New Physics at a TeV and the LHC ‐ IA l t B i d th LHCAccelerator Basics and the LHC
Sreerup Raychaudhuri
Tata Institute of Fundamental Research, Mumbai, India
IPM String School (ISS 2009) Tehran IranIPM String School (ISS 2009), Tehran, IranApril 16, 2009
We learn about nuclear and sub‐nuclear physics in two ways:
1. Indirect way – from energy levels of nuclear/particle states (spectroscopy)
2. Direct way – from scattering experimentsΦd
Typical scattering experiment
1 σd=F
σd=
2M
Two possible designs for a scattering experiment:
1 ‘Fi d’ t t i t1. ‘Fixed’ target experiment
( ) ( )b MkE frame lab in the 0,0,0, and ,0,0,
( )( )
+= bcm
kME
kMEE ,0,0,22
22
( )++−=
−+=
b
b
MEMkE
kME
2222
22
++= b
b
MEMm 222As more and more energy is pumped into the beam, more and more energy is lost in the recoil of the target
∞→≈++= bbbcm
ME
EMEMEMmE
2
as 2222gy g
∞→→≈ bbb
cm EE
M
E
E as 0
2
2. Collider experiment
( ) ( )( )0002
frame lab in the ,0,0, and ,0,0,22
−bb
EE
kEkE
θ( )4
0,0,0,22
22
=
=
b
bcm
E
EE
2= bcm
b
EE
2=b
cm
E
E
Full beam energy is available for the process
bE
LHC 2009
Tevatron1994
LEP 1991
SLAC 1969
How are these high beam energies attained?
Er
Er
Er
Er
E E E E
Vl
l
VE =V
Cannot make plates too close, for then there will be spark di h ith hi h i t d kdischarges even with high vacuum; instead we make voltage high use AC voltage instead of DC voltage
Er
Cannot use a continuous beam any more;Cannot use a continuous beam any more; must send bunches of particles at a time…
p lsed operation timing bet een b nches…pulsed operation : timing between bunches must match RF…
Interaction rate will now depend on bunch crossings…
n n νL σ×R L1 2
4
n n
A
νπ
=L σ= ×R L
Luminosity cm‐2 s‐1 Event rate s‐1
number density of bunchesn =1,2 number density of bunches
number of crossings per second
ti l f b h
n
A
ν
=
=cross-sectional area of bunches
reaction cross section
A
σ==
Event rate : σ×= LRAs data are gathered over time…
No of events σσ ×=×== ∫∫ LdtdtNtt
'' LR
∫=t
dtL 'L00
Integrated luminosity ∫= dtL0
LIntegrated luminosity
If σ Is measured in pb fb etc L is measured in pb‐1 fb‐1 etcIf σ Is measured in pb, fb, etc. , L is measured in pb 1, fb 1, etc.
1 pb = 1000 fb fb‐1 pb‐1
10 nb‐1/s
nb‐1/s
From the BNL home page
How are these high luminosities attained?
1 2
4
n n
A
ν=L
4 Aπ1 2 number density of bunchesn =1,2 y
number of crossings per second
cross sectional area of bunchesA
ν = cross-sectional area of bunches
reaction cross section
A
σ==Packing charged particles like electrons and protons
into very small volumes is difficult because of the strong electrostatic repulsion; requires very strong focussing magnetic fields from superconducting electromagnets etc.
Working Principle of a Storage Ring
Re‐use the same bunches many many times…
8.6 Km
The LHC is just aThe LHC is just a giant storage ring
8.6 Km
Buried ⟨100 m⟩ below ground to shield radiation
Section of LHC tunnel showing beam pipe
Some LHC parameters
Beam energy : 5 TeV ⎯→ 7 TeVCollision energy : 10 TeV ⎯→ 14 TeVCollision energy : 10 TeV → 14 TeV
Luminosity : 10 nb‐1 s‐1 (design)‘I t t d’ l i it 100 fb 1 (d i )‘Integrated’ luminosity: 100 fb‐1 per year (design)
Bunch crossing rate : 4 ×107 s‐1gBunch distance: ~ 7 mBunch size : few cm × 1 mm, 16 μm (collision pt) No of protons/bunch : 1.1 × 1011
No of magnets: 9593 Current: 11 700 ANo of magnets: 9593Magnet temperature: 1.9 K Magnetic field: 8.3 T
Some amusing LHC facts
• LHC will consume as much power as domestic sector in Geneva canton
• LHC budget is comparable to GDP of a small country, e.g. Fiji or Mongoliag y g j g
• Vacuum is 10 times better than the surface of the Moon
• Magnetic fields of 8.3 Tesla are 100,000 times the Earth’s magnetic field
• Magnets will use 700,000 lit of liquid He and 12,000,000 lit of liquid N
• Total length of cable could stretch from Earth to Sun 5 times
• LHC protons will travel at 0.999999991c
• LHC protons will have energies comparable to that of a flying mosquito
• Protons used in 10 years would be equivalent to only 7.5 μg of hydrogen
• LHC beams will together have enough energy to melt 1 tonne of copper
D t ld fill t k f HD DVD 11 K hi h (Mt E t 8 8 K )• Data could fill a stack of HD-DVDs 11 Km high (Mt. Everest: 8.8 Km)
2009,2009,
barrel End cap barrel radiation sensitive;
End-cap radiation hardened;
high efficiencylow efficiency
VXDμCh
VXD
EMCHCAL
VXD
ECALECAL
HCAL
μCh
CMS Detector
μCh
Particle detection at the LHC
No signals at all ; only missing energy
Track in VXD ; energy deposit in ECAL
νe Track in VXD ; energy deposit in ECAL
Track in VXD ; tracks/deposits in μCH
No track in VXD onl deposit in ECAL
eμγ No track in VXD; only deposit in ECAL
Hadronic jets ; signals in all devices
γ/ /q g τ
Decay at the interaction vertex itself
Displaced vertices in VXD; deposit in HCAL
/W Z
b p ; p
Decay at the interaction vertex itself
b/ Ht
Everything must be reconstructed only from these effects
Protons not point particles, but conglomerates of • valence quarks (uud)• valence quarks (uud)• gluons• sea quarks (u d s c b t)• sea quarks (u,d,s,c,b,t)
l k h dMore like two cars crashing and spewing out parts than like the collision of hard billiard balls…
Choice of Variables
kr
k−r
1x kr
2kx−r
k k1x k 2kx
Partonic system has an (unknown) longitudinal boosty ( ) g
1 2x xβ −≈
1 2x xβ
+
h ll ll h d ff βEach collision event will have a different β⇒ we must choose variables which are independent of longitudinal boosts
2 2
Commonest Variables
1. Transverse momentum :2 2
T x yp p p= + 2 2T TE p m= +
1 E p+ 21 x Δ2. Rapidity :1
log2
z
z
E py
E p
+=
−2
1
1log
2
xy
x→ + yΔ
3. Pseudo rapidity : log tan2
θη = − if 0y m≈ →
4. Angular separation : 2 2R η ϕΔ = Δ + Δ
5. Invariant mass : ( )2212 1 2M p p= +
Signal and Background
If a certain final state (including phase space characteristics) is predicted by a theory, the cross‐section for producing that final state is called the signal
S SN σ= L If it is possible to produce the same final state (including phase space characteristics) in an older well established
S SN σL .
phase space characteristics) in an older, well‐established theory (e.g. Standard Model), that cross‐section is called a backgrounda background
B BN σ= L . N Nδ±E i l l ill h exp expN Nδ±Experimental results will have errors:
exp standard deviation N σδ ⇒
What constitutes a discovery?
Excess/depletion over background : exp BN N−d ( ) fl h b b l h hAssuming random (Gaussian) fluctuations, the probability that this
deviation is just a statistical effect is about :
33% if deviation at 67% C LN N Nδ≈ ⇒exp exp
exp exp
33% if deviation at 67% C.L.
5% if 2 deviation at 95% C.L.
B
B
N N N
N N N
δ
δ
− ≈ ⇒
− ≈ ⇒
exp exp 1% if 3 deviation at 99% C.L.
0 01% if 5 d i ti t 99 99%
BN N N
N N N
δ
δ
− ≈ ⇒
C Lexp exp0.01% if 5 deviation at 99.99%BN N Nδ− ≈ ⇒ C.L.
Consensus: 3σ deviation is exciting;5σ deviation constitutes a discovery;8σ deviation leaves no room for doubt
Limiting the parameter space
Once there is a well‐established deviation from the background, we compare it with the signal:
( )exp expS BN N N Nδ≈ − ±
If the numbers match, we can start claiming a discovery…
Usually this matching can always be achieved by tuning the free parameters in the (new) theory…
Comparison essentially serves to constrain the parameter space of the (new) theory
If we must have very small exp BN N≈ expSN Nδ≈
Typical new physics bounds arising when experimental cross‐sections match with backgrounds :sections match with backgrounds :
ggLarge NSexcluded
Small NSallowed
M
allowed
If experimental data are there, this is called an exclusion plot
If h d j d hi i ll d h li iIf the data are projected, this is called a search limit
LHC
If both signal and background are present, the prediction i th t i t ill th f b th di tiis that experiment will see the sum of both predictions.
Typical case: background is large; signal is small
S BN N«S B
In this case and exp BN N≈ exp SN Nδ »Will be very difficult to observe any signal over the experimental error…
p
Require to reduce the background (without reducing the signal)
Kinematic Cuts
1Fermi’s Golden Rule :
21M d
Fσ = Φ∫
Phase space integral has to be over all accessible final states 3
id pdΦ = Π
r
( )32 2i
i
dEπ
Φ = ΠExperimental cross‐section may not be able to (wish to) access all the possible momentum final states ⇒phase space integral must be done with p p gappropriate kinematic cuts
• acceptance cuts : forced on us by the detector properties.acceptance cuts : forced on us by the detector properties.
• selection cuts : chosen to prefer one process over another.
Examples of acceptance cuts:
• minimum pT for the final states : – very soft particles will not cause showering in ECAL/HCAL – different cuts for barrel and endcap– different cuts for barrel and endcap
• maximum η for the final states :d t t i / b i– no detector coverage in/near beam pipe
• isolation cut on Δ R for leptonic final states :– no hadronic deposit within a cone of ΔR = 0.4 – to be sure that the lepton is coming from the interaction point and not from a hadron semileptonicinteraction point and not from a hadron semileptonicdecay inside a jet
Will be somewhat different for ATLAS and CMS
Selection cuts can be of different kinds depending on the process and the purpose for which it is made…
Example of a selection cut:
Suppose we want to select more electrons from the process
(1)pp e e+ −→instead of electrons from the process
(2) pp e e γ+ −→ ( )pp e e γ→From simple energy‐sharing arguments, the electron in (1) will have more p than the electron in (2)have more pT than the electron in (2)
Impose the selection cut : mineT Tp p>
Ensures that the accessible phase space for (2) shrinks without seriously affecting that of (1) → reflected in the cross‐section
A variety of selection cuts can be used to reduce the background without affecting the signal (much)background without affecting the signal (much).
Much of the collider physicist’s ingenuity lies in devising a i bl f l i id f hsuitable set of selection cuts to get rid of the
background(s).
Often the background can be reduced really dramatically – to maybe 1 in 10000…
Nevertheless, often this reduction of backgrounds to negligible values may also backgrounds to negligible values may also reduce the already weak signal to less than one event in the whole running life of LHC!
High luminosity is essential !!
The proton luminosity is not the end of the story…
… actual collisions will happenwill happen
between partons…
⇒ what actually matters are : parton distributions × luminosity
x f(x)
4.0≤x
Parton density functions (PDFs) from the CTEQ‐6 Collaboration (C.P. Yuan et al)
Trade‐off between energy and luminosity…
( )( ) 2ˆ
.22
212
21 ≈+= pppps
( ))TeV14(ˆˆ
.2ˆ
212121
2121212
2211
×≈=≈=
≈≈+=
xxExxsxxsE
sxxppxxpxpxs
)TeV 14( 212121 ×≈≈ xxExxsxxsE cmcm
If x < 0.4, then maximum available energy at gyparton level is only about 5 TeV…
But to observe most new physics high luminosityBut to observe most new physics, high luminosity demand restricts us to x < 0.1, i.e. 1 – 2 TeV.
LHC probes the TeV scale – but only just…
Physics Goals of the LHC
• to test known physics, i.e. SM = QCD + GSW model (H boson)
• to discover new physics, e.g. dark matter, SUSY, extra dim, new symmetries, g , , , y ,
compositeness, …
Q Wh h ld h i t th T V l ?Q. Why should new physics appear at the TeV scale?
Is this just wishful thinking?Is this just wishful thinking?
…or do we have solid reasons?
Significance of the TeV energy scale:
• top‐down approach : • GUT or stringy unification must have low energy consequences; high scale SUSY will have low energy manifestations, extra dimensions will become accessible t hi h h iat high enough energies
• bottom‐up approach : p pp• hierarchy problem, neutrino masses, GUT evolution
th ti h• aesthetic approach :• 18 free parameters in the SM• no QCD‐EW unification• no QCD‐EW unification• desert scenarios
Capabilities of the LHC
Cannot do a blind search…
All important final states req ire a triggerAll important final states require a trigger
• Huge QCD backgrounds… especially if looking for hadronic final stateshadronic final states
• Cannot see very soft pT jets/leptons/photons
LHC has severe limitations….
Sure shots :
Can find the Higgs boson of the SM (if it exists)Can determine t quark properties to precisionCan find the Higgs boson of the SM (if it exists)Can find a SUSY signal if kinematics permits
Can find a resonant new state
LLess sure :
Can measure Higgs boson couplingsCan measure Higgs boson couplingsCan measure SUSY parametersCan discover exotics, e.g. gravitons, monopoles…
How are we so sure?How are we so sure?
… next two lectures….
