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Physics of ep Scattering

Marco StratmannRegensburg / Wűrzburg

RSC meeting, Ames, Iowa, May 16th, 2010

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HERA’s legacyon June 30th, 2007, the DESY-HERA accelerator complex was finally shut down

the world’s only lepton-proton collider so far

16yrs of data taking leave a rich legacy of knowledge & by now textbook results

(steep rise of F2; small-x gluons, diffraction, e-w effects, photoproduction, spin structure, … )

why an EIC ?

• proton beam was unpolarized

• no eN collisions

• many phenomena need more

statistics (HERA: 480pb-1/exp)

to be fully explored/understood

e.g., exclusive processes

• mainly running at one energy

-> difficult to access FL

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disclaimer & outline

fasten your seatbelts for a quick tour of

• The Physics of Parton Densities & electro-weak effects

• QCD Spin Physics

• Photoproduction

• Diffraction A. Stasto (yesterday)

• Exclusive Processes D. Müller (next talk)

The Physics of ep Scattering is a vast field

impossible to review in 30 mins

we need to concentrate on some highlights

I will review HERA’s legacy and highlight opportunities for an EIC

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PHYSICS OF PARTON DENSITIES

reviews on HERA physics: M. Klein, R. Yoshida, arXiv:0805.3334; publications from H1 and ZEUS

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reminder: the DIS process

relevant kinematics:

• Q2 : photon virtuality $ resolution r»1/Q at which the proton is probed

• x: long. momentum fraction of struck parton in the proton

• y: momentum fraction lost by electron in the proton rest frame

• unknown hadronic structure parameterized by DIS structure functions

• pQCD factorization relates measurable structure functions

with non-perturbative but universal parton densities (PDFs)

and calculable coefficient functions

• can be easily generalized to polarized leptons and protons

short distance long

distance

QED

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DIS structure functions

• at a high energy collider life is more complicated: electro-weak effects

can have neutral currents (γ, Z exchange) and charged currents (W exchange)

• HERA also had polarized electrons or positrons to play with

need most general expression for cross section to compare with data

e.g.

the F2,3,L depend on the lepton charge (±) & polarization P and e-w parameters (ai, vi, κ)

to O(αs0) one finds (in this approximation FL=0 -> see later)

• gluons enter only at NLO and indirectly through QCD scaling violations

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inclusive DIS results from HERA• to reduce uncertainties and to produce a final “HERA set”

H1 an ZEUS have started to combine their data DIS data publ. in arXiv:0911.0884

strong positive scaling violations

at small x

gluon distribution

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rise of F2 vs Q2

rise of F2 can be expressed as

driven by evolution ofgluon distribution

F2 flattens around Q2 = 1 GeV2

change from partonic

to hadronic behavior

transition can bedescribed in the

“color dipole model”

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NC & CC DIS: test of e-w theory

NC

CC

σCC vs lepton polarization

extraction of e-w parameters

e-w unification at high Q2

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longitudinal structure function FL

• hard to get; recall

contributes only at large y (=low x)

• indirect measurement from deviation of σr from “F2 only fit”

• slope of y2/Y+ for different S at fixed x and Q2 (HERA had Ep =575 and 460 GeV)

• quark cannot absorb a longitudinal photon (helicity conservation)

• FL starts only at O(αs)

• often confusion about LO FL

• if defined as helicity cons. implies FL=0 (“Callan Gross relation”)

• however in pQCD FL at O(αs) is LO !

• HERA results not very conclusive room for improvement at an EIC

FL

F2

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semi-inclusive DIS processes

• sensitivity to gluon already at LO

through photon-gluon fusion

• factorized cross sections

examples:

• charm contribution to F2

• three-jet cross section

• many more results available

also, great playground for an EIC

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extraction of the strong coupling

10 100ETjet (GeV)

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how to determine PDFs from data?

task: extract reliable pdfs not just compare some curves to data

information on nucleon (spin) structure available from

DIS SIDIS hadron-hadron

a “global QCD analysis” is required

each reaction provides insights into different aspects and kinematics

all processes tied together: universality of pdfs & Q2 - evolution

need at least NLO for quantitative analyses; PDFs are not observables!

information on PDFs “hidden” inside complicated (multi-)convolutions

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global analysis: computational

challenge• one has to deal with O(2800) data points from many processes and experiments

• NLO expressions often very complicated ! computing time becomes excessive ! develop sophisticated algorithms & techniques, e.g., based on Mellin moments

• need to determine O(20-30) parameters describing PDFs at m0

Kosower; Vogt; Vogelsang, MS

data sets & (x,Q2) coverage used in MSTW fitMartin, Stirling, Thorne, Watt,

arXiv:0901.0002

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which data sets determine which

partons

Martin, Stirling, Thorne, Watt, arXiv:0901.0002

NLO fit, 68% C.L.

• notice the huge gluon distribution

• quality of the fit:

• 2543/2699 NLO• 3066/2598 LO

as always: LO not sufficient

c2/ #data pts.

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neural network approach to PDFsForte, Guffanti, Rojo, …, arXiv:1002.4407

• new way to estimate PDF uncertainties

• “issues”: over-learning (?); HQ treatment;

no central fit, need average of replicas

Q2 = 2 GeV2

quark singlet

gluon

strangeness

• strangeness with huge uncertainties

room for improvement at an EIC

through semi-inclusive DIS

(not studied at H1 & ZEUS)

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neural network approach: impact of future

datasee talk of J. Rojo at DIS 2010

• impact of new data through “Bayesian reweighting” – no refitting required !

• example: FL at the LHeC (Ee= 50 GeV, Ep = 1 & 7 TeV)

• further studies for upcoming “LHeC CERN yellow report”:

F2c,b sensitive to gluon; charged current Ws c to access strangeness, ...

desirable to have similar studies for an EIC; get “LHeC people” on board

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opportunities for PDF studies at an

EIC

FL : needs variable beam energy gluon density

HERA has provided a lot of data & unpol. PDFs are rather well known

some “weak spots” though: (improvements require an EIC or the LHeC)

F2c,b & semi-inclusive processes : need excellent particle ID

flavor separation incl. strangeness, charm, bottom

electro-weak precision tests: need luminosity [beam polarization; positrons (?)]

beyond that:

unintegrated kT dependent PDFs largely unknown

repeat HERA program in eN scattering at large √S terra incognita

hadronization flavor separation of fragmentation fcts

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QCD SPIN PHYSICS

reviews/papers: DSSV analysis, arXiv:0904.3821; Burkardt et al., arXiv:0812.2208

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fundamental questions driving spin

physics

explore QCD beyond helicity-averaged case

map out the nucleonits complete spin, flavor, and gluon “landscape”

• study polarized scattering processes quantitatively

• learn about pQCD & factorization in the presence of spin

how do quarks and gluons carry the proton spin: • extract helicity PDFs from data

• what is the role of orbital angular momentum

understand transverse spin phenomena:

what is the distribution of partons in the transverse plane:

• azimuthal asymmetries (Sivers/Collins); role of gauge links; ….

• exclusive processes; generalized parton distributions

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helicity PDFs and proton spin sum

total spin polarizations Sq and Sg helicity parton densities

momentum fraction

s dx

x-moment

1

0

DGLAP scale evolution “only” known up to NLO yet Mertig, van Neerven; Vogelsang

but NNLO emerging Moch, Rogal, Vermaseren, Vogt

need a reliable extraction of helicity PDFs from data

issue: limited x-range of data ! extrapolation to x! 0 and 1, how reliable?

helicity sum rule (A+=0 gauge version)

total u+d+s quark spin

gluon spin

angularmomentum

Jaffe, Manohar; Ji; …

“quotable” properties of the nucleon

an observation about the spin sum

rule

DSSV fit has the property that proton spin is almost entirely OAM for all Q2

recall (at LO)

DSSV Δg is close to “static solution” Dg ' – 0.15

where dDg/dln m = 0

any deeper reason for that ?

in general, Δg evolves logarithmically but there is a “static solution” (in LO)

evolution of 1st moments

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emerging picture: sea polarizations indications for an SU(2) breaking of light u,d sea

breaking of similar size than in unpol. case mainly determined by SIDIS data “bands”: error estimate from Lagr. mult. similar patterns in many models:

large-NC, chiral quark soliton, meson cloudThomas, Signal, Cao; Diakonov, Polyakov, Weiss; …

a strange strangeness polarization

Ds(x) always thought to be negative, but …

mainly determined from SIDIS kaon data consistent with LO-type analyses by HERMES and COMPASS

xneeds further studies – exp. & theory !

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emerging picture: gluon polarization

xcurrently probed by RHIC data 0.05· x · 0.2

Dg suggested to be huge (axial anomaly) – ruled out! Dg(x) very small at medium x still huge uncertainties at small x ! cannot quantify s Dg(x) dx contributing to proton spin

find

to address these questions we need to reduce small x uncertainties

and get a better handle at orbital angular momentum

unique case for a high-energy polarized ep-collider

in addition:

indications from lattice QCD that

quark OAM might be small as well

-> who is carrying the proton spin?

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DIS @ small x

x

translates in

to p

ositiv

e D

g

interesting questions at small x

• charm contribution to g1

• any deviations from DGLAP behavior?

• precision study of Bjorken sum rule

(rare example of a well understood

fundamental quantity in QCD)

charm contribution to g1

• so far safely ignored

<< 1% to existing g1 data

• but ≈ 20% contribution to F2

at small x seen at HERA

LO estimates from 1996 MS, Vogelsang

• expect g1charm of O(10%)

at an EIC depending on Δg

• problem: PGF g*(Q2)g ! cc

only known to LO in pol. case

• no variable flavor scheme

a la CTEQ, MRST developed yet

≈ ΔPcg ln [Q2/m2]

NLO: work in progress MS

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e.g.,

flavor separation

extension to SIDIS ?

Contreras et al.

new sum rules, e.g.,

MS, Vogelsang, Weber

electro-weak effects at high Q2

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transverse spin phenomena

renaissance of transverse spin studies in recent years both in ep and in pp

very active field both in experiment and theory

here, only a snapshot of some of the physics involved:

• transversity

• completes the set of leading twist PDFs: f(x), Δf(x), δf(x)

• chiral odd -> involves helicity flip; no gluon transversity;

• not accessible in inclusive DIS

• difference of Δq and δq probes relativistic effects

(boosts and rotations do not commute)

• fundamental tensor charge (calculable on the lattice)

• no reason to believe that transverity is small (lattice)

• 1st extraction from data recently Anselmino et al.

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azimuthal/single-spin asymmetries in

SIDIS

• explanation of observed effects requires non-trivial QCD dynamics:

transverse momentum dependent PDFs and/or parton-parton correlations

• many observables possible in lp -> lhX if intrinsic pT included and Φ kept

e.g. “left-right asymmetries” in the direction of produced hadron

SIDIS cross section: Kotzinian; Mulders, Tangermann; Boer, Mulders. …

“Sivers effect”

“Collins effect”

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• effect seen, rather large

• Collins fragmentation function :

correlation of transverse spin of fragmenting quark and PT

h

• universal, can be determined in e+e-

• allows extraction of transversity δq

from combined fit Anselmino et al.

BELLE

x

physics of the “Collins effect”

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physics of the “Sivers effect”

• again, effect seen (some tension between HERMES & COMPASS data)

• Sivers function :

correlation of transverse spin of proton with kT of unpolarized quark

• probes overlap of proton wave fct.

with JZ = +1\2 and -1/2

-> involves orbital angular momentum

• not universal through gauge-links;

has profound physics implication:

“repulsive”“attractive”(to be tested experimentally)

Collins; Belitsky, Ji, Yuan;Boer, Mulders, Pijlman; … ; talk by Ted Rogers

Burkardt; Brodsky et al; …

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opportunities for spin physics studies at

an EIC

small x region: crucial for all sum rules (“proton spin”, “Bjorken”, …) unknown

so far, our knowledge on polarized (SI)DIS is based on fixed target experiments

many “weak spots” & room for new “spin surprises”:

flavor separation: SU(2) breaking, strangeness largely unknown

electro-weak effects/structure fcts. never measured

full understanding of transverse spin phenomena still in early stages

repeat full HERA program in polarized high energy ep scattering

with good particle ID & ability to measure exclusive processes

issues with factorization for Sivers TMD intriguing

role of orbital angular momentum largely unknown

plus: spin phenomena in diffraction, photoproduction, hadronization, …

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PHOTOPRODUCTION

reviews/papers: M. Klasen, hep-ph/0206169; publications from H1 and ZEUS

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photoproduction basics

• bulk of events at low Q2 – pQCD applicable if another hard scale (pT) is present

• studies of photoproduction processes are one of the great successes of HERA

• H1 and ZEUS have studied various different final-states; jets most interesting

pQCD framework for photoproduction is more involved than for DIS:

• sum of two contributions, e.g., 2-jet production at LO :

“resolved photon”contribution

“direct photon”contribution

of same orderin couplings

need to be added forphysical cross sections

linked through factorization

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photon flux

• flux of photons usually estimated by equivalent photon approximationWeizsacker, Williams

consequences/complications:

• energy of “target” photon not fixed

but smeared

• “electron PDFs” more appropriate:

• strong dilution of polarization

for

y: energy fraction transferred from the lepton to the photon

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photonic parton densities• evolution eqs. differ from hadronic (proton) case by an inhomogeneous term

arising from the pointlike coupling of photon to quarks:

where

inhomog.“pointlike”

part

homogeneous“hadron-like”contribution

• solution is given by sum of pointlike and hadronic

part which contribute at different x values

shows behavior; dominates at large x

requires non-perturbative input

based on VMD ideas

hadron-like x-shape, dominates at small x

GRV – Gluck, Reya, Vogt

fit based on LEP data

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selected results from HERA

despite the wealth of HERA data, all fits are based on DIS (mainly from LEP)

• single-inclusive probes• data agree well with NLO calculations

• jet results need up to 30% correction

for hadronization effects (1+δhadr)

• large uncertainties = opportunities for an EIC

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selected results from HERA

• less inclusive probes: di-jet photoproduction

great advantage: can experimentally define a “resolved” sample

(valid to LO approximation)

use ET’s and η’s of the jets:

• clear evidence for resolved part

• again hadronization effects (1+δhadr)

• theo. issue: asymmetric ET values for IR safety

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spin dependent photoproduction

same suite of HERA measurements can be repeated at an EIC with polarization

• novel probe for polarized proton PDFs, in particular Δg

• unique handle at unknown PDFs of circularly polarized photons

to estimate the sensitivity of such probes we need to rely on models for ΔfΥ :

Gluck, MS, Vogelsang

• evolution known to NLO

• use positivity

at some low scale around 1 GeV

• max. input:

• min. input:

(pointlike at all scales)

MS, Vogelsang

expectations for the EIC

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• many studies available at NLO for the EIC

(1-jet, 1-hadron inclusive, charm, …)

JägerarXiv:0807.0066

lepton

xg ' 1

probes proton PDFs

proton

xg¿ 1

probes unknown photon PDFs

1-jet

Jäger,MS,Vogelsang; Jäger; Bojak, MS; Riedl, Schäfer, MS; Hendlmeier, Schäfer, MS

differentassumptions

about

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opportunities for photoproduction studies at

an EIC

access to hadronic structure of photons many aspects unknown

photoproduction processes were a core part of the HERA program

many probes were limited by statistics or never studied:

spin structure unknown

diffraction (factorization, diffrative PDFs, …) intriguing

…

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DIFFRACTIONreviews: workshop on the implications of HERA for LHC physics, hep-ph/0601013; arXiv:0903.3861

recall Anna Stasto’s talk yesterday

EXCLUSIVE PROCESSES & GPDS

reviews on GPDs: M. Diehl, hep-ph/0307382; A.V. Belitsky and A.V. Radyushkin, hep-ph/0504030 43

see Dieter Müller’s talk next

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final remarks

there is a compelling physics case both in ep and in eA

to go beyond what was already achieved at HERA an EIC needs to have

• variable beam energy (FL in ep and eA, …) & large luminosity (electroweak, GPDs,…)• large variety of nuclei (eA physics)• high polarization (spin, electroweak); perhaps positron beams (electroweak)• large enough c.m.s. energy (small x; saturation regime; electroweak; …)• excellent detectors: particle ID (SIDIS, …); VTX (charm); “exclusivity” (diffraction, GPD); low Q2 tag (photoproduction); …

but not a “discovery machine” we need to demonstrate that an EIC

can deliver answers to the questions we ask

need to define and carefully phrase a few “milestones”

which are convincing for the entire nuclear physics community

need to make the case for an EIC soon• high risk to loose crumbling European “ep community”• need to keep in touch with LHeC studies (some overlap; “CERN yellow book” soon)