

dx1dx2 fa/A(x1, μ2F )fb/B(x2, μ

2F ) σab→Φ(s, μ

2F , μ2

R)

where

x1,2 are momentum fractions w.r.t. the hadron, s = x1x2s;

σab→Φ(s, μ2F , μ2

R) is the parton-level cross section,

and where fa/A(x ,Q2) is the parton distribution function (PDF).

F. Krauss IPPP



Scattering amplitudes

Tree-level matrix elements

Simple scattering cross sections

Detailed look into master formula above:Convolution of parton-level cross section σ with PDFs.

Must evaluate σ as phase-space integral, respecting four-momentumconservation of amplitude squared:

dσab→Φ =1

4√(papb)2 − p2ap

2b

|Mab→Φ(pa, pb, p1, . . . , pN)|2

NΦ∏i=1

[d4pi

(2π)4(2π)δ(p2i − m2

i )θ(Ei )

](2π)4δ4(pa + pb −

∑pi ) .

Note: Have to normalise on Lorentz-invariant flux.

Smart choices for phase space integration helpful.

F. Krauss IPPP


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Generic Lorentz-invariant quantities

Use Mandelstam variables (especially for 2 → 2 scatterings):

s = (pa + pb)2 = (p1 + p2)

2

t = (pa − p1)2 = (pb − p2)

2

u = (pa − p2)2 = (pb − p1)

2 .

Relation to masses

s + t + u = m2a + m2

b + m21 + m2

2massless−→ 0 .

In the massless case

dσab→12

dt=

1

2s

|Mab→12|28πs

.

F. Krauss IPPP




Kinematics at hadron collidersTypically, at hadron colliders: transverse momentum p⊥ and rapidityy characterise kinematics.

Note rapidity y vs. pseudorapidity η (identical for m = 0 only):

y =1

2ln

E + pz

E − pz

←→ η = − ln tanϑ

2.

Rewrite four-momentum (m2⊥ = p2⊥ +m2)

pμ = (E , px , py , pz) = (m⊥ cosh y , p⊥ sinφ, p⊥ cosφ,m⊥ sinh y) .

One-particle phase space element:

d4p(2π)4

(2π)δ(p2 − m2)θ(E ) =d3p

(2π3)2E=

dy

4π

d2p⊥(2π)2

.

F. Krauss IPPP


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Resonance production (2 → 1 processes)

Assume massless incoming partons: pa,b = x1,2(E , 0, 0, ±E ).(Here, E is beam energy in c.m. system of collider, s = 4E2.)

Special form of cross section: σab→Φ = gσ(s,m2Φ) δ(s − m2

Φ).

Example: qq → V with vector and axial vector coupling V and A.(Add normalisation: average over incoming degrees of freedom, include incoming flux.)

|Mqq→V |2 =1

3M2

V (V2 + A2)

σqq→V =π

3(V 2 + A2)δ(s − M2

V ) .

Trivial relation to partial decay widths of the produced particles:(|MV→qq |2 = 36/3|Mqq→V |2.)

dΓ =1

8πM|MV→qq|2 .

F. Krauss IPPP




Resonance production (cont’d)

Then

s = x1x2s and y =1

2ln

x1 + x2 + x1 − x2

x1 + x2 − x1 + x2=

1

2ln

x1

x2.

Relation of Bjorken-x and rapidity:

x1,2 =

√s

se±y and y =

1

2ln

x21 s

m2φ

≤ ln2E

mφ

= ymax .

Together (sdx1dx2 = dsdy):

σAB→Φ =∑ab

ymax∫−ymax

dy x1fa/A(x1, μ2F )x2fb/B(x2, μ2

F )gσ(m

2φ, m2

φ)

m2φ

.

F. Krauss IPPP


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Resonance production (cont’d)

Note: Only dependence onrapidity through the PDFs=⇒ rapidity distribution of Φcontains information on thePDFs of partons a and b.

(Remember: x1,2 = mφ/se±y .)

Obvious consequence: Thehigher the mass of the producedsystem the more central it is.

10-7 10-6 10-5 10-4 10-3 10-2 10-1 100100

101

102

103

104

105

106

107

108

109

fixedtarget

HERA

x1,2

= (M/14 TeV) exp(±y)

Q = M

LHC parton kinematics

M = 10 GeV

M = 100 GeV

M = 1 TeV

M = 10 TeV

66y = 40 224

Q2

(GeV

2 )

x

(Plot from MSTW homepage)

F. Krauss IPPP




Aside: Rapidities of gauge bosons

From the Tevatron to the LHC

F. Krauss IPPP


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Kinematics of 2 → 2 processes

Use transverse momenta and (pseudo-) rapidities: p⊥, y3, y4.

Introduce average (centre-of-mass) rapidity and rapidity distance,

y = (y3 + y4)/2 and y∗ = (y3 − y4)/2.

Relate rapidities to Bjorken-x :

x1,2 =p⊥√2

(e±y3 + e±y4

)=

p⊥

2√

se±y cosh y∗.

Therefore: s = M212 = 4p2⊥ cosh y∗.

Similarly t, u = − s

2(1∓ tanh y∗).

F. Krauss IPPP




Kinematics of 2 → 2 processes (cont’d)

Partonic cross section (keep all massless) reads

σab→12 =1

2s

∫d3p1

(2π)32E1

d3p2(2π)32E2

|Mab→12|2

(2π)4δ4(pa + pb − p1 − p2)

=1

2s2

∫d2p⊥(2π)2

|Mab→12|2 .

Fold in the PDFs (sum over a, b, integrate over x1,2):

σAB→12 =∑ab

∫dy1dy2d2p⊥16π2s2

fa(x1, μF )fb(x2, μF )

x1x2|Mab→12|2 .

Note: Do not forget a factor 1/(1 + δ12) for identical final states.

F. Krauss IPPP


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QCD matrix elements

Common feature: t-channeldominance

(If existing, “elastic” scattering wins.)

Note: Typicallyt → 0 ⇐⇒ p2⊥ → 0.

Consequence: parton-partoncross section grows fast forp⊥ → 0.

Effect further enhanced byrunning αs .

(Would use μR = p⊥ as scale.))

Examples:

qq′ → qq′ 49

s2+u2

t2

qq → q′q′ 49

t2+u2

s2

qq → gg 3227

t2+u2

t u− 8

3t2+u2

s2

qg → qg s2+u2

t2− 4

9s2+u2

s u

gg → qq 16

t2+u2

t u− 3

8t2+u2

s2

gg → gg 92

(3− t u

s2− s u

t2− s t

u2

)qq → gγ 8

9t2+u2+2s(s+t+u)

t u

qg → qγ − 13

s2+u2+2t(s+t+u)s u

Note: For real photons t + u + s = 0

(multiply with couplings, e.g. g4 = (4παs )2, g2e2e2q )

F. Krauss IPPP




Jet production at Tevatron

(GeV/c)JETTP

0 100 200 300 400 500 600 700

(GeV

/c)

nb

T

dY

dP�2 d

-1410

-1110

-810

-510

-210

10

410

710

1010

1310

)6|Y|<0.1 (x10

)3

0.1<|Y|<0.7 (x10

0.7<|Y|<1.1

)-3

1.1<|Y|<1.6 (x10

)-6

1.6<|Y|<2.1 (x10

=0.75mergeMidpoint: R=0.7, f

) -1CDF Run II Preliminary (L=1.13 fb

Data corrected to the hadron level

Systematic uncertainty

=1.3sep/2, RJETT=PμNLOJET++ CTEQ 6.1M

F. Krauss IPPP


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Higher-order corrections

Specifying higher-order corrections: γ∗ → hadrons

In general: NnLO ↔ O(αns )

But: only for inclusive quantities(e.g.: total xsecs like γ∗ →hadrons).

Counter-example: thrust distribution

In general, distributions are HO.

Distinguish real & virtual emissions:Real emissions → mainly distributions,virtual emissions → mainly normalisation.

F. Krauss IPPP




Anatomy of HO calculations: Virtual and real corrections

NLO corrections: O(αs)Virtual corrections = extra loopsReal corrections = extra legs

UV-divergences in virtual graphs → renormalisation

But also: IR-divergences in real & virtual contributionsMust cancel each other (Kinoshita-Lee-Nauenberg &Bloch-Nordsieck theorems),non-trivial to see: N vs. N + 1 particle FS, divergence in PS vs. loop

F. Krauss IPPP


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Cancelling the IR divergences: Subtraction method

Total NLO xsec: σNLO = σBorn +∫

dDk|M|2V +∫

d4k|M|2RIR div. in real piece → regularise:

∫d4k|M|2R → ∫

dDk|M|2RConstruct subtraction term with same IR structure:∫

dDk(|M|2R − |M|2S

)=

∫d4k|M|2RS = finite.

Possible:∫

dDk|M|2S = σBorn

∫dDk|S|2, universal |S|2.∫

dDk|M|2V + σBorn

∫dDk|S|2 = finite (analytical)

Has been automated in various programs.

Remark: Part of the collinear divergences in initial state absorbed inPDFs.

(This introduces scheme dependence and spoils probabilistic interpretation of PDFs.)

F. Krauss IPPP




Cross sections @ hadron colliders

Availability of exact calculations

donefor some processesfirst solutions

n legs

m loops

1 2 3 4 5 6 7 8 9

1

2

0

F. Krauss IPPP


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Tree-level tools (publicly available)Models 2 → n Ampl. Integ. lang.

Alpgen SM n = 8 rec. Multi FortranAmegic SM,MSSM,ADD n = 6 hel. Multi C++CompHep SM,MSSM n = 4 trace 1Channel CCOMIX SM n = 8 rec. Multi C++HELAC SM n = 8 rec. Multi FortranMadEvent SM,MSSM,UED n = 6 hel. Multi FortranO’Mega SM,MSSM,LH n = 8 rec. Multi O’Caml

(One-)Loop-level tools (publicly available)Processes lang.

MCFM SM, 3-particle FS FortranNLOJET++ up to 3 light jets C++Prospino MSSM pair production Fortran

F. Krauss IPPP



PDFs

PDFs and factorisation

Parton picture

Parton picture: Hadrons made from partons.

Distribution(s) of partons in hadrons:not from first principles, only from measurements.

First idea: probability to find parton a in hadron h only dependenton Bjorken-x (x = Ea/Eh or similar) – “Bjorken-scaling”P(a|h) = f h

a (x) (LO interpretation of PDF).

But QCD: Partons in partons in partons=⇒ scaling behaviour of PDFs: f = f (x , Q2).

Still: PDFs must be measured, but scaling in Q2 from theory(DGLAP, resums large logs of Q2)

F. Krauss IPPP


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PDFs

Space-time picture of hard interactions

Partons “collinear” with hadron: k⊥ � 1/Rhad .

Lifetime of partons τ ∼ 1/x , r ∼ 1/Q.

Hard interaction at scales Qhard � 1/Rhad .

Too “fast” for colour field - only one parton takes part.

Other partons feel absence only when trying to recombine.

Universality (process-independence) of PDFs.

Collinear factorisation.

F. Krauss IPPP



PDFs

Revealing the inner structure: ep-scattering

A detour: Elastic scattering & Form factors

Extended objects have a matter density ρ(�r).

Normalisation:∫

d3r ρ(�r) = 1

Its Fourier transform is called a form factor:

F (�q) =

∫d3r exp[−i�q�r ]ρ(�r) =⇒ F (0) = 1

Naive modification of cross sections for scattering on such objects:

dσ

d2Ω

∣∣∣∣ptlike

=⇒ dσ

d2Ω

∣∣∣∣extended

≈ dσ

d2Ω

∣∣∣∣ptlike

|F (q)|2

F. Krauss IPPP


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PDFs

Elastic ep scattering and the Rosenbluth formula

Simple test of proton’s charge distribution: elastic ep scattering(exchange of a photon). Elastic: Nucleon remains intact.

Rosenbluth-formula (E and E ′ are energies of electron before andafter scattering, M is the proton mass, q2 is the space-likemomentum transfer, and θ is the scattering angle):

dσ

d2Ω=

α2 cos2 θ

2

4E 2 sin4 θ

2

E ′

E

[(F 21 (q

2)− κ2q2

4M2F 22 (q

2)

)− q2

2M2

(F1(q

2) + κF2(q2))2tan2

θ

2

]Compare with Rutherford scattering (on very massive objects):

dσ

d2Ω=

α2

4E 2 sin4 θ

2

F. Krauss IPPP



PDFs

Elastic ep scattering and charge radius of the proton

Differences due to relativistic kinematics plus recoil of the protons(in Rutherford scattering, the nuclei stay at rest).

Also inner structure: there are two form factors F1,2. They arerelated to the electric and magnetic form factors, and areparametrised as

F1,2 ≈[

1

1− q2/0.71GeV2

]2Connection to charge radius: Assume F1 = F2 and

F (q2) =

∫d3r ρ(�r) exp[−i�q�r ] ≈ 1− �q2

6〈r2〉+ . . .

Therefore: rproton ≡ 〈r2〉1/2 ≈ 0.75± 0.25 fm.

F. Krauss IPPP


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PDFs

Deep-inelastic scattering: The process

Terminology arises because in contrast to elastic scattering thenucleon nearly always disintegrates.

Typically in DIS proton is probed with γ’s.From p ≈ 1/λ: If momentum transfer larger than 1 GeV,(≈ 1/0.2fm) then inner structure revealed.

Kinematics:

k′μ

pμ

xpμ

kμ

qμ = (k − k′)μ

θ

inv.mass W

ν = 2pqmp

−→ E − E ′

(energy transfer)

x = Q2

2pq−→ Q2

E−E ′(momentum fraction of parton)

Q2 = −q2 = −2EE ′(1− cos θ)(momentum transfer squared)

F. Krauss IPPP



PDFs

Two basic ideas

Typically, the behaviour of the cross section with varying x (or,alternatively ν) and Q2 is being measured.In addition, νp-scattering with W exchange is considered.

Two basic ideas:

The parton model (by R.Feynman):The nucleon is made of smaller bits (partons). Later knowledge: Canbe identified with quarks and gluons. But: In addition to the threevalence quarks, carrying the quantum numbers (e.g. |p〉 = |uud〉),there are virtual quarks and gluons, the sea.The scaling hypothesis (by J.D.Bjorken):At large energies and momentum transfers, the cross section dependson one variable only. Reason: The photon ceases to scattercoherently off the nucleon, but solely sees the individual, point-likepartons.

F. Krauss IPPP


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PDFs

Bjorken-scaling

Equation for cross section (cf. elastic scattering, replacing formfactors F1,2(q

2) with structure functions W1,2(ν,Q2)):

dσ

d2Ω=

α2 cos2 θ

2

4E 2 sin4 θ

2

[W2(ν,Q2) + 2W1(ν,Q2)

]Bjorken scaling implies thatwith no special scale presentin the dynamics of thescattering the W1,2(ν,Q2)can be replaced:

mpW1(ν,Q2) −→ F1(x)

Q2

2mpxW2(ν,Q2) −→ F2(x) ,

Independence of W2 on q2:

F. Krauss IPPP



PDFs

The spin of the quarks: The Callan-Gross relation

Bjorken scaling established that DIS in fact must be described interms of parton-photon processes.But what are the properties of these point-like constituents?

In 1969 Callan and Grosssuggested that Bjorken’sscaling functions are related:

2xF1(x) = F2(x) .

This reflects the assumptionthat the partons inside theproton are indeed quarks,i.e. spin-1/2 particles(spin-0 for example wouldlead to 2xF1(x)/F2(x) = 0.)

Measuring the quark spin

F. Krauss IPPP


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PDFs

Deriving the Callan-Gross relation

Basic idea: Compare eq-scattering cross section (free quark) withthe DIS ep cross section and assume identity:

d2σeq

d2ΩdE ′=

α2 cos2 θ

2

4E 2 sin4 θ

2

[1 +

Q2

2m2p

tan2θ

2

]δ

(ν − Q2

2mpx

)d2σep

d2ΩdE ′=

α2 cos2 θ

2

4E 2 sin4 θ

2

[1

νF2(x) +

2

mp

tan2θ

2F1(x)

]

F. Krauss IPPP



PDFs

Parton distributions and sum rules

Define probabilities (possible at LO only) fa(x) to find a parton oftype a with energy fraction between x and x + dx :

F1(x) =∑

a

q2a fa(x) , qa = parton’s charge.

The parton momenta must add to the proton momentum:∫ 1

0

dx x [fu(x) + fu(x) + fd(x) + fd(x) + fs(x) + fs(x) + . . . ] = 1 .

The parton types must yield a “net proton”, p〉 = |uud〉:1∫0

dx [fu(x)− fu(x)] = 21∫0

dx [fd(x)− fd(x)] = 1

1∫0

dx [fs(x)− fs(x)] = 01∫0

dx [fc(x)− fc(x)] = 0 .

F. Krauss IPPP


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PDFs

QCD effect on structure functions: Scaling violations

Now it is possible toquantify the picture of“proton = quarks + stuff”

Leads to evolutionequations: “Russian dolls”

This implies dependence of F1,2on the momentum transfer.

Therefore: F1,2 depend on bothx and Q2 - not constant in Q2

any more.

F. Krauss IPPP



PDFs

Quantifying scaling violations: Evolution equations

Explanation: As the proton is hit harder and harder (i.e. at largerQ2), the virtual photon starts resolving gluons and quark-antiquarkfluctuations (partons in partons!).

The scale Q2 plays the role of a “resolution parameter”.

Described by the DGLAP equations. Basic structure:

dq(x ,Q2)

d lnQ2= αs(Q

2)

1∫x

dy

[q(y ,Q2)Pq→qg

(x

y

)

+g(y ,Q2)Pg→qq

(x

y

)]Here the quark at x can come from a quark (gluon) at y , thefunctions P encode the details of the decays q → qg (g → qq)responsible for it.

F. Krauss IPPP


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PDFs

Aside: The “running” coupling in QCD & asymptotic freedom

Reassuring: Can understand the proton structure at large Q2 interms of perturbative objects (quarks and gluons). This implies thatthe coupling gs is sufficiently small there:

Asymptotic freedom.

But measurements (left) andcalculation show that the couplingbecomes stronger the lower the scale(� Q2), i.e. the larger the distance.

In fact, the perturbative αs diverges forμ = ΛQCD ≈ 300 MeV, signalling thebreakdown of the expansion.

αs = g2s /(4π)

1 2 5 10 20 50 100 2000.0

0.1

0.2

0.3

0.4

μ (GeV)

�s(μ)

Non-perturbative regime, where only colour-less states can exist:Confinement.

Therefore, only hadrons (no quarks or gluons) as observable initialand final states in experiments.

F. Krauss IPPP



PDFs

Fitting PDFs: Strategy in a nutshell

Ansatz g(x) for PDFs at some fixed valueof Q2

0 = Q2 ≈ 1GeV2.For example, MRST/MSTW: (personal Durham bias)

xuv = Auxη1 (1 − x)

η2 (1 + εu√

x + γux)

xdv = Ad xη2 (1 − x)

η4 (1 + εd√

x + γd x)

xs = AS x−λS (1 − x)

ηS (1 + εS√

x + γS x)

xg = Ag x−λg (1 − x)

ηg (1 + εg√

x + γg x)

Collect data at various x , Q2, use DGLAPequation to evolve down to Q2

0 , also fix αs .

Order of fit ⇐⇒ order of kernels.

Enforce sum rules (momentum, . . . )(Partially relaxed for LO∗ and LO∗∗ .)

Generic structureLarge sea for x → 0

Valence at x ≈ 0.15

F. Krauss IPPP


- 235 -


PDFs

Determination of PDFs: Data input

Example: MSTW parameterisation and their effect:

(From R.Thorne’s talk at DIS 2007)

F. Krauss IPPP



PDFs

Uncertainties of global PDFs: CTEQ65E vs. MSTW2008 NLO

xu(x, Q2 = 10000GeV2) xu(x, Q2 = 10000GeV2) xg(x, Q2 = 10000GeV2)

(From Hepdata base)

F. Krauss IPPP


- 236 -


PDFs

Remark on scales and PDF choices

In perturbative calculations at hadron colliders, two (unphysical)scales enter:

Renormalisation scale μR (scale for coupling constants)Factorisation scale μF (scale for PDFs)

In principle, all-orders results would be independent,in practise, results shows a dependence on scales.

This dependence decreases by adding more orders.

Smart process-dependent choices can mimic some HO effects.

A common recipe to estimate higher-order effects and the relateduncertainty is to vary both scales by a factor (typically 2).This is not always reliable ⇐⇒ nothing replaces the true HOcalculation

. . . especially if we want to know for sure . . . .

F. Krauss IPPP



PDFs

Understanding of perturbative QCD

1

10

10 2

10 102

103

inclusive jet productionin hadron-induced processes

fastNLOwww.cedar.ac.uk/fastnlo

DIS

pp-bar

�s = 300 GeV

�s = 630 GeV

�s = 1800 GeV

�s = 1960 GeV

100 < Q2 < 500 GeV2

500 < Q2 < 10 000 GeV2

H1 150 < Q2 < 200 GeV2

H1 200 < Q2 < 300 GeV2

H1 300 < Q2 < 600 GeV2

ZEUS 125 < Q2 < 250 GeV2

ZEUS 250 < Q2 < 500 GeV2

H1 600 < Q2 < 3000 GeV2

ZEUS 500 < Q2 < 1000 GeV2

ZEUS 1000 < Q2 < 2000 GeV2

ZEUS 2000 < Q2 < 5000 GeV2

DØ |y| < 0.5

CDF 0.1 < |y| < 0.7DØ 0.0 < |y| < 0.5DØ 0.5 < |y| < 1.0

CDF cone algorithmCDF kT algorithm

(� 100)

(� 40)

(� 8)

(� 3)

(� 1)

all pQCD calculations by fastNLO:

�s(MZ)=0.118 | CTEQ6.1 PDFs | μr = μf = pT

DIS in NLO | pp in NLO + NNLO-NLL | plus non-perturbative corrections

pT (GeV/c)

data

/ th

eory

F. Krauss IPPP


- 237 -


PDFs

PDFs: From Tevatron to LHC

101 1021

10

100

qq

ratios of parton luminositiesat 10 TeV LHC and 1.96 TeV Tevatron

lu

min

osity

rat

io

MX (GeV)

gg

MSTW2008NLO

101 1021

10

100

qq

ratios of parton luminositiesat 14 TeV LHC and 1.96 TeV Tevatron

lum

inos

ity r

atio

MX (GeV)

gg

MSTW2008NLO

(From MSTW homepage.)

F. Krauss IPPP



PDFs

PDF uncertainties at LHC(Propaganda plot by MSTW collaboration, CTEQ similar.)

102 103-15

-10

-5

0

5

10

15

g g � X q qbar � X G G � X

where G = g + 4/9 q(q + qbar)

|yX| < 2.5

parton luminosity uncertaintiesat LHC (MSTW2008NLO)

lum

inos

ity u

ncer

tain

ty (

%)

MX (GeV)

F. Krauss IPPP


- 238 -


From parton to hadron level

Limitations of parton level calculations

Fixed order parton level (LO, NLO, . . . ) implies fixed multiplicity=⇒ no clean way toward exclusive final states.

No control over potentially large logs(appear when two partons come close to each other).

Parton level is parton levelexperimental definition of observables relies on hadrons.

Therefore: Need hadron level!Must dress partons with radiation!(will also enable universal hadronisation)

F. Krauss IPPP



Origin of radiation

Accelerated charges radiate

Well-known: Accelerated charges radiate

QED: Electrons (charged) emit photonsPhotons split into electron-positron pairs

QCD: Quarks (coloured) emit gluonsGluons split into quark pairs

Difference: Gluons are coloured (photons are not charged)Hence: Gluons emit gluons!

Cascade of emissions: Parton shower

F. Krauss IPPP


- 239 -


Pattern of QCD radiation

Pattern of radiation

Leading logs: e+e− → jets

Differential cross section:

dσee→3j

dx1dx2

= σee→2j

CF αs

π

x21 + x22

(1 − x1)(1 − x2)

Singular for x1,2 → 1.

Rewrite with opening angle θqg

and gluon energy fraction x3 = 2Eg/Ec.m.:

dσee→3j

d cos θqg dx3

= σee→2j

CF αs

π

24 2

sin2 θqg

1 + (1 − x3)2

x3

− x3

35

Singular for x3 → 0 (“soft”), sin θqg → 0 (“collinear”).

F. Krauss IPPP




Leading logs: Collinear singularities

Use

2d cos θqg

sin2 θqg

=d cos θqg

1 − cos θqg

+d cos θqg

1 + cos θqg

=d cos θqg

1 − cos θqg

+d cos θqg

1 − cos θqg

≈dθ2qg

θ2qg

+dθ2qg

θ2qg

Independent evolution of two jets (q and q):

dσee→3j ≈ σee→2j

∑j∈{q,q}

CFαs

2π

dθ2jgθ2jg

P(z) ,

where P(z) = 1+(1−z)2

z(DGLAP splitting function)

F. Krauss IPPP


- 240 -



Leading logs: Parton resolution

What is a parton?Collinear pair/soft parton recombine!

Introduce resolution criterion k⊥ > Q0.

Combine virtual contributions with unresolvable emissions:Cancels infrared divergences =⇒ Finite at O(αs)

(Kinoshita-Lee-Nauenberg, Bloch-Nordsieck theorems)

Unitarity: Probabilities add up to oneP(resolved) + P(unresolved) = 1.

+ =1.

F. Krauss IPPP




Occurrence of large logarithms

Many emissions: Parton parted partons

Iterate emissions (jets)

Maximal result for t1 > t2 > . . . tn:

dσ ∝ σ0

Q2∫Q20

dt1

t1

t1∫Q20

dt2

t2. . .

tn−1∫Q20

dtn

tn∝ logn Q2

Q20

How about Q2? Process-dependent!

F. Krauss IPPP


- 241 -



Towards a parton cascade/shower

Ordering the emissions : Pattern of parton parted partons

q21 > q22 > q23 , q21 > q′22

F. Krauss IPPP




Aside: Inclusion of quantum effects

Running coupling

Effect of summing up higher orders (loops): αs → αs(k2⊥)

Much faster parton proliferation, especially for small k2⊥.

Must avoid Landau pole: k2⊥ > Q20 � Λ2QCD

=⇒ Q20 = physical parameter.

F. Krauss IPPP


- 242 -



Soft logarithms : Angular ordering

In principle, independence on collinear variable:t (inv.mass), k2⊥, θ all lead to same leading logs

But: Soft limit for single emission also universal

Problem: Soft gluons come from all over (not collinear!)Quantum interference? Still independent evolution?

Answer: Not quite independent.Assume photon into e+e− at θee and photon off electron at θ

Transverse momentum and wavelength of photon: kγ⊥ ∼ zpθ, λ

γ⊥ ∼ 1/k

γ⊥ = 1/(zpθ).

Formation time of photon: Δt ∼ 1/ΔE , ΔE ∼ θ/λγ⊥ ∼ zpθ2.

ee-separation: Δb ∼ θeeΔt ∼ θee/(zpθ2).

Must be larger than transverse wavelength: Δb > λγ⊥ =⇒ θee > θ

Thus: Angular ordering takes care of soft limit.

F. Krauss IPPP




Soft logarithms : Angular ordering in pictures

=⇒Gluons at large angle from combined colour charge!

F. Krauss IPPP


- 243 -



Experimental manifestation of angular ordering

ΔR of 2nd & 3rd jet in multi-jet events in pp-collisions @ Tevatron

(from CDF, Phys. Rev. D50 (1994) 5562)

F. Krauss IPPP



Parton showers

Parton showers

Simulating parton radiation

Catch: Can exponentiate all emissions due to universal log pattern.

For parton showers use Sudakov form factor:

Δq(Q2,Q2

0 ) = exp

⎡⎢⎣− Q2∫Q20

dk2

k2

∫dz

αs [k2⊥(z , k2)]

2πP(z)

⎤⎥⎦= exp

⎡⎢⎣− Q2∫Q20

dk2

k2P(k2)

⎤⎥⎦ ≈ exp

[−CF

αs

2πlog2

Q2

Q20

]

Interpretation: No-emission probability between Q2 and Q20 .

F. Krauss IPPP


- 244 -


Parton showers

Parton showers

Tools

Shower variable A0? lang.Pythia inv.mass: t approx. FortranPythia8 transv.mom.: k2⊥ yes(?) C++Herwig opening angle yes FortranHerwig++ mod.opening angle yes C++Ariadne dipole transv.mom. yes FortranSherpa 2 showers: t and k2⊥ varying C++

F. Krauss IPPP



Some basics

What are jets?

Jets = collimated hadronic energy

Jets (unavoidably) happenin high-energy events:a collimated bunch ofhadrons flying roughly inthe same direction.

Note: hundreds of hadronscontain a lot of information.

More than we can hope tomake use of.

F. Krauss IPPP


- 245 -


Some basics

What are jets?


Often you don’t need afancy algorithm to “see”the jets.

But you do to give them aprecise and quantitativemeaning.

F. Krauss IPPP



Some basics

What are jets?


Jets are usually related tosome underlyingperturbative dynamics (i.e.quarks and gluons).

The purpose of a “jetalgorithm” is then to reducethe complexity of the finalstate, simplifying manyhadrons to simpler objectsthat one can hope tocalculate.

F. Krauss IPPP


- 246 -


Some basics

What are jets?


A jet algorithm maps themomenta of the final stateparticles into the momentaof a certain number of jets:

{pi} jet algo←→ {jl}It can act on momenta, calotowers, etc..

Most algorithms contain aresolution parameter, R,which controls the extensionof the jet.

F. Krauss IPPP



Some basics

Linking partons and detector signals

Jets occur in decays of heavy objects:Z , W± bosons, tops, SUSY, . . .Example: top-decays

Tau + jets

Tau

+ je

ts

Fully hadronic: Jets

TausTau + jets Tau + lepton

Tau

+ le

pton

Lepton + Jets

Lep

ton

+ J

ets

Leptons

Event rates for 10 fb−1:Process Number

tt 107

QCD Multijets3 9 · 1084 7 · 1075 6 · 1066 3 · 1057 2 · 1048 2 · 103

Tree-level (parton-level) numbers

pjet⊥ > 60 GeV, θij > π/6, |yi | < 3

Draggiotis, Kleiss & Papdopoulos ’02

F. Krauss IPPP


- 247 -


Some basics

But: Jets �= partons!

Jets are unavoidable whenever partons scatter.

Perturbative picture well understood.Example: Jet cross sections

Partons fragment through multiple parton emissions:

Soft & collinear divergences dominateLarge logs overcome “small” coupling

No quantitative understanding for transition to hadrons(fate of non-perturbative QCD)

But: Fragmentation & hadronisation dominated by low p⊥ .

Therefore: Partons result in collimated bunches of hadrons (GeV/c)JET

TP0 100 200 300 400 500 600 700

(GeV

/c)

nb

T

dY

dP�2 d

-1410

-1110

-810

-510

-210

10

410

710

1010

1310

)6|Y|<0.1 (x10

)3

0.1<|Y|<0.7 (x10

0.7<|Y|<1.1

)-3

1.1<|Y|<1.6 (x10

)-6

1.6<|Y|<2.1 (x10

=0.75mergeMidpoint: R=0.7, f

) -1CDF Run II Preliminary (L=1.13 fb

Data corrected to the hadron level

Systematic uncertainty

=1.3sep/2, RJETT=PμNLOJET++ CTEQ 6.1M

F. Krauss IPPP



Some basics

Jet definitions

General considerationsA jet definition is a set of rules to project large numbers of objects(dozens of partons, hundred’s of hadrons, thousand’s of calorimetertowers) onto a small number of parton-like objects with one well-definedfour-momentum each.For this jet definition to be useful,

the rules must be the same, independent of the level of application:QCD resilience/robustness;

the rules must be complete, with no ambiguities;

the rules must be experimental feasible and theoretically sensible.=⇒ Infrared safety crucial!

F. Krauss IPPP


- 248 -


Some basics

Robustness

Figure from G.Salam

F. Krauss IPPP



Some basics

Collinear/infrared safety

jet 2jet 1jet 1jet 1 jet 1

�s x (+ )�n

�s x (� )�n

�s x (+ )�n

�s x (� )�n

Collinear Safe Collinear Unsafe

Infinities cancel Infinities do not cancel

Figure from G.Salam

F. Krauss IPPP


- 249 -


Modern jet definitions

Cone jets: Fixed cone, progressive removal

Main idea: Define jets geometrically,remove found jets.

Take hardest particle = cone axis.

Draw cone around it.

Convert contents into a “jet” andremove them.

Repeat until no particles left.

Parameters: Cone-size, pmin⊥

good feature: Simple.

Bad feature: Infrared safe.

60

50

40

20

00 1 2 3 4 y

30

10

pt/GeV

(from G.Salam)

F. Krauss IPPP













60

50

40

20

00 1 2 3 4 y

30

10

pt/GeV Hardest particle as axis

(from G.Salam)

F. Krauss IPPP


- 250 -












60

50

40

20

00 1 2 3 4 y

30

10

pt/GeV Draw cone

(from G.Salam)

F. Krauss IPPP













60

50

40

20

00 1 2 3 4 y

30

10

pt/GeV Convert into jet

(from G.Salam)

F. Krauss IPPP


- 251 -












60

50

40

20

00 1 2 3 4 y

30

10


(from G.Salam)

F. Krauss IPPP













60

50

40

20

00 1 2 3 4 y

30

10

pt/GeV Draw cone

(from G.Salam)

F. Krauss IPPP


- 252 -












60

50

40

20

00 1 2 3 4 y

30

10


(from G.Salam)

F. Krauss IPPP













60

50

40

20

00 1 2 3 4 y

30

10


(from G.Salam)

F. Krauss IPPP


- 253 -












60

50

40

20

00 1 2 3 4 y

30

10

pt/GeV Draw cone

(from G.Salam)

F. Krauss IPPP













60

50

40

20

00 1 2 3 4 y

30

10


(from G.Salam)

F. Krauss IPPP


- 254 -



Cone jets: IR safety does matter(stolen from M.Cacciari)

All cone jets apart from SIS-cone are not infrared safe.

The best ones typically fail at (3+1) partons, others already at(2+1).

Last meaningful orderProcess JetClu, Atlas cone MidPoint CMS, it.cone Known at

incl.jets LO NLO NLO NLO (→ NNLO)V + 1 jet LO NLO NLO NLO3 jets none LO LO NLOV + 2 jets none LO LO NLOmjet in 2j + X none none none LO

But: HO calculations cost real money(100 theorists × 15 years ≈ 100 MEuro.)

Using unsafe tools makes them pretty much useless.

F. Krauss IPPP




Cone jets: IR safety does matter(stolen from M.Cacciari)

Question: How often are hard jets changes by soft stuff?

Generate events with2 < N < 10 hard partons &find jets.

Add 1 < Nsoft < 5 softparticles & repeat.

How often do we end upwith different jets?

F. Krauss IPPP


- 255 -



k⊥ jets

Main idea: Sequential recombination

Distance between two objects i and j :dij = min{p2i,⊥, p2j,⊥}ΔRij ,

Rij = [cosh2Δηij + cos2Δφij ]/D2.

“Cone-size” D.

Include beams, distance to beam:diB = p2i,⊥.

Combine two objects with smallestdij , until smallest dij > dcut.

Good feature: Infrared safe.

pt/GeV

60

50

40

20

00 1 2 3 4 y

30

10

(from G.Salam)

F. Krauss IPPP




k⊥ jets




“Cone-size” D.




pt/GeV

60

50

40

20

00 1 2 3 4 y

30

10

dmin is dij = 2.0263

(from G.Salam)

F. Krauss IPPP


- 256 -



k⊥ jets




“Cone-size” D.




pt/GeV

60

50

40

20

00 1 2 3 4 y

30

10

(from G.Salam)

F. Krauss IPPP




k⊥ jets




“Cone-size” D.




pt/GeV

60

50

40

20

00 1 2 3 4 y

30

10


(from G.Salam)

F. Krauss IPPP


- 257 -



k⊥ jets




“Cone-size” D.




pt/GeV

60

50

40

20

00 1 2 3 4 y

30

10

(from G.Salam)

F. Krauss IPPP




k⊥ jets




“Cone-size” D.




pt/GeV

60

50

40

20

00 1 2 3 4 y

30

10


(from G.Salam)

F. Krauss IPPP


- 258 -



k⊥ jets




“Cone-size” D.




pt/GeV

60

50

40

20

00 1 2 3 4 y

30

10

(from G.Salam)

F. Krauss IPPP




k⊥ jets




“Cone-size” D.




pt/GeV

60

50

40

20

00 1 2 3 4 y

30

10


(from G.Salam)

F. Krauss IPPP


- 259 -



k⊥ jets




“Cone-size” D.




pt/GeV

60

50

40

20

00 1 2 3 4 y

30

10

(from G.Salam)

F. Krauss IPPP




k⊥ jets




“Cone-size” D.




pt/GeV

60

50

40

20

00 1 2 3 4 y

30

10


(from G.Salam)

F. Krauss IPPP


- 260 -



k⊥ jets




“Cone-size” D.




pt/GeV

60

50

40

20

00 1 2 3 4 y

30

10

(from G.Salam)

F. Krauss IPPP




k⊥ jets




“Cone-size” D.




pt/GeV

60

50

40

20

00 1 2 3 4 y

30

10


(from G.Salam)

F. Krauss IPPP


- 261 -



k⊥ jets




“Cone-size” D.




pt/GeV

60

50

40

20

00 1 2 3 4 y

30

10

(from G.Salam)

F. Krauss IPPP




k⊥ jets




“Cone-size” D.




pt/GeV

60

50

40

20

00 1 2 3 4 y

30

10


(from G.Salam)

F. Krauss IPPP


- 262 -



k⊥ jets




“Cone-size” D.




pt/GeV

60

50

40

20

00 1 2 3 4 y

30

10

(from G.Salam)

F. Krauss IPPP




k⊥ jets




“Cone-size” D.




pt/GeV

60

50

40

20

00 1 2 3 4 y

30

10

dmin is diB = 154.864

(from G.Salam)

F. Krauss IPPP


- 263 -



k⊥ jets




“Cone-size” D.




pt/GeV

60

50

40

20

00 1 2 3 4 y

30

10

(from G.Salam)

F. Krauss IPPP




k⊥ jets




“Cone-size” D.




pt/GeV

60

50

40

20

00 1 2 3 4 y

30

10

dmin is diB = 1007

(from G.Salam)

F. Krauss IPPP


- 264 -



k⊥ jets




“Cone-size” D.




pt/GeV

60

50

40

20

00 1 2 3 4 y

30

10

(from G.Salam)

F. Krauss IPPP




k⊥ jets




“Cone-size” D.




pt/GeV

60

50

40

20

00 1 2 3 4 y

30

10


(from G.Salam)

F. Krauss IPPP


- 265 -



k⊥ jets




“Cone-size” D.




pt/GeV

60

50

40

20

00 1 2 3 4 y

30

10

(from G.Salam)

F. Krauss IPPP




k⊥ jets




“Cone-size” D.




pt/GeV

60

50

40

20

00 1 2 3 4 y

30

10


(from G.Salam)

F. Krauss IPPP


- 266 -



k⊥ jets




“Cone-size” D.




pt/GeV

60

50

40

20

00 1 2 3 4 y

30

10

(from G.Salam)

F. Krauss IPPP




Different jet algorithms(stolen from M.Cacciari)

F. Krauss IPPP


- 267 -


To take home

LHC, the QCD machineThere are no LHC events without QCD!!!

Perturbative expansion in αS sufficiently well understood,but: hard to calculate beyond (N)LO.

Important input to xsec calculations: PDFsMust be taken from data, only scaling from QCD

Order of an calculation is observable-dependentmake sure you know what you’re talking about.

F. Krauss IPPP



To take home

Parton-parted partons

QCD radiation (bremsstrahlung) important

Dominated by collinear & soft emissions

Universal pattern of QCD bremsstrahlung

Fills the phase space between large scales of signal creation and lowscales of hadronisation

Well understood in leading log approximation, gives rise to aprobabilistic picture: parton showers.

F. Krauss IPPP


- 268 -


To take home

A jet is (not) a jet is (not) a jet

Jets are direct result of QCD in hard reactions - your primaryexperimental QCD entities.

But: A parton is not a jet - a jet is what it is defined to be

Jet definitions must match experimental and theoretical needsotherwise meaningless for comparison

Infrared safety is a theoretical key requirement

Many jet algorithms, presumably the “best” one does not exist

F. Krauss IPPP


- 269 -

Interpretations Gauge sector of the SM Flavor physics Top physics Summary


[Part 2: SM measurements]

Frank Krauss

IPPP Durham


F. Krauss IPPP

Phenomenology at collider experiments [Part 2: SM measurements]


Outline

1 Introduction: Signal or not?

2 Gauge sector of the Standard modelPrecision physics at LHC: The W -boson propertiesBoson pairs: Backgrounds and new physicsA practical application: Luminosity monitors

3 Some remarks on flavorThe unitarity triangle: Importance of 3rd generationNew physics in B physics

4 Top-quark physicsThe top massTop properties: Single-top production, top couplings etc.

5 Summary

F. Krauss IPPP


- 270 -


Know your Standard Model

Historical example: Mono-jets at SppS

In Phys. Lett. B139 (1984) 115, the UA1 collaboration reported

5 events with E⊥,miss > 40 GeV+a narrow jet and2 events with E⊥,miss > 40 GeV+a neutral EM cluster

They could “not find a Standard Model explanation” for them,compared their findings with a calculation of SUSY pair-production

(J.Ellis & H.Kowalski, Nucl. Phys. B246 (1984) 189),and they deduced a gluino mass larger than around 40 GeV.

In Phys. Lett. B139 (1984) 105, the UA2 collaboration describessimilar events, also after 113 nb−1, without indicating anyinterpretation as strongly as UA1.

In Phys. Lett. B158 (1985) 341, S.Ellis, R.Kleiss, and J.Stirlingcalculated the backgrounds to that process more carefully, andshowed agreement with the Standard Model.

F. Krauss IPPP



Example: PDF uncertainty or new physics

Consider the ADD model of extra dimensions (KK towers of gravitons)and its effect on the dijet cross section:

(Note: Destructive interference with SM)

Figure from S.Ferrag, hep-ph/0407303

F. Krauss IPPP


- 271 -


Example: Inclusive SUSY searches Typical process

Shape of tt-events

F. Krauss IPPP



To take homeIt is simple to “find” new physics by misunderstanding,mismeasuring, or misinterpreting “old” physics, i.e. the SM

Therefore: Control of backgrounds paramount to discovery!!!

Know your Standard Model and its inputs

Don’t trust just one Monte Carlo/one theorist/one calculation:Be sceptical!

If possible, infer from well-understood data.

Also: New measurements for important SM parameters (see below).

F. Krauss IPPP


- 272 -


Precision physics

W mass measurements

Why is this important?

The EW sector of the SM can be parameterized by 4 parameters.Example: α, sin2 θW , v , λ

But other observables related to them: MW , MZ , MH , GF , . . . .This is due to the mechanism of EWSB underlying the SM.

Example: At tree-level weak and electromagnetic coupling related by

GF =πα√

2m2W sin2 θtree

W

Natural question: Is the picture consistent?This is a precision test of the SM and its underlying dynamics.

First tests: SM passed triumphantly, seems okay even at loop-level.

F. Krauss IPPP



Precision physics

Why is this important? (cont’d)

Naively ρ =m2

W

m2Zcos2 θW

connects masses with ew mixing angle.

(Weinberg-angle, θW )

Loop-corrections to it from self-energies etc..

Interesting correction:

Δρs.e. =3GFm2

W

8√

2π2

»m2

t

m2W

−sin2 θW

cos2 θW

„ln

m2H

m2W

−5

6

«+ . . .

–

Relates mW , mt , mH .

For a long time, mt was most significant uncertainty in this relation;by now, mW has more than caught up.

F. Krauss IPPP


- 273 -


Precision physics

Why is this important? (cont’d)

80.3

80.4

80.5

150 175 200

mH [GeV]114 300 1000

mt [GeV]

mW

[G

eV]

68% CL

��

LEP1 and SLD

LEP2 and Tevatron (prel.)

August 2009

0

1

2

3

4

5

6

10030 300

mH [GeV]

��

2

Excluded Preliminary

��had =��(5)

0.02758±0.00035

0.02749±0.00012

incl. low Q2 data

Theory uncertaintyAugust 2009 mLimit = 157 GeV

F. Krauss IPPP



Precision physics

Some technical aspects of the measurement

But: How to measure the mass?

From LEP: Direct measurements.Hampered by comparably low statsand jet-energy uncertainties.

Tevatron: Measurement in leptonicmode, but then the ν’s escape.

So, how to do it at a hadron collider?

Jacobean peak in p�

⊥

Even better: transverse mass

M�ν

⊥ =√2p�

⊥E/⊥(1− cos θ�,miss)

Their position relates to mW

QCD effects controlled by Z . / GeV p

20 40 60 80 100 120 140 160 180

) [

pb

/GeV

]-

(eT

/dp

�d

-310

-210

-110

1

10

210

SHERPA

W + XW + 0jetW + 1jetW + 2jetsW + 3jets

F. Krauss IPPP


- 274 -


Precision physics

Anticipated sensitivity

F. Krauss IPPP



Precision physics

Actual measurementsW-Boson Mass [GeV]

mW [GeV]

80 80.2 80.4 80.6

�2/DoF: 0.9 / 1

TEVATRON 80.420 ± 0.031

LEP2 80.376 ± 0.033

Average 80.399 ± 0.023

NuTeV 80.136 ± 0.084

LEP1/SLD 80.363 ± 0.032

LEP1/SLD/mt 80.364 ± 0.020

August 2009

Projection to LHC

Already now, each modernRun-2 measurement moreprecise than any individualLEP-2 measurement.

(Single most precise measurement by D0, 2009, 1fb−1:

ΔMW = 43 MeV)

Accuracy goal for LHC:15 MeV.

With current theoreticaltechnology (MC@NLO etc.)this is a close call.

Probably need high-precisiontools, including QED, weakcorrections mixed with QCD.

F. Krauss IPPP


- 275 -


Precision physics

LHC: First serious look into acceptances

F. Krauss IPPP



Precision physics

W width measurements


Naively, in the SM (massless fermions):ΓW→��′ = mW

αNc

12 sin2 θW|VCKM|2, Nc = 1, 3 for leptons/quarks

Loop corrections: Another precision test of the SM.

Are there other decay channels?

Method 1: IndirectBasic idea: Z properties well-known, relate W and Z .

Assume W - and Z -production cross section well-known as well asΓW→�ν .

Then measure leptonic W branching ratio through:σpp→W→ ν

σpp→Z→ =

σpp→W

σpp→Z× BR(W→�ν)

BR(Z→��)

Can translate BR to width, since partial width well-known.

F. Krauss IPPP


- 276 -


Precision physics

Method 2: Direct

Idea: While peak of transversemass distribution determined bymW , shape defined by ΓW .

Therefore: Build MC templatesfor varying ΓW (or even betterin mW -ΓW plane) and fit.

Quality control again throughZ -bosons.

Note: This is almostmodel-independent.

F. Krauss IPPP



Precision physics

Results from Tevatron

W-Boson Width [GeV]

�W [GeV]

2 2.2 2.4

�2/DoF: 2.1 / 1

TEVATRON 2.050 ± 0.058

LEP2 2.196 ± 0.083

Average 2.098 ± 0.048

pp� indirect 2.141 ± 0.057

LEP1/SLD 2.091 ± 0.003

LEP1/SLD/mt 2.091 ± 0.002

August 2009 (%)Br(W�l�)

TeVEWWG

preliminary

preliminary

Standard Model

CDF Ia(e)D0 Ia+b(e)

Run I combined

CDF II(e)CDF II(μ)

D0 II(e)Run II combined

TevatronRun I + II combined

World Average (RPP 2002)(includes Run I results)

F. Krauss IPPP


- 277 -


Precision physics

W± charge assymetries at Tevatron


Define the forward direction at Tevatron as the direction of theproton, and the backward direction through the antiproton/

The different valence content leads to W+ bosons produced with aforward tilt asnd the W− bosons with a backward tilt (see firstlecture).

Measuring the assymetry of leptons emerging from the W ’s allowsthen for a check of the PDFs.

Use the μ-assymetry

A(μ) =Nμ+(η)− Nμ−(η)

Nμ+(η) + Nμ−(η).

F. Krauss IPPP



Precision physics

ResultsExample: Muons with p⊥ > 35 GeV.

Pseudorapidity-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Asy

mm

etry

-0.25

-0.2

-0.15

-0.1

-0.05

-0

0.05

0.1

0.15

0.2

0.25

Run IIa

Run IIb

CTEQ6.6 central value

CTEQ6.6 uncertainty band

DØ Preliminary-1L = 4.9 fb

> 35 GeVμT,

p > 20 GeV�T,

p

F. Krauss IPPP


- 278 -


Boson pairs

Boson pair production


Major background to current measurements (tt, H → WW ) andfuture discoveries (χ±-pair production etc.).

Interesting in its own right:

With no Higgs boson or similar: Cross section would explodeor WW -scattering becomes strongly-interacting.Maybe the first mode where alternatives to the Higgs scenario show.Structure of interactions entirely dominated by gauge principle,but: are there non-Standard exotic couplings?

F. Krauss IPPP



Boson pairs

H → WW and backgrounds

F. Krauss IPPP


- 279 -


Boson pairs

Cross sections in ee-annihilation

0

5

10

15

20

160 170 180 190 200 210

Ecm [GeV]

�W

W [

pb]

LEP Preliminary02/03/2001

RacoonWW / YFSWW 1.14

0

5

10

15

20

160 170 180 190 200 210

16

17

18

RacoonWWYFSWW 1.14

0

5

10

15

20

160 170 180 190 200 2100

0.5

1

1.5

170 180 190 200

Ecm [GeV]

�Z

Z

NC

02 [

pb]

LEP Preliminary02/03/2001

±2.0% uncertainty

ZZTO

YFSZZ

F. Krauss IPPP



Boson pairs

Cross sections in hadronic collisions

Typically factor of 2 suppression per W → Z .

In HE limit dominated by sea (pp → pp).

Theory consistent with experiment.

F. Krauss IPPP


- 280 -


Boson pairs

Example: WW & WZ in jj + E/⊥ final states(Recent measurement by CDF, 3.5 fb−1)

Motivation (1): Check for consistency with SM.

Motivation (2): Topologically similar to VH

=⇒ An excellent bootcamp analysis!

Backgrounds: EWK (V+ jets, tt, single top) + QCD.

F. Krauss IPPP



Boson pairs

Example: WW & WZ in jj + E/⊥ final states(Recent measurement by CDF, 3.5 fb−1)

Final result: σ = 18± 2.8(stat)± 2.4(syst)± 1.1(lumi) pb, inagreement with SM.

F. Krauss IPPP


- 281 -


Boson pairs

Testing anomalous gauge couplings at Tevatron

In principle gauge structure and gauge self-interactions defined byform of gauge-covariant derivative Dμ = ∂μ + (i/g)Aμ andFμν = [Dμ, Dν ].If fields do not commute, terms like [Aμ, Aν ] emerge. They result inself-interactions with structure constants f abc , coming fromAμ = Aμ

a T a (the T a are generators of the group - matrices), andwith f abcT c ∝ [T a, T b].

But there are other gauge-invariant options for the gaugeself-interactions.Example: WW γ vertex.

LWWγ = −ie[(W†μνW

μA

ν − W†μW

μνA

ν) + iκW

†μWνF

μν

+λ

m2W

W†μν W

μρF

νρ + κW

†μWν F

μν+

λ

m2W

W†μνW

μρF

νρ ]

(Terms λ and κ are CP-violating, λ − 1 and κ violate parity.)

F. Krauss IPPP



Boson pairs

Testing anomalous gauge couplings in W γ at Tevatron

Simple test for anomalous WW γ couplings at Tevatron in W γ-FS.

Good observables: pγ

⊥ and Q�δη�γ with � from W decay.

The latter is result of “radiation zero” due to interference ofdiagrams.

Various backgrounds: e.g. QCD (with j → γ conversion)

Need cuts on γ: minimal p⊥ etc..

F. Krauss IPPP


- 282 -


Practical application

Solution for a technical problem: luminosity measurement

The need for a standard candle

For many measurements (total cross sections): Need luminosityL[fb−1s−1]× σ[fb] = event rate[s−1] .

But design luminosity �= real luminosity.

So, we need a way to measure instantaneous luminosity.

Simple idea: Use equation above with a process yielding sufficientlylarge event rates (then statistical error small)−→ maybe σtot

pp ?

Problem: We do not know it well enough. There’s some fitparameterizations, but it is soft QCD physics, so no a prioritheoretical knowledge.(At Tevatron: typically error of O(10%) due to lumi)

Solution: Use best known process (from theory point of view).

F. Krauss IPPP




Luminosity measurement with gauge bosons: Theoreticalprecision

Drell-Yan type processes bestknown processes at hadroncolliders.

Results available up to NNLO(the 2 → 1 case!).

Due to dependence on x1,2only, also differential xsec w.r.t.rapidity known up to NNLO.That’s great to get theacceptance correct. (from C. Anastasiou et al., Phys. Rev. D 69 (2004) 094008)

There will be ≈ 20 leptonic W /s at LHC, in principle enough for asufficiently precise measurement of luminosity.

F. Krauss IPPP


- 283 -



Theory vs. Tevatron data

F. Krauss IPPP




Theoretical precision

(from C. Anastasiou et al., Phys. Rev. D 69 (2004) 094008)

F. Krauss IPPP


- 284 -



Systematic uncertainties

Seemingly, main uncertainty from PDFs.Ratios may be a way to overcome this( at least partially).

F. Krauss IPPP



Unitarity triangle

Flavor physics

CKM matrixInter-generation transitionsdominated by mass spectrumand CKM matrix;

Relative size of CKM Matrix (not to scale)

dominant: t → b, b → c , . . . .

Basic properties

Up to O(λ3):

VCKM =

0BBB@

1 − λ2

2λ Aλ3(ρ − iη)

λ 1 − λ2

2Aλ2

Aλ3(1 − ρ − iη) −Aλ2 1

1CCCA

Source of CP-violation in V13-elementsbut cosmologically not sufficient;

unitarity of CKM matrix: triangles(VikV ∗

kj= δij );

size of CP-violation in SM given byarea of the triangle.

F. Krauss IPPP


- 285 -


Unitarity triangle

“The” unitarity triangle

D.Hitlin, Talk at “Flavor in the Era of LHC”, 2005)

F. Krauss IPPP



Unitarity triangle

Turning measurements into the CKM framework

(from D.Hitlin, Talk at “Flavor in the Era of LHC”, 2005)

�

�

dm�

K�

K�

sm� & dm�

ubV

sin 2

(excl. at CL > 0.95) < 0sol. w/ cos 2

excluded at CL > 0.95

�

�

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0

�

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5excluded area has CL > 0.95

ICHEP 08

CKMf i t t e r

(from CKMFitter homepage)

F. Krauss IPPP


- 286 -


New physics

The B-physics relation to new phenomena

There is an amazing consistency of the current flavor-physicsmeasurements: The CKM-picture seems to be about right.

However, many new physics models can have a similar pattern intheir flavor sector (they need to, to survive!).

So, important question: where to look for new physics?

FCNC processes (flavor-changing neutral current).Forbidden at tree-level in the SM (no Z → bs-vertex etc.).Come through loops −→ next transparency.Rare processes (like B+ → τ

+ντ ) and CP-asymmetries

F. Krauss IPPP



New physics

Flavor physics

FCNC as window to new physics

In SM: Only charged flavor changes, due to CKM matrix.

Therefore: FCNC like b → s or BB-mixing always loop-induced:

W

u, c, tb s

γ

q = u, c, tq = u, c, t

s, db

s, d bW

W

Heavy particles running in loop (W , t): FCNC tests scales similar topotential new physics scales.

F. Krauss IPPP


- 287 -


New physics

B-physics: Bs → μμ

General comments

Two contributions (SM): Penguin & Box

Both suppressed by VtbV∗ts

BR(SM)Bs,d→μμ

≈ 10−9

u, c, t

u, c, t

γ,ZW

μ+

μ−

b

s

μ+

μ−

u, c, t

W

Ws

b

νμ

Prospects at LHC

Simple: leptonic final state

Minor theoretical uncertainties

But: Huge background

Mass resolution paramountExp. ATLAS CMS LHCb

σm (MeV) 77 36 18 (from T.Nakada, Talk at “Flavor in the Era of LHC”, 2007)

F. Krauss IPPP



New physics

Mixing phenomena: BsBs-mixing

Theoretical background

Mixing phenomena transmitted by boxes inSM: ∝ |VtsV

∗tb|2 due to GIM.

Bs Bs -mixing very important for unitaritytriangle (ratio with Bd Bd cancels hadronicuncertainties)

But: high oscillation frequency inBs Bs -mixing −→ tricky to see!

Especially complicated: Tag the flavor - isit a b or a b decaying.

One of Tevatron’s strategies: check for aneighboring K from fragmentation.

s, db

s, d b

W

q = u, c, t

q = u, c, t

WW

q = u, c, tq = u, c, t

s, db

s, d bW

W

F. Krauss IPPP


- 288 -


New physics

Results for Bs-mixing(Recent measurement by CDF, 1 fb−1)

]-1 [pssm�0 5 10 15 20 25 30 35

log(

L)�

-30

-20

-10

0

10

20

30 data

expected no signal

expected signal

]-1 [pssm�15 16 17 18 19 20

log(

L)�

-10

0

10

20

30combinedhadronic

semileptonic

CDF Run II Preliminary -1L = 1.0 fb

Final result: Δms = 17.77± 0.10(statstat)± 0.07(sys)|Vtd ||Vts | = 0.2060± 0.0007(exp)± 0.008(theo)

F. Krauss IPPP



Top mass

Top-physics: Mass measurements


Strong correlation of top- and W -mass(self-consistency check of SM)

A change in mt by 2 GeVshifts SM expectation of mH by 15%.

Once the Higgs-boson is found:Do mass and Yukawa-coupling agree?

Important input in many (loop)calculations.Example: FCNC processes.

80.3

80.4

80.5

150 175 200

mH [GeV]114 300 1000

mt [GeV]

mW

[G

eV]

68% CL

��

LEP1 and SLD

LEP2 and Tevatron (prel.)

March 2009

F. Krauss IPPP


- 289 -


Top mass

Experimental techniques: Upshot

Typically, three different channels considered separately:dileptons (bb�ν�′ν′), semi-leptonic (bb�νjj), hadronic (bbjjjj).

Three different methods: Template, matrix element, cross section(see next transparencies).

Depend partly on top-reconstruction.

Main systematics: jet energy scale (JES).Solution: “in situ”-calibrationthrough W → qq′ (mW known).

(from C.Schwanenberger’s talk at

ICHEP08)

F. Krauss IPPP



Top mass

Template method

Basic idea: Run many MC samples fordifferent values of mt & compareobservables (distributions) withexperiment.

Use observables strongly correlated withmt : Naive choice mreco..

Alternatively, look for observables that areleast sensitive to badly controlled inputs(like JES).

Examples: p�

⊥, vertex displacement ofb-decay (see next slide)

(from C.Schwanenberger’s talk at ICHEP08)

F. Krauss IPPP


- 290 -


Top mass

Alternative template method


F. Krauss IPPP



Top mass

Matrix element methodPer event define a probability for being signal-or background-like:

P(Xseen) ∝ |Mab→X |2|〈X |Xseen〉|2

Here |〈X |Xseen〉|2 is “transfer function”:Probability to see Xseen when X was produced−→ needs to be taken from MC& checked with control data.

At Tevatron: LO-matrix element Mab→X forX = tt+decays.

Results

Mtop [GeV/c2]

Mass of the Top Quark (*Preliminary)

March 2008

Measurement Mtop [GeV/c2]

CDF-I di-l 167.4 ± 11.4

D�-I di-l 168.4 ± 12.8

CDF-II di-l* 171.2 ± 3.9

D�-II di-l* 173.7 ± 6.4

CDF-I l+j 176.1 ± 7.3

D�-I l+j 180.1 ± 5.3

CDF-II l+j* 172.4 ± 2.1

D�-II l+j/a* 170.5 ± 2.9

D�-II l+j/b* 173.0 ± 2.2

CDF-I all-j 186.0 ± 11.5

CDF-II all-j* 177.0 ± 4.1

CDF-II lxy 180.7 ± 16.8

�2 / dof = 6.9 / 11

Tevatron Run-I/II* 172.6 ± 1.4

150 170 190

(from joint CDF/D0,

CDF/9225, D0/5626)

F. Krauss IPPP


- 291 -


Top mass

Some remarks on mt from mreco

Need mt in well-defined renormalization scheme:at NLO: |mMS

t (mt)− mon−shellt (mt)| ≈ 8 GeV!!!

Then: Which top-mass has been measured?

Answer: We do not know.Due to comparison with MC, it is a LO mt with QCD partonshowers (some HO QCD) and modelling of fragmentation,underlying event, color-reconnection, . . . .My suspicion: It is an “MC”-scheme, close to on-shell.

But therefore, need either to understand underlying MC betteror use better observables, independent of reco and MC.

Examples for better observables: σtt , dσtt/dMtt .

F. Krauss IPPP



Top mass

Top-mass from σtt

Production cross section depends on mt :

(from S.Moch & P.Uwer, arXiv:0804.1476)

Main theoretical uncertainties due to HO, around 8-10 %.

F. Krauss IPPP


- 292 -


Top mass

Top-mass from σtt : Results


F. Krauss IPPP



Top mass

Taking the top-mass from dσtt/dMtt

(from R.Frederix & F.Maltoni, arXiv:0712.2355)

Theory uncertainty: 0.25δmtt/mtt at NLO.

F. Krauss IPPP


- 293 -


Top properties

Single-top production

Process characteristicsImportant: Only direct, model-independent measurement of Vtb

tt

bWq

W

q

q

b

q b

g

W

t

At Tevatron: important background to WH

Cross section quite large, ≈ 40 % of σtt .

Tricky signature, huge backgrounds: especially top-pairs (sometimes“irreducible”: tW at NLO), W+jets, etc..

Involved analysis techniques: matrix elements, neural networks,boosted decision trees.

F. Krauss IPPP



Top properties

Single-top production: Combination of results

Cross sections at Tevatron

Single Top Quark Cross Section

B.W. Harris et al., PRD 66, 054024 (2002)

N. Kidonakis, PRD 74, 114012 (2006)

August 2009

mtop = 170 GeV

2.17 pb

5.0 pb

3.94 pb

2.76 pb

+0.56 0.55

+2.6 2.3

+0.88 0.88

+0.58 0.47

CDF Lepton+jets 3.2 fb 1

CDF MET+jets 2.1 fb 1

D Lepton+jets 2.3 fb 1

Tevatron CombinationPreliminary

0 2 4 6 8

(from arXiv:/0908.2171 [hep-ex])

F. Krauss IPPP


- 294 -


Top properties

New physics aspects in single-top production

Sensitive to new physics, different impact in different channels(t-channel, s-channel and T -W associated)

σ(Tevatron)singlet σ

(LHC)singlet

(from T.Tait & C.P.Yuan, Phys. Rev. D 63 (2001) 014018)

F. Krauss IPPP



Top properties

The charge of the top-quark

Basic idea

In the SM, Qt = 2/3, so a charge measurement confirms that thetop quark fits the pattern of the isodoublets in the quark sector.

There are potentially two ways to determine the charge of the top:

Check the strength of the coupling to the photon directly, throughthe ttγ coupling, e.g. by building the ratio σttγ/σttg .This seems feasible at a linear collider, at Tevatron/LHC it is moredifficult due to initial state radiation.Infer the charge from the decay products, i.e. from the W and the b.This is the method used at Tevatron.

The trick is to make pairings of W ’s, where the charge is knownfrom the lepton, and the b-jet, such that mbW ≈ mt . The problemis to check whether the jet originated from a b or a b, leading tocharges 2/3 (SM) or 4/3 (XM), respectively, for a top-quark.

F. Krauss IPPP


- 295 -


Top properties

Measuring the charge of the top(from CDF-Note 8967)

Jet charge

Consider cone jets with R = 0.4and p⊥ > 20 GeV.

Define jet charge by

QJ =

Pi∈tracks

Qi (�pi ·�pJ )η

Pi∈tracks

(�pi ·�pJ )η

.

η = 1/2 has been optimizedwith MC.

Label each pair as being SM(f+ = 1) or XM-like (f+ = 0),measure 〈f+〉.

Result: Qt = 2/3

F. Krauss IPPP



Top properties

Top decays

Vtb from top decays

tagN0 1 2�

even

tN

0

200

400

600 )-1Data ( L=0.9 fb

R=1tt

R=0.5tt

R=0tt

Background

DØ RunII

R

0.8 0.9 1 1.1 1.2

(pb

)tt

�

5

6

7

8

9

10

11

95% C.L.68% C.L.

-1DØ Run II L=0.9 fb

(from D0, Phys. Rev. Lett. 100 (2008) 192003)

Simultaneous fit to σtt and BR(t → Wb)/BR(t → Wq)

Underlying assumption:∑q

BR(t → Wq) = 1

F. Krauss IPPP


- 296 -


Top properties

W -helicity in top-quark decays


F. Krauss IPPP



Top properties

Measurement of the W -helicity in top-quark decays

Measure cos θ∗

from ∠�t = ∠�b in W -rest frame.

P(cos θ∗) = f0w0 + f+w+ + f−w−

with w0 =34 (1− cos2 θ∗)

w+ = 38 (1 + cos θ∗)2

w− = 38 (1− cos θ∗)2.

SM: f0 = 0.697± 0.002, f+ = O(10−4),f− = 1− f0 − f+.

f0 = 0.66± 0.16 & f+ = −0.03± 0.07(recent CDF-measurement) (from CDF-Note 9431)

F. Krauss IPPP


- 297 -


Top properties

Charged Higgs bosons in top decays?

Theory considerations

If mH± < mt − mb decay mode is, inprinciple, open.

If decays of H± along CKM picture,H± → τν and H± → cs dominant:

�tan 1 10

Bra

nch

ing

Rat

io

0

0.2

0.4

0.6

0.8

1

decay± H

cs� ±H� � ±H

t*b� ±H0A± W� ±H

0h± W� ±H

Hb)�B(t

2 = 100 GeV/c±Hm

�tan 1 10

Bra

nch

ing

Rat

io

0

0.2

0.4

0.6

0.8

1

Experimental results

l+jets 1 tag l+jets 2 tag dilepton +lepton

even

tN

10

210

310 )=1� � +Br(H

) -1Data (L= 1.0 fb

b)=0.0+ H� Br(t tt

b)=0.3+ H� Br(t tt

b)=0.6+ H� Br(t tt

background

DØ RunII Preliminary

l+jets 1 tag l+jets 2 tag dilepton +lepton

even

tN

10

210

310)=1s c � +Br(H

) -1Data (L= 1.0 fb

b)=0.0+ H� Br(t tt

b)=0.3+ H� Br(t tt

b)=0.6+ H� Br(t tt

background

DØ RunII Preliminary

(from D0-conf/5715)

F. Krauss IPPP



Top properties

The next generation(s)?

Theoretical background

There is no a priori reason to assume 3 generations only.

Some models, like, e.g. little Higgs, predict the existence of furtherelementary fermions, like t ′.

Reason against 4th generation: Only 3 ν’s with mν < mZ/2 at LEP.

F. Krauss IPPP


- 298 -


Gauge sector of the SM

To take homeThe gauge sector is THE crucial point for the SM.

There is an intricate interplay with other parameters, especially mt .(Remark: Adopt the following point: all matter particles want tohave masses ≈ v , so the real question is not why the top is so heavybut why the electron is so light!)

Need to check the consistency: shed light on mechanism of EWSB.

Even after Higgs boson will be found: Must match the pattern!

Potentially a window to new physics, in particular through VV -pairproduction: Unitarity (see lecture 5), anomalous gauge couplingsetc..

F. Krauss IPPP



Flavor sector of the SM

To take homeThere are many interesting questions in the flavor sector:

Rare/FCNC decays of b (and of t)Check properties, especially of the top-quark: coupling, CKMelements, charge.mtop is an important input, but more (theoretical) work needed toensure that meaningful results at sufficient accuracy have beenextracted from data.

Top production (single and in pairs) is a relevant background tonearly all new physics searches at LHC −→ we need to understandthis as good as possible.

LHC is a top-factory! Can go for high precision:not only mass, also Vtb, width, rare decays, . . .

F. Krauss IPPP


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Higgs mechanism SM Higgs boson searches SM Higgs boson properties More Higgs bosons


[Part 3: The Higgs boson]

Frank Krauss

IPPP Durham


F. Krauss IPPP

Phenomenology at collider experiments [Part 3: The Higgs boson]


Outline

1 Reviewing the Higgs mechanismBasic idea of the Higgs mechanismRestoring unitarity of WW -scattering

2 SM Higgs boson searches at collidersDesigning Higgs boson searchesResults from the TevatronProspects for the LHC

3 Measuring the SM Higgs boson propertiesThings the LHC can doThe case for the ILC

4 Extended Higgs sectorsMotivationZoology

F. Krauss IPPP


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Basics

Reminder: The Higgs mechanism

Masses and gauge invariance

SM contains gauge and matter fields: spin-1 bosons and spin- 12

fermions

Massless fields guarantee good features:

Gauge invariance under SU(2)L ⊗ U(1)Y

Renormalisability of theory

Could introduce mass terms “by hand”:Lm ∝ m2

AAμAμ + mf (ΨRΨL + ΨLΨR)

Violates gauge invariance, since

Aμ → Aμ + 1g∂

μθ, therefore AμAμ yields terms ∝ θ after gauge trafo.

ΨL and ΨR transform differently under SU(2)L

(ΨR is singlet = neutral), therefore terms ∝ θ do not cancel.

This is bad: We love the local gauge principle!

F. Krauss IPPP



Basics

Generating mass from the vacuum expectation value

Add complex doublet under SU(2)L (4 d.o.f.),couple it gauge-invariantly with the vectors: LΦA = (DμΦ)(DμΦ)

Add interaction term with fermions:LΦΨ = gf ΨLΦΨR + h.c.(need Φ for down-type fermions and iσ2Φ

∗ for up-types)

Add potential with non-trivial structure(infinite number of equivalent minima needed)

Pick one minimum and expand around it:

One radial and three circular modesCircular modes “gauged away”−→ “eaten” by bosonsvev (energy of minimum) −→ masses

F. Krauss IPPP


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Basics

Fixing the parameters

From the structure above:

(DμΦ)2 −→ g2v2

4 WμW μ −→ M2W = g2v2

4gf ΨLΦΨR −→ gf

v√2ΨLΦΨR −→ mf =

gf v√2

λ(|Φ|2 − v2/2)2 −→ λv2H2 −→ M2H = 2λv2

Fixed relation between mass and coupling to (surviving) Higgs scalar.

Therefore, to verify EWSB:

find H

check it’s a scalarverify coupling ∝ massmeasure potential through self-interactions

F. Krauss IPPP



Unitarity in WW -scattering

Why the Higgs boson cannot decouple

Restoring unitarity of WW → WW -scattering

(from O.Brein)

F. Krauss IPPP


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(from O.Brein)

F. Krauss IPPP






(from O.Brein)

F. Krauss IPPP


- 303 -





(from O.Brein)

F. Krauss IPPP




Fixing the parameters - once more

Consider W+W− → W+W−

Without H: violates unitarity at ≈ 1 TeV.

Therefore: Must add H with gWWH ∝ mW .

Repeat for WW → ZZ −→ gZZH ∝ mZ .

Repeat for WW → f f −→ gf f H ∝ mf .

Test in WW → WWH −→ gHHH ∝ m2H/mW .

Test in WW → HHH −→ gHHHH ∝ m2H/m2

W .

Once it is there, the functional dependenceof the Higgs boson couplings is fixedby the unitarity requirement of the theory.

W+W+ W+

Z, γ

Z, γ

W− W− W−

W+W+

W− W−

HH

W+

W− W−

H

W+

H

W+

W−

H

F. Krauss IPPP


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Designing searches

Tayloring search channels

Limits on mH

Unitarity: < 1 TeV.

EW precision tests: < 250 GeV.

LEP searches: > 114 GeV.

0

1

2

3

4

5

6

10030 300

mH [GeV]

��

2

Excluded Preliminary

��had =��(5)

0.02758±0.00035

0.02749±0.00012

incl. low Q2 data

Theory uncertaintyJuly 2008 mLimit = 154 GeV

(from LEPEWWG)

Basic considerationsSignal rates defined by triggers:you won’t measure what youdon’t see.

Significance: S/√

B vs. S/B.

Important: Control systematics.Avoid embarrassment.

Mass resolution for mH anddecay products: may help tosuppress backgrounds

Any topological help?

F. Krauss IPPP



Designing searches

Higgs production processes at hadron colliders

Common feature: Couple to heavy objects (top, W , Z )

Gluon fusion:

f

Higgs-Strahlung:

V = W,Z

Quark-associated: Weak boson fusion (WBF/VBF):

V = W,Z

V = W,Z

F. Krauss IPPP


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Designing searches

Higgs production cross sections at hadron colliders

(from M.Spira, hep-ph/9810289)

F. Krauss IPPP



Designing searches

Higgs decays

Individual decay channels:decay mode width Γ

H → f fGF MH8π

√2

· 2m2fNc

1 − 4m2

fm2

H

! 32

H → W+W− GF MH8π

√2

· m2H

1 − 4m2

Wm2

H

+12m4

Wm4

H

! 1 − 4m2

Wm2

H

! 12

H → ZZGF MH8π

√2

· m2H

m2W

2m2Z

1 − 4m2

Zm2

H

+12m4

Zm4

H

! 1 − 4m2

Zm2

H

! 12

H → γγGF MH8π

√2

· m2H

“α4π

”2 ·“43

Nc Q2t

”2(2mt > mH )

H → ggGF MH8π

√2

· m2H

“αs4π

”2 ·“23

”2(2mt > mH )

H → VV∗ more complicated, but important for mH<∼ 2mV

mH < 2mW : Higgs boson quite narrow, ΓH = O(MeV).mH > 2mW : H becomes obese, ΓH(mH = 1TeV) ≈ 0.5 TeV.

At large mH : decay into VV dominant, ΓH→WW : ΓH→ZZ ≈ 2 : 1.

F. Krauss IPPP


- 306 -


Designing searches

Higgs decays

(from V.Buescher & K.Jakobs, Int. J. Mod. Phys. A 20 (2005) 2523)

F. Krauss IPPP



Designing searches

Some typical channels (mostly @ Tevatron)

gg → H → W+W− → ��′ + E/⊥: “golden plated”No mass peak, but background partially killed with ∠��′ etc..

qq → ZH → ��bb: only limits on σKey ingredient: b-tagging efficiencies, mass resolution for jets tosuppress QCD backgrounds.

qq′ → WH → �νbb: like above.

qq′ → WH → E/⊥ + bb: only limits on σcombination of the two above, with Z → νν

qq′ → W±H → W±W+W−: only limits on σsame sign leptons, other W goes hadronically (xsec!).

F. Krauss IPPP


- 307 -


Designing searches

Some typical channels (mostly @ LHC)

gg → H → ZZ → 4μ, 2e2μ: “Golden plated” for mH > 140 GeV.Key ingredients: Mass peak from excellent mass resolution (leptons).

gg → H → W+W− → ��′ + E/⊥: nearly as good as ZZ

but no mass peak. Background killed with ∠��′ etc..Very similar to Tevatron analysis with huge stats.

gg → H → γγ: Good for small mH<∼ 120 GeV.

Key ingredient: mass resolution for γ’s & veto on π0’s.

WBF → H → ττ : Popular modeKey ingredient: QCD-backgrounds killed with rapidity gap

WBF → H → WW : ditto.

WBF → H → bb: in principle dittobut: Hard to trigger, pure QCD-like objects (jets)

F. Krauss IPPP



Designing searches

Difficult channels (mostly @ LHC)

top-associated production and H → bb: xsec okay, but difficult.Potential show-stopper: backgrounds from tt+jets W+jets, etc.,many jets to be reconstructed, combinatorics from tt-reco . . . .

top-associated production and H → γγ: xsec small, difficult.

top-associated production and H → ττ : xsec okay, but difficult.Potential show-stopper: backgrounds from tt + Z , W ,Z+jets, etc.,many jets to be reconstructed, combinatoric backgrounds fromt-reco, find the τ ’s (only 1/3 into leptons) . . . .

Higgs decays into μ: small BR, could be useful for SUSY.

F. Krauss IPPP


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Designing searches

Remarks on resonance production

Simple “rule of the thump” to calculate xsec

Consider processes like gg → H → ZZ etc.: resonant production.

If width small: can cut internal resonant propagator.

Two-body decay R → ab: Γab =|〈ab|R〉|2

16πmR

Resonance production in cd → R: σcd = 2π|〈R|cd〉|2

m2R

mRΓR

π[(s−m2R)2+Γ2

Rm2

R]

Use peak at s = m2R (will yield a δ function)

Therefore σab→R→cd = 32πm2

R

BR(R → ab)BR(R → cd)

If width not so small: include Breit-Wigner.

At hadron colliders: Need to integrate over Bjorken-x .

F. Krauss IPPP



Results from the Tevatron

Search channel: gg → H → WW → ��′νν @ Tevatron

Short intro(from D0 Note-5757Conf)

Consider ee, eμ, and μμ final states, each with 2 neutrinos

Use mH in steps of 5 GeV, from 115 to 200 GeV.

Backgrounds: direct WW , WZ , ZZ , tt, DY, QCD, W+jets

Main cuts (acceptance and background suppression):lepton isolation etc., |ηe,μ < 3, 2.

pe,μ⊥ > 15, 10 GeV, E/⊥ > 20 GeV (anti-DY)

some protection against wrong E

M > 15 GeVΔφ

′ < 2 . . . 2.5 (channel-dep.):

most background like back-to-back, H likes small.

Neural network, trained with O(15) observables (some shown below)

Similar analysis for CDF, public page

Up-to date analysis: 4.2 fb−1.

F. Krauss IPPP


- 309 -



Distributions for signals and backgrounds(from D0 Note-5757Conf)

F. Krauss IPPP




Search channel: qq′ → ZH → ��bb @ Tevatron

Distributions for signals and backgrounds(from CDF public homepage, also D0-Note 5570/Conf)

Use � = e, μ, major backgrounds: Z+jets, ZZ , WZ , WW , tt.

Signal- or background-like? ME method (CDF, 2 fb−1).

Relevant observable: mbb, need b-tagging to kill jj-pairs and similar

Finally bound: σsignal ≤ 15 · σH(SM) at 95% C.L..

Similar analysis with more data and NN (CDF& D0).

F. Krauss IPPP


- 310 -



Combined searches @ Tevatron

Significances vs. luminosity(from combination D0+CDF 2009, up to 4.2 fb−1)

0

10

20

30

40

50

60

70

80

0 1 2 3 4 5 6Integrated Expected Signal

Cum

ulat

ive

Eve

nts

Signal+BackgroundBackgroundTevatron Data

mH=115 GeV

Tevatron Run II Preliminary, L=0.9-4.2 fb-1

0

20

40

60

80

100

120

0 2 4 6 8 10 12 14 16 18 20Integrated Expected Signal

Cum

ulat

ive

Eve

nts

Signal+BackgroundBackgroundTevatron Data

mH=165 GeV


F. Krauss IPPP




Ratio: Signal/SM(-Higgs)(from combination D0+CDF 2009, up to 4.2 fb−1)

1

10

100 110 120 130 140 150 160 170 180 190 200

1

10

mH(GeV/c2)

95%

CL

Lim

it/S

M


ExpectedObserved±1� Expected±2� Expected

LEP Exclusion TevatronExclusion

SMMarch 5, 2009

(obtained with Bayesian statistics)F. Krauss IPPP


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Prospects for the LHC

Prospects for Higgs boson searches @ LHC

Search channel: gg → H → γγ

Characteristic: Bump on asmooth background−→ side-band subtraction

Trick: Mass resolution of γγ(problems there: converted γ’s, j(π0) → γ conversions,

γ direction, . . . )

δmγγ ≈ 1.5 GeV.

S/√

B(30fb−1) ≈ 6 formH ∈ [120, 140] GeV

(from ATLAS-Note Pub-2007-013)

F. Krauss IPPP




Prospects for Higgs boson searches @ LHC

Search channel: gg → H → γγ

Characteristic: Bump on asmooth background−→ side-band subtraction

Trick: Mass resolution of γγ(problems there: converted γ’s, j(π0) → γ conversions,

γ direction, . . . )

δmγγ ≈ 1.5 GeV.

S/√

B(30fb−1) ≈ 6 formH ∈ [120, 140] GeV

(from CMS-Note Pub-2006-112)

F. Krauss IPPP


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Weak boson fusion processes

CharacteristicsAt LO: No colour exchange between protonsTag-jets tend to be forward, at low p⊥ ≈ mH/2,colour connected with “adjacent” proton remnants−→ hadronic activity mostly forward

(between tag jet and proton rump)−→ no hadronic activity at centre−→ rapidity gap for signal

Rapidity gap filled by Higgs boson and its decay products

Typical backgrounds: W ,Z+jets, tt, W ,Z -pairs, QCDall of them typically have colour exchange between protons−→ no rapidity gap for background

F. Krauss IPPP




Example: WBF, H → ττ

(from CMS-Note 2006-088)

F. Krauss IPPP


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Example: WBF, H → ττ

Many backgrounds with 3rd jet - typically quite central,i.e. between the hardest two (tag) jets

Quantify by “Zeppenfeld”-variable: η∗3 = η3 − η1+η2

2


F. Krauss IPPP




WBF, H → ττ → �jE/⊥

Results


F. Krauss IPPP


- 314 -



WBF, H → ττ → �jE/⊥

Results: mH and significance


F. Krauss IPPP




A new idea: Higgs-Strahlung @ LHC(from J.M.Butterworth et al., Phys. Rev. Lett. 100 (2008) 242001)

Basic ideaZH and WH production not really considered up to now

Obstacle: if produced at low mass

Good fraction of σprod out of acceptanceDecay products often with too low p⊥

Typically: Huge backgrounds (e.g. tt at same scales)

So: Why not try to produce at large p⊥, back-to-back?(p⊥ > 200 GeV, σZH,boosted ≈ 0.05× σZH,tot)

Large boosts: decay products in relatively small cones

Kills also backgrounds such as tops (Impossible to have bb with large boost in one direction and

W → ν in other direction without having massive QCD radiation.)

Added benefit: For Z → νν massive E/⊥.

F. Krauss IPPP


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Key: Structure of boosted H → bb

Boosted H will produce a “fat” jet with two b’s in it.

Distance of the two b’s in LEGO: Rbb ≈ mH

pH⊥

1√z(1−z)

For resolution use k⊥-like algorithm

The last two sub-jets must have b-tags, and there must not be a toolarge mass drop between them (m1 > μm2)

F. Krauss IPPP




Results: Signal in four regions

ZH → ��bb ZH → ννbb

WH → �νbb Combination

F. Krauss IPPP


- 316 -



SM-Higgs boson searches at LHC: upshot

Sensitivities after 30 fb−1


F. Krauss IPPP



Measuring the properties of the Higgs boson

Reminder: Why do we care?

Okay, so we’ve found plenty of evidence for a “bump” in somedistributions, i.e. a new particle.

Is this enough to claim victory and for P.Higgs to book flights?

Question: How do we know the bump is the Higgs boson?Answer: It must be the scalar responsible for mass generation!Therefore:

1 Is it a scalar, i.e. spin-0 and even CP?2 Is the coupling to the other fields proportional to their mass?3 Is this an accident or the result of the potential/self-interactions?

Answers to all three questions may not be available quickly.

F. Krauss IPPP


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Things the LHC can do

Test 1: Spin and CP

Measuring the H-spin its decays: H → ZZ(from S.Y.Choi et al., Phys. Lett. B 553 (2003) 61)

Basic idea: polarisations of Z bosons correlated, must be visible.

Check differential cross sections/distributions of Z -decay products.

For scalar particles, all Z polarisations contribute:M+ ∼ ε1 · ε2

(including the longitudinal ones which are dominant for large mH).

For pseudoscalar particles, only the transverse polarisationscontribute:

M− ∼ εμνρσkμ

1 kν

2 ερ

1εσ

1 ∼ �k1 · (�ε1 × �ε2)

Will give rise to different distributions.

F. Krauss IPPP





Differential cross sections:dΓ

±H

d cos θ1d cos θ2

∼ A±θ

sin2

θ1 sin2

θ2 + B±θ

(1 + cos2

θ1)(1 + cos2

θ2) + C±θ

cos θ1 cos θ2

dΓH

dφ∼ A

±φ

+ B±φ

cos φ + C±φ

cos(2φ) ,

where {A, B, C}±φ,θ

depend on CP state (±) of the Higgs boson and on Zf f couplings and kinematics.

F. Krauss IPPP


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(after 300 fb−1)

Difference between M+ and M−,persists for the “normality” towers−→ can rule out 0−, 1+, 2− etc..

Can rule out odd spins (1−):missing A+

θ= 0 (Bose symmetry)

Need other decays for even spins (2+)

F. Krauss IPPP




Test 2: Yukawa couplings

Strategy

Yukawa couplings ∝ masses −→ light particles (u, d , . . . ) hopeless

Typically: Extract couplings from total cross section measurements

As we’ve seen before, this is often more than challenging:lumi/PDF uncertainties, systematics of the process itself, . . .

Ratios might be better/more sensitive due to cancellations:but maybe not sensitive to new physics in Higgs sector

F. Krauss IPPP


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Some results

[GeV]Hm110 120 130 140 150 160 170 180 190

(H,X

)2

g(H

,X)

2 g

�

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1(H,Z)2g

(H,W)2g

)�(H,2g

(H,b)2g

(H,t)2g

H

without Syst. uncertainty

2 Experiments-1

L dt=2*30 fb�

[GeV]Hm110 120 130 140 150 160 170 180 190

(H,X

)2

g(H

,X)

2 g

�

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1(H,Z)2g

(H,W)2g

)�(H,2g

(H,b)2g

(H,t)2g

H�

without Syst. uncertainty

2 Experiments-1

L dt=2*300 fb�-1WBF: 2*100 fb

F. Krauss IPPP




Test 2: Yukawa couplings

Projection: From LHC to ILC

F. Krauss IPPP


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The case for the ILC

Test 3: Higgs potential and self-interactions

Or: Why to build the ILC

It does not seem as if the Higgspotential and the HHH

self-interactions are accessible in theSM Higgs-sector at the LHC.Of course, this is different in theMSSM, if mH0 > 2mh0 (resonantproduction of the heavy Higgs)

It does seem, however, as if this isaccessible in the SM Higgs-sector atthe ILC, operating at 500 GeVc.m.-energy.

Cross sections fore+e− → μ+μ− + 4b [fb]

QCD HHH on HHH off

yes 3.096(60)·10−2 6.308(24)·10−3

no 2.34(12)·10−2 3.704(15)·10−3

(from T.Gleisberg et al.,

Eur. Phys. J. C 34 (2004) 173)

F. Krauss IPPP



Motivation

Non-minimal Higgs sectors

MotivationAdding one complex scalar doublet is a minimal version, why notmore fields and a more involved theory?

The SM Higgs-boson is under some stress from data(EW precision wants it lighter than 100 GeV, LEP bound wants itbeyond 114 GeV).

In many attractive models (SUSY, extra dimensions) the Higgssector becomes larger - either enforced in order to make sure that allparticles gain masses in a gauge invariant way (SUSY), or throughreplica of the original single doublet (ED).

But: Need to be careful!Typically constraints from absence of FCNC at tree-level (chargedHiggs should couple � VCKM , EW precision data (Δρ, mass ratios ofweak bosons should be respected) etc..

F. Krauss IPPP


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Zoology

The simplest solution: THDM

Basic ideaThe idea behind the THDM is to add another Higgs doublet.

There are various versions (types) to do that, respectingCP-invariance or adding CP-violation to the theory.

Full Lagrangian introduces O(10) new parameters.

Most interesting THDM-II: Interesting in its own right, but mostlybecause the SUSY-Higgs sector looks like a constrained THDM-II.

SUSY-Higgs sector described by two new parameters:mA0 and tanβ.

Indirect constraints from rare processes in K - and B-sector, EWprecision data, cosmology.

Will concentrate on it in the next few slides.

F. Krauss IPPP



Zoology

Non-minimal Higgs sectors: THDM/MSSM

Theory setup: upshot

Two doublets with two vevs: v1,2v21 + v22 = v2 ≈ (246GeV)2 , tanβ = v2/v1.

H1 doublet gives mass to the up-type fermions, H2 for thedown-types, both together are responsible for the gauge bosons.

After EWSB and mixing to mass eigenstates:5 fields (h0, H0, A0, H±) as linear combinations of original fields.

Immediate consequence: VVH-couplings reduced w.r.t. the SM,f fH-coupling altered by tanβ: ddH enhanced, uuH reduced.

Tree-level mass relations (big loop-corrections, esp. for mh0):m2

H± = m2A0 + m2

W , m2H0 + m2

h0= m2

A0+ m2

Z

At tree-level, typically: mh0 < mZ ! (after loops: mh0 < 140 GeV)

F. Krauss IPPP


- 322 -


Zoology

MSSM Higgs searches

Searches for h0

Typical feature: decays to vector bosons less dominant.

Relevant channels are: h0 → γγ, h0 → ZZ → 4�, tth0 withh0 → bb and WBF with h0 → τ τ .

At small tanβ, searches very similar to the SM,gluon fusion gg → h0 a good process.

At large tanβ, gg → h0 enhanced due to b-triangle,decays to τ ’s gain significance.

With 100 fb−1 they cover nearly the full mA0 -tanβ plane in eachexperiment individually (with a hole around mA0 ∈ [90, 130] GeV)

F. Krauss IPPP



Zoology

MSSM Higgs searches

Searches for H0/A0

Typical feature: decays to vector bosons less dominant.

At large tanβ, b-associated production is dominant, the final statebbτ τ covers a good fraction of the parameters space.In addition, decays to μμ benefit from good mass resolution(this does not work for h0 due to the Z nearby)

At small tanβ, A0 → Zh0 is a good candidate (Zhh absent in theSM): good for mA0 ∈ [200GeV, 2mt ]for mA0 > 2mt , both A0 and H0 decay predominantly into tt

−→ look for resonances.

F. Krauss IPPP


- 323 -


Zoology

Neutral Higgs bosons at Tevatron

Discovery contours

F. Krauss IPPP



Zoology

MSSM Higgs searches

Searches for H±

Relevant production processes: t → H+b (small mH±),already being studied at the Tevatron:

F. Krauss IPPP


- 324 -


Zoology

MSSM Higgs searches

Searches for H±

Relevant processes gg → tbH±, pair production andWH±-associated production (large mH±).

Relevant decays: H± → τν, H± → cs, H± → tb, H± → Wh0;at larger tanβ, τν is a good candidate.

Interesting case: gb → H±t → τ± + E/⊥ + 2jb, τ → ν+ hadrons.Then transverse mass of τ -jet and E/⊥ is a good S-B discriminator:Yields a Jacobean peak at mH± .

F. Krauss IPPP



Zoology

MSSM Higgs searches

gb → H±t → τ± + E/⊥ + 2jb, τ → ν+ hadrons

Tricks & cuts:

Only 3 high-p⊥ jets, one b-tagged;use hard hadron spectrum from H± (harder than W+)(cut on 80% of visible energy reduces tt by 300, signal to 10-20%)


F. Krauss IPPP


- 325 -


Zoology

MSSM-Higgs boson searches at LHC: upshot

Sensitivities in the mA-tanβ plane


F. Krauss IPPP



Zoology

A more exotic solution: Adding extra singlets

Basic idea

Add a further Higgs singlet φ (real or complex) + interactions withthe SM Higgs-sector through L ∝ (Φ†Φ)(φ∗φ).(Note: No renormalisable interactions with the SM gauge sector for φ.)

Typical result: mixing of the scalar fields to mass eigenstates:

Complex φ, no further interactions (“phantom model”):H01 , H0

2 , massless A0 (goldstone of broken U(1)),the latter with potentially large coupling to H0

i .Complex φ + additional U(1): A0 is eaten by Z ′.Real φ: H0

1 and H02

Consequence: reduced couplings to SM fields - can make life hard.

Perversion of the above: Many singlets −→ can make H totallyinvisible due to huge width and small coupling to individual modes.

F. Krauss IPPP


- 326 -

BSM motivation Supersymmetry Other models

Phenomenologyat collider experiments[Part 4: BSM physics]

Frank Krauss

IPPP Durham


F. Krauss IPPP

Phenomenology at collider experiments [Part 4: BSM physics]


Outline

1 Beyond the Standard Model: Why?

2 SupersymmetryMotivation & basic ideaThe minimal SUSY model (MSSM)

3 Other modelsExtra dimensionsTechnicolour

F. Krauss IPPP


- 327 -


Looking for physics beyond the Standard Model

Motivation

SM is a model with 18(+1) parameters, can this be reduced?

Somewhat related: Can a GUT be constructed -a theory with only one interaction rather than three?

If there is a GUT, it presumably lives at scales O(1016GeV).A big desert from μEWSB to μGUT?(The “philosophical” hierarchy problem)

How can gravity be incorporated at all?Gauge constructions of gravity are tricky.

If dark matter is fundamental, where is it?The SM has no viable candidates.

Let’s not even start with dark energy/cosmological constant.

F. Krauss IPPP



Another nasty feature: The technical hierarchy problem

Consider two corrections to the mass of the Higgs boson:

∝ λHΛ2 ∝ −λ2tΛ

2

Each of them is quadratically divergent, with a brute-force cutoff Λ.(Think of it as limit of validity of SM, μGUT , or scale of new physics kicking in)

Remark: In QED, the fermion self-energy is only log-divergent due to gauge symmetry. Not a help here.

Huge fine-tuning of renormalisation mandatory to keep mH ≈ vev .(One-loop correction terms alone ∝ μ2

GUT)

Two solutions: Lower Λ (idea behind extra dimensions)or introduce a symmetry, e.g. λH = λ2t (SUSY)

F. Krauss IPPP


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Aside: Could the Standard Model survive up to μPlanck?

Remember: m2H = λv2

(v = vev = 246 GeV)

Two constraints on mass:1 Keep perturbativity:

λ → ∞ forbidden.2 Keep vacuum structure:

λ → 0 forbidden.

Therefore: “Stable island”in the middle

F. Krauss IPPP



Motivation & basic idea

The idea behind supersymmetry

What is supersymmetry?

Remember quantisation through operators:

Have creation and annihilation operators a(†): a†|n〉 ∝ |n + 1〉,a|n〉 ∝ |n − 1〉, and a|0〉 = 0.Quantisation achieved through fixing their relationCommutator: [a, a†] ∝ i , [a, a] = [a†

, a†] = 0

Commutator for bosonic degrees of freedom.

Anticommutator {f1, f2} = f1f2 + f2f1 for fermionic d.o.f..

Supersymmetry:

Construct operation Q linking bosonic and fermionic states:Q|b〉 = |f 〉 & Q†|f 〉 = |b〉.Demand invariance under this operationTherefore: For each bosonic d.o.f. in your model a fermionic one ismandatory and vice versa =⇒ b, f ∈ one “superfield”(This is the symmetry from above: Scalar and fermion belong to same superfield, therefore same coupling)

F. Krauss IPPP


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The benefits of supersymmetry

A collection of reasons why this is a good model

Two “philosophical” in principle reasons:

1 The Coleman-Mandula Theorem statesthat the construction of a quantum theory of gravitation in form ofa local gauge theory is feasible only in the framework ofsupersymmetric theories.

2 The Haag-Sohnius-Lopuszanski Theorem statesthat the maximal symmetry of the S-matrix of a consistent QFT isgiven by the direct product of Lorentz-invariance, gauge symmetryand supersymmetry.

F. Krauss IPPP




The benefits of supersymmetry

Some more “technological” remarks

Quadratic divergences are cancelled.For each loop with bosonic d.o.f. (sign = +), there is one withfermionic d.o.f. (sign = -) with exactly the same coupling, mass etc.:only difference is the sign!=⇒ Perfect cancellation of quadratic divergences.

Extra particles may help in enforcing unification of couplings.

The vacuum energy arising in second quantisation (zero-modeenergy of harmonic oscillator) is exactly cancelled by fermions=⇒ Vacuum energy is exactly 0

(Compare: Cosmological constant)

Typically, SUSY models have a natural dark matter candidate(a stable WIMP=LSP) with reasonable mass for CDM.

(Caveat: Only after SUSY-breaking)

F. Krauss IPPP


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The minimal SUSY model (MSSM)

Field content before EWSB/SUSY breaking: all massless

Matter fields:left-handed doublets

right-handed singlets

Weyl-spinors/complex scalars

generations J = 1, 2, 3

(uJ

dJ

)L

, uJR , dJ

R(νJ

�J

)L

, �JR

(uJ

dJ

)L

, uJR , dJ

R(νJ

�J

)L

, �JR

Gauge fields:spin-1 bosons/Weyl-spinors

generators a = 1 . . . ng

G aμ, W±,0

μ, Bμ ψa

G , ψ±,0W , ψB

Higgs fields:2 doublets (i=1,2) of

Complex scalars/Weyl-spinors

(H1

i

H2i

)L

(ψ1

Hi

ψ2Hi

)L

F. Krauss IPPP




Breaking SUSY . . .

. . . is unfortunately necessary

Pattern: SUSY partners with quantum numbers as SM particles,differing just in spin by a half unit

SUSY must be broken: no superpartner (with identical mass) found

Various mechanisms advocated, barely tractable

Way out: Breaking by hand through “soft term”(Terms that do not spoil the nice features, like absence of quadratic divergences)

This introduces ≈ 100 new parameters in MSSM:mostly boiling down to all possible mixings.

Typically imposed: R-parityPictorial: SUSY particles always pairwise in vertex!Consequence: A lightest stable SUSY particle (LSP).

F. Krauss IPPP


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The MSSM spectrum after EWSB/SUSY breaking

The SM matter content (apart from Higgs sector) remains.

In the Higgs sector, the 8 scalar real Higgs fields are reduced to 5:

2 neutral scalars: h0 & H0, 1 neutral pseudoscalar: A0,2 charged scalars H±

the three other fields are “eaten” by gauge bosons(Higgs-mechanism a la SM)

The up-type and down type sfermions mix (6×6 matrix),typically only L − R mixing in third generation important,inter-generations still by CKM (helps with flavour constraints)

Neutral Weyl spinors (ψB , ψW 0 , ψH01, & ψH0

2) → 4 neutralinos

Charged Weyl spinors (ψW± & ψH±) → 2 charginos

F. Krauss IPPP




Order from chaos

. . . or: the striking power of (over-)simplification

Prospect of measuring O(100) new parameters a nightmare

Maybe better to cook up theory-inspired “SUSY-breaking scenarios”

Various such scenarios on the market:gauge-mediation, anomaly-mediation, mSUGRa

Common feature:Have an extra sector of the theory, potentially “GUTty”,will not respect SUSY and mediates information in some way.

Benefit: Few parameters (O(5)) to describe spectrum + interaction.

In mSUGRA/CMSSM:

mA, tan β for Higgs sector - we’ve been therem1.2, m0, A for soft breaking terms (mass+trilinear couplings)

F. Krauss IPPP


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Searching for SUSY

Some wild collection of signals

With R-parity: Everything eventually decays into LSP (χ01)

−→ short or long decay chains

Most prominent production: sQCD pair production (g g , g q, . . . )will lead to signatures E/⊥+ jets, eventually with leptons

(the latter from decays like χ02 → χ0

1 + or χ±1

→ ±νχ01 along the decay chain)

Also well studied:

-pair production: Kinematically like Drell-Yan of heavy lepton with(long) decay chain of → χ

0i → . . .

χ02χ

±1 , yielding a tri-lepton signal.

F. Krauss IPPP




Searching for SUSY

Example cross sections

10-2

10-1

1

10

10 2

10 3

100 150 200 250 300 350 400 450 500

�2o�1

+

t1t�

1

qq�

gg

��

�2og

�2oq

NLOLO

�S = 14 TeV

m [GeV]

�tot[pb]: pp � gg, qq�, t1t

�

1, �2o�1

+, ��, �2

og, �2oq

Prospino2 (T Plehn)

F. Krauss IPPP


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Extra dimensions

The idea behind extra dimensionsRemember the hierarchy problem:Quadratic divergences pull mH towards highest scale.mPlanck is the scale where the pure SM (no new physics) breaksdown, since gravitation becomes quantum.

So, the problem is maybe not the divergence structure, but mPlanck.

Connection with gravitational force: GN = 1(16πmPlanck)2

Size of Planck scale maybe due to too weak gravitation?

Could play with it by changing geometrical setup (more dims),dimensions are finite (size R), typically “curled up”

Particles allowed to propagate in extra dimensions will show apattern of Kaluza-Klein towers:Equidistant excitations with ΔM ∝ 1/R

F. Krauss IPPP



Extra dimensions

Construction of large extra dimensions (ADD)

Einstein-Hilbert action for true Planck scale M∗:S = − 1

2

∫d4x√|g |M2

∗Λ −→ − 12

∫d4+nx√|g |M2+n

∗ Λ

Compactify additional dimensions on torus R:S −→ − 1

2 (2πR)n∫

d4x√|g |M2+n

∗ Λ

Match to “measured” Planck scale:S = − 1

2

∫d4x√|g |m2

PlanckΛ

Therefore: mPlanck = M∗(2πRM∗)n/2

Want RM∗ � 1.

Numbers for M∗ ≈ 1 TeV in table

Check gravity at mm scales.

n R

1 1012 m2 10−3 m3 10−8 m...

...6 10−11 m

F. Krauss IPPP


- 334 -


Extra dimensions

Zoology of extra dimensions

Large extra dimensions/ADD:

Have only gravity propagating in “bulk”, SM on “brane”KK towers of gravitons with small mass distance 1/R

Gravitons couple weakly to SM particles with energy-momentumtensor Tμν

/Mplanck

Look for spin-2 exchange with “continuous mass” or graviton leavingdetector (signature: single photon or jet + =⇒ E/T ).

Universal extra dimensions/small extra dimensions:

All particles in “bulk”, typically 1-2 EDEvery SM particle gains KK towers with sizable distance 1/R

F. Krauss IPPP



Technicolour

The idea behind technicolourProblem with Higgs boson self-energy, because it is an elementaryscalar, and no gauge prevents quadratic divergences

Make the Higgs boson composite!

Analogy: Pions made off quarks (χSB)

Add extra (techni-)fermions with new strong (techni-)interaction

Main problems:

Strong coupling for bound states, make sure it does not run too fast.Solution: Use different representation for fermions.

(Walking technicolour)

May have to add leptons to kill anomalies.

Technifermions form technimesons, partially eaten by gauge bosons

Survivors of the multiplets (techni-ρ’s etc.) visible at the LHCsimilar to Z ′, W ′: resonances from Z ′ → f f etc..

F. Krauss IPPP


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Technicolour

A last announcementDon’t forget to apply for YETI 2010!

Dates: 12.1.-14.1.2010 in the beautiful North East (Durham)

Title:A window to the dark world, cosmology to LHC

For more information visit:http://www.ippp.dur.ac.uk/Workshops/YETI.html

F. Krauss IPPP


- 336 -

Orientation MC integration Reminder: ME’s Reminder: QCD showers Hadronization Underlying Event Upshot

Phenomenologyat collider experiments[Part 5: MC generators]

Frank Krauss

IPPP Durham

HEP Summer School 31.8.-12.9.2008, RAL

F. Krauss IPPP

Phenomenology at collider experiments [Part 5: MC generators]


Outline

1 Orientation

2 Monte Carlo integration

3 Reminder: Hard cross sections

4 Reminder: Parton showers

5 Hadronization

6 Underlying Event

7 Upshot

F. Krauss IPPP


- 337 -


Simulation’s paradigm

Basic strategy

Divide event into stages,separated by different scales.

Signal/background:Exact matrix elements.

QCD-Bremsstrahlung:Parton showers (also in initial state).

Multiple interactions:Beyond factorization: Modeling.

Hadronization:

Non-perturbative QCD: Modeling.

Sketch of an event

F. Krauss IPPP



Monte Carlo integration

Convergence of numerical integration

Consider I =1∫0

dxD f (�x).

Convergence behavior crucial for numerical evaluations.For integration (N = number of evaluations of f ):

Trapezium rule 1/N2/D

Simpson’s rule 1/N4/D

Central limit theorem 1/

√N.

Therefore: Use central limit theorem.

F. Krauss IPPP


- 338 -




Use random vectors �xi −→:Evaluate estimate of the integral 〈I 〉 rather than I .

〈I (f )〉 = 1N

N∑i=1

f (�xi ).

(This is the original meaning of Monte Carlo: Use random numbers for integration.)

Quality of estimate given by error estimator (variance)〈E (f )〉2 = 1

N−1

[〈I 2(f )〉 − 〈I (f )〉2].Name of the game: Minimize 〈E (f )〉.Problem: Large fluctuations in integrand f

Solution: Smart sampling methods

F. Krauss IPPP




Importance sampling

Basic idea: Put more samples in regions, where f largest=⇒ improves convergence behavior(corresponds to a Jacobian transformation).

Assume a function g(�x) similarto f (�x);

obviously then, f (�x)/g(�x) iscomparably smooth, hence〈E (f /g)〉 is small.

F. Krauss IPPP


- 339 -



Stratified sampling

Basic idea: Decompose integral in M sub-integrals

〈I (f )〉 =M∑

j=1

〈Ij(f )〉, 〈E (f )〉2 =M∑

j=1

〈Ej(f )〉2

Then: Overall variance smallest, if “equally distributed”.=⇒ Sample, where the fluctuations are.

Divide interval in bins;

adjust bin-size or weight per bin suchthat variance identical in all bins.

〈I〉 = 0.637 ± 0.147/√

N

F. Krauss IPPP




Example for stratified sampling: VEGAS

Assume m bins in each dimension of�x .

For each bin k in each dimension η ∈ [1, n] assume a weight

(probability) α(η)k

for xk to be in that bin.

Condition(s) on the weights:

α(η)k

∈ [0, 1],Pm

k=1 α(η)k

= 1.

For each bin in each dimension calculate 〈I(η)k

〉 and 〈E(η)k

〉.

Obviously, for all η, 〈I〉 =Pm

k=1〈I(η)k

〉, but error estimates different.

In each dimensions, iterate and update the α(η)k

;

example for updating:

α(η)k

(rm new) ∝ α(η)k

(rm old)

0@ E

(η)k

Etot.(η)

1A

κ

.

Problem with this simple algorithm:Gets a hold only on fluctuations ‖ to binning axes.

F. Krauss IPPP


- 340 -



Multichannel sampling

Basic idea: Use a sum of functions gi (�x) as Jacobian g(�x).

=⇒ g(�x) =∑N

i=1 αigi (�x);=⇒ condition on weights like stratified sampling;(“Combination” of importance & stratified sampling).

Algorithm for one iteration:

Select gi with probability αi → �xj .

Calculate total weight g(�xj ) and partial weights gi (�xj )

Add f (�xj )/g(�xj ) to total result and f (�xj )/gi (�xj ) to partial

(channel-) results.

After N sampling steps, update a-priori weights.

This is the method of choice for parton level event generation!

F. Krauss IPPP




Selecting after sampling: Unweighting efficiency

Basic idea: Use hit-or-miss method;Generate �x with integration method,compare actual f (�x) with maximal value during sampling;=⇒ “Unweighted events”.

Comments:unweighting efficiency, weff = 〈f (�xj )/fmax〉 = number of trials for each event.

Good measure for integration performance.

Expect log10 weff ≈ 3 − 5 for good integration of multi-particle final states at tree-level.

Maybe acceptable to use fmax,eff = Kfmax with K < 1.

Problem: what to do with events where f (�xj )/fmax,eff > 1?

Answer: Add int[f (�xj )/fmax,eff ] = k events and perform hit-or-miss on f (�xj )/fmax,eff − k.

F. Krauss IPPP


- 341 -



Particle physics example: Evaluation of cross sections

Simple example: t → bW+ → blνl :

|M|2 =1

2

8πα

sin2 θW

!2 pt · pν pb · pl

(p2W

− M2W

)2 + Γ2W

M2W

Phase space integration (5-dim)

Γ =1

2mt

1

128π3

Zdp

2W

d2ΩW

4π

d2Ω

4π

0@1 −

p2W

m2t

1A |M|2

AdvantagesThrow 5 random numbers, construct four-momenta (=⇒ full kinematics, “events”)

Apply smearing and/or arbitrary cuts.

Simply histogram any quantity of interest - no new calculation for each observable

F. Krauss IPPP



Parton level simulations

Stating the problem(s)

Multi-particle final states for signals & backgrounds.

Need to evaluate dσN :∫cuts

[N∏

i=1

d3qi

(2π)32Ei

]δ4

(p1 + p2 −

∑i

qi

)|Mp1p2→N |2 .

Problem 1: Factorial growth of number of amplitudes.

Problem 2: Complicated phase-space structure.

Solutions: Numerical methods.

F. Krauss IPPP


- 342 -


Factorial growth

Example: e+e− → qq + ng

n #diags

0 11 22 83 484 384

1 2 3 4

Number of gluons 1

10

100

1000

Num

ber

of d

iagr

ams

F. Krauss IPPP



Phase space integration

Integration methods: Multi-channeling

Basic idea: Translate Feynman diagrams into channels=⇒ decays, s- and t-channel props as building blocks.R.Kleiss and R.Pittau, Comput. Phys. Commun. 83 (1994) 141

Integration methods: “Democratic” methods

Rambo/Mambo: Flat & isotropicR.Kleiss, W.J.Stirling and S.D.Ellis, Comput. Phys. Commun. 40 (1986) 359;

HAAG: Follows QCD antenna patternA.van Hameren and C.G.Papadopoulos, Eur. Phys. J. C 25 (2002) 563.

F. Krauss IPPP


- 343 -


Limitations of parton level simulation

Factorial growth

. . . persists due to the number of color configurations(e.g. (n − 1)! permutations for n external gluons).

Solution: Sampling over colors,but correlations with phase space=⇒ Best recipe not (yet) found.

New scheme for color: color dressing(C.Duhr, S.Hoche and F.Maltoni,JHEP 0608 (2006) 062)

F. Krauss IPPP




Factorial growth

Off-shell vs. on-shell recursion relations:

Time [s] for the evaluation of 104 phase space points, sampled overhelicities & color.

F. Krauss IPPP


- 344 -



Efficient phase space integration

Main problem: Adaptive multi-channel sampling translates“Feynman diagrams” into integration channels

=⇒ hence subject to growth.

But it is practical only for 1000-10000 channels.

Therefore: Need better sampling procedures =⇒ openquestion with little activity.

(Private suspicion: Lack of glamour)

F. Krauss IPPP




General

Fixed order parton level (LO, NLO, . . . ) implies fixed multiplicity

No control over potentially large logs(appear when two partons come close to each other).

Parton level is parton levelexperimental definition of observables relies on hadrons.

Therefore: Need hadron level event generators!

F. Krauss IPPP


- 345 -


Motivation: Why parton showers?

Some more refined reasonsExperimental definition of jets based on hadrons.

But: Hadronization through phenomenological models(need to be tuned to data).

Wanted: Universality of hadronization parameters(independence of hard process important).

Link to fragmentation needed: Model softer radiation(inner jet evolution).

Similar to PDFs (factorization) just the other way around(fragmentation functions at low scale,

parton shower connects high with low scale).

Practical: In MC’s typically start with 2 → 2 process(Further jets from QCD shower)

(This approximation has been overcome only ≈ 5 years ago!)

F. Krauss IPPP



Motivation: Why parton showers?

Common wisdomWell-known: Accelerated charges radiate

QED: Electrons (charged) emit photonsPhotons split into electron-positron pairs

QCD: Quarks (colored) emit gluonsGluons split into quark pairs

Difference: Gluons are colored (photons are not charged)Hence: Gluons emit gluons!

Cascade of emissions: Parton shower

F. Krauss IPPP


- 346 -



The Sudakov form factor

Diff. probability for emission between q2 and q2 + dq2:

dP = αs

2πdq2

q2

1−Q20/q2∫

Q20/q2

dzP(z) =: dq2

q2P(q2) .

No-emission probability Δ(Q2, q2) between Q2 and q2.

Evolution equation for Δ: −dΔ(Q2, q2)

dq2= Δ(Q2, q2) P

dq2.

=⇒ Δ(Q2, q2) = exp

[−

Q2∫q2

dk2

k2P(k2)

].

F. Krauss IPPP




Many emissions

Iterate emissions (jets)

Maximal result for t1 > t2 > . . . tn:

dσ ∝ σ0

Q2∫Q20

dt1

t1

t1∫Q20

dt2

t2. . .

tn−1∫Q20

dtn

tn∝ logn Q2

Q20

How about Q2? Process-dependent!

F. Krauss IPPP


- 347 -



Ordering the emissions : Radiation pattern

q21 > q22 > q23 , q21 > q′22

F. Krauss IPPP




Forward vs. backward evolution: Pictorially

F. Krauss IPPP


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Use of DGLAP evolution

DGLAP evolution:PDFs at (x, Q2) as function of PDFs at (x0, Q2

0 ).

Backward evolution:start from hard scattering at (x, Q2) and work down in q2 and

up in x .

Change in algorithm:Δi (q

2) =⇒ Δi (q2)/fi (xi , q2).

F. Krauss IPPP



Inclusion of quantum effects

Resummed jet rates in e+e− → hadronsS.Catani et al. Phys. Lett. B269 (1991) 432

Use Durham jet measure (k⊥-type):

k2⊥,ij = 2min(E

2i , E

2j )(1 − cos θij ) > Q

2jet .

Remember prob. interpret. of Sudakov form factor:

R2(Qjet) =hΔq (Ec.m., Qjet)

i2

R3(Qjet) = 2Δq (Ec.m., Qjet)

·Z

dq

24αs (q)Pq (Ec.m., q)

Δq (Ec.m., Qjet)

Δq (q, Qjet)Δq (q, Qjet)Δg (q, Qjet)

35

F. Krauss IPPP


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Hadronization

ConfinementConsider dipoles in QED and QCD

QED:

QCD:

F. Krauss IPPP



Hadronization

Linear QCD potential in quarkonia

F. Krauss IPPP


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Hadronization

Some experimental facts → naive parameterizations

In e+e− → hadrons: Limits p⊥, flat plateau in y .

Try “smearing”: ρ(p2⊥) ∼ exp(−p2⊥/σ2)

F. Krauss IPPP



Hadronization

Effect of naive parameterizations

Use parameterization to “guesstimate” hadronization effects:

E =

ZY

0dydp

2⊥ρ(p

2⊥)p⊥ cosh y = λ sinh Y

P =

ZY

0dydp

2⊥ρ(p

2⊥)p⊥ sinh y = λ(cosh Y − 1) ≈ E − λ

λ =

Zdp

2⊥ρ(p

2⊥)p⊥ = 〈p⊥〉 .

Estimate λ ∼ 1/Rhad ≈ mhad, with mhad 0.1-1 GeV.

Effect: Jet acquire non-perturbative mass ∼ 2λE

(O(10GeV) for jets with energy O(100GeV)).

F. Krauss IPPP


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Hadronization

Implementation of naive parameterizations

Feynman-Field independent fragmentation.R.D.Field and R.P.Feynman, Nucl. Phys. B 136 (1978) 1

Recursively fragment q → q′+ had, where

Transverse momentum from (fitted) Gaussian;longitudinal momentum arbitrary (hence from measurements);flavor from symmetry arguments + measurements.

Problems: frame dependent, “last quark”, infrared safety, no directlink to perturbation theory, . . . .

F. Krauss IPPP



Hadronization

Yoyo-strings as model of mesonsB.Andersson, G.Gustafson, G.Ingelman and T.Sjostrand, Phys. Rept. 97 (1983) 31.

Light quarks connected by string: area law m2 ∝area.L=0 mesons only have ’yo-yo’ modes:

F. Krauss IPPP


- 352 -


Hadronization

Dynamical strings in e+e− → qqB.Andersson, G.Gustafson, G.Ingelman and T.Sjostrand, Phys. Rept. 97 (1983) 31.

Ignoring gluon radiation: Point-like source of string.

Intense chromomagnetic field within string:More qq pairs created by tunnelling.

Analogy with QED (Schwinger mechanism):dP ∼ dxdt exp

(−πm2q/κ), κ = “string tension”.

F. Krauss IPPP



Hadronization

Gluons in strings = kinksB.Andersson, G.Gustafson, G.Ingelman and T.Sjostrand, Phys. Rept. 97 (1983) 31.

String model = well motivated model, constraints on fragmentation(Lorentz-invariance, left-right symmetry, . . . )

Gluon = kinks on string? Check by “string-effect”

Infrared-safe, advantage: smooth matching with PS.

F. Krauss IPPP


- 353 -


Hadronization

Preconfinement

Underlying: Large Nc -limit (planar graphs).

Follows evolution of color in parton showers:at the end of shower color singlets close in phase space.

Mass of singlets: peaked at low scales ≈ Q20 .

F. Krauss IPPP



Hadronization

Primordial cluster mass distributionStarting point: Preconfinement;

split gluons into qq-pairs;

adjacent pairs color connected,form colorless (white) clusters.

Clusters (“≈ excited hadrons)decay into hadrons

F. Krauss IPPP


- 354 -


Hadronization

Cluster modelB.R.Webber, Nucl. Phys. B 238 (1984) 492.

Split gluons into qq pairs, form singlet clusters:=⇒ continuum of meson resonances.

Decay heavy clusters into lighter ones;(here, many improvements to ensure leading hadron spectrum hardenough, overall effect: cluster model becomes more string-like);

if light enough, clusters → hadrons.

Naively: spin information washed out, decay determined throughphase space only → heavy hadrons suppressed (baryon/strangenesssuppression).

F. Krauss IPPP



Underlying Event

Multiple parton scattering?

Hadrons = extended objects!

No guarantee for one scattering only.

Running of αS=⇒ preference for soft scattering.

F. Krauss IPPP


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Underlying Event

Evidence for multiple parton scattering

Events with γ + 3 jets:

Cone jets, R = 0.7,ET > 5 GeV; |ηj | <1.3;“clean sample”: twosoftest jets with ET < 7GeV;

σDPS =σγjσjj

σeff, σeff ≈ 14± 4

mb.

CDF collaboration, Phys. Rev. D56 (1997) 3811.

F. Krauss IPPP



Underlying Event

Definition(s)

��

��

��

��

��

��

1 Everything apart from the hard interaction including IS showers, FSshowers, remnant hadronization.

2 Remnant-remnant interactions, soft and/or hard.

=⇒ Lesson: hard to define

F. Krauss IPPP


- 356 -


Underlying event

Model: Multiple parton interactions

To understand the origin of MPS, realize that

σhard(p⊥,min) =

s/4∫p2⊥,min

dp2⊥dσ(p2⊥)

dp2⊥> σpp,total

for low p⊥,min. Here:dσ(p2⊥)

dp2⊥=

1R0

dx1dx2dtf (x1, q2)f (x2, q2)dσ2→2dp2⊥

δ“1 − t u

s

”(f (x, q2) =PDF, σ2→2 =parton-parton x-sec)

〈σhard(p⊥,min)/σpp,total〉 ≥ 1

Depends strongly on cut-off p⊥,min (Energy-dependent)!

F. Krauss IPPP



Underlying event

Old Pythia model: Algorithm, simplifiedT.Sjostrand and M.van Zijl, Phys. Rev. D 36 (1987) 2019.

Start with hard interaction, at scale Q2hard.

Select a new scale p2⊥(according to f =

dσ2→2(p2⊥)

dp2⊥with p2⊥ ∈ [p2⊥,min

, Q2])

Rescale proton momentum (“proton-parton = proton with reduced energy”).

Repeat until below p2⊥,min.

May add impact-parameter dependence, showers, etc..

Treat intrinsic k⊥ of partons (→ parameter)

Model proton remnants (→ parameter)

F. Krauss IPPP


- 357 -


Underlying Event

In the following: Data from CDF, PRD 65 (2002) 092002, plots partially from C.Buttar

Observables

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F. Krauss IPPP



Underlying event

Hard component in transverse region

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F. Krauss IPPP


- 358 -


Underlying event

Energy extrapolation

F. Krauss IPPP



Underlying event

General facts on current modelsNo first-principles approach for underlying event:

Multiple-parton interactions: beyond factorization

Factorization (simplified) = no process-dependence in use of PDFs.

Models usually based on xsecs in collinear factorization:dσ/dp⊥ ∝ p4−8

⊥ =⇒ strong dependence on cut-off pmin⊥ .

“Regularization”: dσ/dp⊥ ∝ (p2⊥ + p20)2−4, also in αS .

Model for scaling behavior of pmin⊥ (s) ∝ pmin

⊥ (s0)(s/s0)λ, λ =?

Two Pythia tunes: λ = 0.16, λ = 0.25.

Herwig model similar to old Pythia and SHERPA

New Pythia model: Correlate parton interactions with showers, more parameters.

F. Krauss IPPP


- 359 -


To take home

Hard MEsTheoretically very well understood, realm of perturbation theory.

Fully automated tools at tree-level available,2 → 6 no problem at all.

Obstacle(s) for higher multiplicities:factorial growth, phase space integration.

NLO calculations much more involved, no fully automated tool, onlylibraries for specific processes (MCFM, NLOJET++), typically up to2 → 3.

NNLO only for a small number of processes.

F. Krauss IPPP



To take home

Parton showersTheoretically well understood, still in realm of perturbation theory,but beyond fixed order.

Consistent treatment of leading logs in soft/collinear limit, formallyequivalent formulations lead to different results because ofnon-trivial choices (evolution parameter, etc.).

Can be improved through matrix elements in many ways.Keywords: MC@NLO, Multijet-merging, ME-corrections

F. Krauss IPPP


- 360 -


To take home

HadronizationVarious phenomenological models;

different levels of sophistication,different number of parameters;

tuned to LEP data, overall agreement satisfying;

validity for hadron data not quite clear - differences possible (beamremnant fragmentation not in LEP).

F. Krauss IPPP



To take home

Underlying event

Various definitions for this phenomenon.

Theoretically not understood, in fact: beyond theory understanding(breaks factorization);

models typically based on collinear factorization andsemi-independent multi-parton scattering

=⇒ very naive;

models highly parameter-dependent, leading to large differences inpredictions;

connection to minimum bias, diffraction etc.?

even unclear: good observables to distinguish models.

F. Krauss IPPP


- 361 -

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hepss09 proceedings v7 - PPD · IPPP Durham RAL HEP Summer School 7.9.-18.9.2009 F. Krauss IPPP...

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