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Physics of ep Scattering
Marco StratmannRegensburg / Wűrzburg
RSC meeting, Ames, Iowa, May 16th, 2010
2
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
3
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
4
PHYSICS OF PARTON DENSITIES
reviews on HERA physics: M. Klein, R. Yoshida, arXiv:0805.3334; publications from H1 and ZEUS
5
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
6
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
7
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
8
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”
9
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
10
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
11
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
12
extraction of the strong coupling
10 100ETjet (GeV)
13
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
14
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
15
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.
16
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)
17
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
18
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
19
QCD SPIN PHYSICS
reviews/papers: DSSV analysis, arXiv:0904.3821; Burkardt et al., arXiv:0812.2208
20
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
21
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
23
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 !
24
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?
25
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
27
e.g.,
flavor separation
extension to SIDIS ?
Contreras et al.
new sum rules, e.g.,
MS, Vogelsang, Weber
electro-weak effects at high Q2
28
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.
29
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”
30
• 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”
31
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; …
32
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, …
33
PHOTOPRODUCTION
reviews/papers: M. Klasen, hep-ph/0206169; publications from H1 and ZEUS
34
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
35
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
36
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
37
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
38
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
39
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
40
• 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
41
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
…
42
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
44
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)