Physics of ep Scattering

1. Physics of ep Scattering Marco Stratmann Regensburg / Wűrzburg RSC meeting, Ames, Iowa, May 16th, 2010

2. HERA’s legacy on June 30th, 2007, the DESY-HERA accelerator complex was finally shut down 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 the world’s only lepton-proton collider so far

3. disclaimer & outline The Physics of ep Scattering is a vast field impossible to review in30 mins we need to concentrate onsome highlights 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 (nexttalk) 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 QED short distance long distance

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,Ldepend 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 of gluon distribution F2 flattens around Q2 = 1 GeV2 change from partonic to hadronic behavior transition can be described in the “color dipole model”

9. NC & CC DIS: test of e-w theory NC CC • σCC vs lepton polarization • e-w unification at high Q2 • extraction of e-w parameters

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 alongitudinal 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 ! F2 FL • HERA results not very conclusive •  roomforimprovement at an EIC

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 10 100 ETjet (GeV)

13. how to determine PDFs from data? information on nucleon (spin) structure available from DIS SIDIS hadron-hadron • all processes tied together: universality of pdfs & Q2 - evolution • each reaction provides insights into different aspects and kinematics • need at least NLO for quantitative analyses; PDFs are not observables! • information on PDFs “hidden” inside complicated (multi-)convolutions task: extract reliable pdfs not just compare some curves to data  a “global QCD analysis” is required

14. global analysis: computational challenge data sets & (x,Q2) coverage used in MSTW fit Martin, Stirling, Thorne, Watt, arXiv:0901.0002 • one has to deal with O(2800) data points from many processes and experiments • need to determine O(20-30) parameters describing PDFs at m0 • NLO expressions often very complicated !computing time becomes excessive • !develop sophisticated algorithms & techniques, e.g., based on Mellin moments Kosower; Vogt; Vogelsang, MS

15. which data sets determine which partons NLO fit, 68% C.L. Martin, Stirling, Thorne, Watt, arXiv:0901.0002 • notice the huge gluon distribution • quality of the fit: • 2543/2699 NLO • 3066/2598 LO c2/ #data pts. as always: LO not sufficient

16. neural network approach toPDFs Forte, 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 strangeness • strangeness with huge uncertainties gluon roomforimprovement at an EIC throughsemi-inclusive DIS (notstudied at H1 & ZEUS)

17. neural network approach: impact of future data see 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 “LHeCCERN yellow report”: • F2c,bsensitive to gluon; chargedcurrent Ws  c to accessstrangeness, ... desirable to have similar studies for an EIC; get “LHeC people” on board

18. opportunities for PDF studies at an EIC HERA has provided a lot of data & unpol. PDFs are rather well known some “weak spots” though: (improvements require an EIC or the LHeC) • FL : needs variable beam energy gluon density • 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: • hadronizationflavor separation of fragmentation fcts • unintegratedkT dependent PDFslargely unknown • repeat HERA program ineN scattering at large √Sterra incognita

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 • study polarized scattering processes quantitatively • learn about pQCD & factorization in the presence of spin • how do quarks and gluons carry the proton spin: • extract helicityPDFs from data • what is the role of orbital angular momentum • understand transverse spin phenomena: • azimuthal asymmetries (Sivers/Collins); role of gauge links; …. • what is the distribution of partons in the transverse plane: • exclusive processes; generalized parton distributions map out the nucleon its complete spin, flavor, and gluon “landscape”

21. helicityPDFs and proton spin sum need a reliable extraction of helicityPDFs from data DGLAP scale evolution “only” known up to NLO yetMertig, van Neerven; Vogelsang but NNLO emergingMoch, Rogal, Vermaseren, Vogt issue:limited x-range of data !extrapolation to x! 0 and 1, how reliable? momentum fraction total spin polarizations Sq and Sg x-moment 1 helicityparton densities sdx 0 helicity sum rule (A+=0 gauge version) Jaffe, Manohar; Ji; … total u+d+s quark spin gluon spin angular momentum “quotable” properties of the nucleon

22. an observation about the spin sum rule DSSV fit has the property that protonspinisalmostentirely OAM for all Q2 recall (at LO) in general, Δg evolves logarithmically but there is a “static solution” (in LO) evolution of 1st moments DSSVΔgis close to “static solution” Dg '– 0.15 wheredDg/dlnm= 0 any deeper reason for that ?

23. emerging picture: sea polarizations x • 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 cloud Thomas, 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 andCOMPASS needs further studies – exp. & theory !

24. emerging picture: gluon polarization x find • Dgsuggested to be huge (axial anomaly) – ruled out! • Dg(x)very small at medium x • still huge uncertainties at small x !cannot quantify sDg(x) dx contributing to proton spin in addition: indications from lattice QCD that quark OAM might be small as well -> who is carrying the proton spin? currently probed by RHIC data 0.05·x· 0.2 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

25. DIS @ small x translates into x interesting questions at small x • charm contribution to g1 • any deviations from DGLAP behavior? • precision study of Bjorken sum rule positiveDg (rare example of a well understood fundamental quantity in QCD)

26. charm contribution to g1 • so far safely ignored • << 1% to existing g1 data • but ≈ 20% contribution to F2 • at small x seen at HERA • expect g1charm of O(10%) • at an EIC depending onΔg • problem: PGF g*(Q2)g ! cc • only known to LO in pol. case NLO: work in progress MS • no variable flavor scheme • a la CTEQ, MRSTdeveloped yet ≈ΔPcgln [Q2/m2] LO estimates from 1996 MS, Vogelsang

27. electro-weak effects at high Q2 Contreras et al. e.g.,  flavor separation extension to SIDIS ? new sum rules, e.g., MS, Vogelsang, Weber

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. physics of the “Collins effect” • effect seen, rather large • Collins fragmentation function : • correlation of transverse spin of • fragmenting quark and PTh • universal, can be determined in e+e- • allows extraction of transversityδq • from combined fit Anselmino et al. BELLE x

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: Burkardt; Brodsky et al; … Collins; Belitsky, Ji, Yuan; Boer, Mulders, Pijlman; … ; talk by Ted Rogers (to be tested experimentally) “attractive” “repulsive”

32. opportunities for spin physics studies at an EIC so far, our knowledge on polarized (SI)DIS is based on fixed target experiments many “weak spots” & room for new “spin surprises”: • small x region: crucial for all sum rules (“proton spin”, “Bjorken”, …) unknown • flavor separation: SU(2) breaking, strangeness largely unknown • electro-weak effects/structure fcts. never measured • full understanding of transverse spin phenomenastill in early stages • issues with factorization for Sivers TMDintriguing • role of orbital angular momentum largely unknown • plus: spin phenomena in diffraction, photoproduction, hadronization, … repeat full HERA program in polarized high energy ep scattering with good particle ID & ability to measure exclusive processes

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 : need to be added for physical cross sections “direct photon” contribution “resolved photon” contribution linked through factorization of same order in couplings

35. photon flux • flux of photons usually estimated by equivalent photon approximation Weizsacker, Williams y: energy fraction transferred from the lepton to the photon consequences/complications: • energy of “target” photon not fixed • but smeared • “electron PDFs” more appropriate: • strong dilution of polarization • for

36. photonicparton densities • evolution eqs. differ from hadronic (proton) case by an inhomogeneousterm • arising from the pointlike coupling of photon to quarks: where inhomog. “pointlike” part homogeneous “hadron-like” contribution GRV – Gluck, Reya, Vogt • 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 fit based on LEP data hadron-like x-shape, dominates at small x

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 MS, Vogelsang • max. input: • min. input: (pointlike at all scales)

40. expectations for the EIC Jäger,MS,Vogelsang; Jäger; Bojak, MS; Riedl, Schäfer, MS; Hendlmeier, Schäfer, MS • many studies available at NLO for the EIC • (1-jet, 1-hadron inclusive, charm, …) 1-jet different assumptions about Jäger arXiv:0807.0066 lepton proton xg¿ 1 probes unknown photon PDFs xg' 1 probes proton PDFs

41. opportunities for photoproduction studies at an EIC photoproduction processes were a core part of the HERA program many probes were limited by statistics or never studied: • access to hadronic structure of photonsmany aspects unknown • spin structureunknown • diffraction (factorization, diffrativePDFs, …) intriguing • …

42. Diffraction recall Anna Stasto’s talk yesterday reviews: workshop on the implications of HERA for LHC physics, hep-ph/0601013; arXiv:0903.3861

43. Exclusive Processes & GPDs see Dieter Müller’s talk next reviews on GPDs: M. Diehl, hep-ph/0307382; A.V. Belitsky and A.V. Radyushkin, hep-ph/0504030

44. final remarks 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); … there is a compelling physics case both in ep and in eA but not a “discovery machine”  weneed 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)