Deep Inelastic Scattering

1. Deep Inelastic Scattering José Repond Argonne National Laboratory CTEQ Summer School 2002, Madison, Wisconsin, June 2- 20, 2002

2. Introduction: What is Deep Inelastic Scattering? Consider electron – proton scattering Q2 = -q2 … mass of exchanged γ* squared ~ energy of photon in p rest mass Probing the proton with a wavelength or resolving power λ = ħ/√Q2 e.g. Q2 = 10 5 GeV2: λ ~ 10-18 m or 10-3 ·Rp γ* Deep ≡high resolving power ≡ high Q2 W2 = (P+q)2 … mass of scattering γ* and p mass of hadronic final state X Inelastic ≡ proton breaks up ≡ high W J Repond - DIS

3. More variables… s = (k + p)2 ~ 4EeEp…total center of mass energy squared Consider elastic e – q scattering with x the momentum fraction of the proton carried by the struck q 4- momentum of outgoing quark xP+q mass of outgoing quark 0 = (xP + q)2 ~ q2 + 2xP·q x = Q2/2P·q … Bjorken x y = P·q/P·k …Inelasticity Fraction of k carried by the γ* Related to scattering angle of e, q in their center of mass system J Repond - DIS

4. Relations between variables… e’(θ,E) e Easy to show that… Q2 = sxy W2 ≈ Q2(1-x)/x At fixed center of mass energy s only 2 independent Q2, x variables needed x, y W2, Q2 …. to describe inclusive deep inelastic scattering J Repond - DIS

5. Introduction: History of Deep Inelastic Scattering 1911 Rutherford Elastic scattering of α – particles on atoms Discovery of atomic nucleus Size of nucleus 10-5 size of atom 1968 SLAC-MIT Deep inelastic scattering of e- of p, d Observation of ~flat Q2 dependence of R= σinel/σMott R can be interpreted as form factor (describing form of scatterer) R~const → pointlike scatterers inside proton Partons later identified with quarks J Repond - DIS

6. Gargamelle(Bubble chamber at CERN) 1973 Observation of With no outgoing μ!!! ν ν Z0 p hadrons Distance in detector Discovery of neutral current interactions (mediated by Z0 boson) J Repond - DIS

7. European Muon Collaboration at CERN 1988 Scattering of Study of spin asymmetries Integral of spin structure function g_1 related to contributions of quarks to p spin (Expected Σ =1 from valence quarks) Contribution of quarks to p spin small J Repond - DIS

8. Introduction: The HERA Collider e± p 27.5 GeV 920 GeV First and only ep collider √s = 318 GeV Equivalent to fixed target experiment with 50.6 TeV e± Located in Hamburg (Germany) J Repond - DIS

9. World’s most complicated collider Two independent storage rings H1 – ZEUS Colliding beam experiments H1 HERA-B Uses p beam on wire target Goal: B - physics HERMES HERA-B HERMES Uses e± beam on gas jet target Both lepton and target polarized Measurement of polarized structure functions ZEUS J Repond - DIS

10. HERA Performance and Future Commissioned in 1992 Ran almost continuously until 2000 Performance improved over years Delivered Total Shutdown in September 2000 Insertion of quadropoles close to IR → Increase of Luminosity by a factor of 5 Insertion of spin rotators around H1-ZEUS → Longitudinally polarized e± HERA II Program To be completed by 2006/7 Expect J Repond - DIS

11. Introduction: The Collider Experiments H1 Detector Complete 4π detector with Tracking Si-μVTX Central drift chamber Liquid Ar calorimeter Rear Pb-scintillator calorimeter μ chambers and much more… J Repond - DIS

12. ZEUS Detector Complete 4π detector with Tracking Si-μVTX Central drift chamber Uranium-Scintillator calorimeter μ chambers and much more… Both detectors asymmetric J Repond - DIS

13. e’ e γ, Z0 q q’ e p e’ e p Introduction: Physics Processes Neutral Current Interactions Photoproduction Q2 ~ 0 GeV2 (real γ) Deep Inelastic Scattering e’ Q2≥ 4 GeV2 (virtual γ*, Z0) pT of events balanced J Repond - DIS

14. e W± q q’ e p Charged Current Interactions ν ν pT of events not balanced e’(θ,E) e Inclusive scattering described by 2 variables e.g. x, Q2 Details of hadronic final state ignored Charged current kinematics reconstructed with hadronic final state J Repond - DIS

15. e’ e γ, Z0 g Studies of Hadronic Final State in DIS Multi-jet Production in NC events Boson-gluon Fusion QCD Compton e’ e γ, Z0 αS Need additional variables to describe events e.g. NJet, ηJet, pTJet… Thrust, Sphericity… Ncharged tracks, Nπ… g Processes in Leading – Order in αS J Repond - DIS

16. Diffractive events e’ e γ, Z0 e p p p Gap in rapidity η Color neutral exchange: P or 2 gluons Approximately 10% of the events Proton stays intact Additional variables: xP, ηmax, β… J Repond - DIS

17. Kinematic Regions of DIS Reaching values of Q2 > 104 GeV2 Kinematic limit defined by Q2 = sxy sHERA = 100000 GeV2 Previous fixed target experiments Reaching values of x < 10-6 HERA: extension by several orders of magnitude J Repond - DIS

18. Outline of Lectures Exclusive measurements Jet production Jets in DIS Extraction of αS Jets in photoproduction Heavy flavor production Charm production cross sections Interpretations Charm fragmentation Beauty production cross sections J/ψ production cross sections Diffraction Rate of inclusive diffraction Interpretations Vector-meson production Inclusive measurements Total γp cross section Neutral current scattering Structure function F2 Interpretations Extraction of parton densities Measurements of FL Measurement of xF3 Valence quarks Contributions of charm to F2 Charged current scattering Outlook and conclusions Polarized structure functions Exotic searches Leptoquarks, SUSY signatures, Contact Interactions… J Repond - DIS

19. Total γP cross section Most fundamental measurement at HERA Consider e± as source of (real ) photons Inclusive measurement with only 1 variable WγP … center of mass of γ and proton or … Inelasticity J Repond - DIS

20. 35 m Count events Nγ (syst) nb-1 105 m Measurement Tag events at low Q2 < 0.02 GeV2 with e± tagger at 35 m from IP Reconstruct W from Ee’ e’ Bethe-Heitler Bremsstrahlungs process ep → eγp Require O(1GeV) in calorimeter Count events Ne(y) γ γ tagger Acceptance: real challenge! Can be calculated with high accuracy J Repond - DIS

21. Acceptance Ae = A35m ACAL Major uncertainty of measurement! Reliably calculable for 12 < Ee’ < 16 GeV corresponds to 0.56 > y > 0.42 or 225 > W > 194 GeV Requires simulation of all physics processes Fraction determined in separate measurements in fits to detector observables J Repond - DIS

22. Extraction of γP Cross Section Measurement of How to extract σγP(W) ??? Equivalent Photon Approximation relates the two Qmin … minimum Q given by finite e± mass σT … cross section for transversely polarized γ σL … cross section for longitudinally polarized γ → expected to be very small Integration over Q2 Qmax … maximum Q defined by experimental conditions Photon flux factor fγ(y) J Repond - DIS

23. Result Rise parameterized as sα with α = 0.08 Same value as in pp, pp, πp, Kp γp scattering behaves like hadron-hadron scattering At low Q2: γ is just a hadron J Repond - DIS

24. Proton Structure Function from NC DIS LμνLepton tensor calculable in QED WμνHadron tensor contains 3 ‘a priori’ unknown structure functions Fi Cross section calculated as convolution of Coupling Helicity structure: Jz= 0 → 1 1 → (1 - y)2 Propagator F2… Parity conserving structure function (γ and Z0 exchange plus interference) FL … Longitudinal structure function (exchange of longitudinally polarized γ/Z0) xF3 … Parity violating structure function (pure Z0 exchange and interference) J Repond - DIS

25. Measurement of F2(x,Q2) For Q2« MZ2 → xF3 negligible FL only important at high y Both FL and xF3 ~ calculable in QCD Correct for higher order QED radiation Extract F2(x,Q2) from measurement of Difficult measurements: Nevertheless high precision: errors of 2-3% J Repond - DIS

26. J Repond - DIS

27. Scaling and its violations (non) – dependence on Q2 Elastic scattering off pointlike and free partons → does not depend on Q2 ‘a point is a point’ Scaling violations Scaling Result of emission of gluons from partons inside proton Scaling violations Depletion at high x → quarks emit gluons Increase at low x → quarks having emitted gluons Effect increases with αslog Q2 J Repond - DIS

28. Interpretation: DGLAP evolution F2(x,Q2) can in principle be calculated on the Lattice → Some results emerged in the last few years Standard analysis assumes that F2(x,Q2) not calculable However: evolution with Q2 calculable in pQCD Dokshitzer, Gribov, Lipatov, Altarelli, Parisi (DGLAP): Parton Density Functions (PDFs) qi(x,Q2) … Density of quark i at given x, Q2 g(x,Q2) … Density of gluons at given x, Q2 Pij(x/z) … Splitting functions Quark-Parton Model (QPM) …in DIS scheme J Repond - DIS

29. Pqq Pqg Pgq Pgg Splitting FunctionsPij(z) Probability of parton i going into parton j with momentum fraction z Calculable in pQCD as expansions in αS In Leading Order Pij(z) take simple forms J Repond - DIS

30. Fit to DGLAP equations I) Rewrite DGLAP equations a) Simplify notation i) ii) b) Sum i) over q and q separately ia) ib) Nf … number of flavors c) Define: Valence quark density Singlet quark density ← u,u,d J Repond - DIS

31. d) Rewrite DGLAP equations Valence quark density decouples from g(x,Q2) Only evolves via gluon emission depending on Pqq II) DGLAP equations govern evolution with Q2 Do not predict x dependence: Parameterize x-dependence at a given Q2 = Q20 = 4 – 7 GeV2 55 parameters High x behaviour: valence quarks Low x behaviour J Repond - DIS

32. III) Sum rules and simplifying assumptions Valence distributions 2 valence up-quarks 1 valence down quarks Symmetric sea Treatment of heavy flavors (different treatments available…) BelowmHF: Above mHF: generate dynamically via DGLAP evolution Momentum sum rule: proton momentum conserved Effect number of parameters: 55 (parameters) – 3 (sum rules) – 13 (symmetric sea) – 22(heavy flavors) = 17 Difficult fits, involving different data sets with systematic errors… J Repond - DIS

33. Several groups perform global fits CTEQ: currently CTEQ6 MRS: currently MRST2001 GRV: currently GRV98 Experiments: H1, ZEUS Overall good agreement between fits Despite some differenent assumptions Results of fits I Fit quality: excellent everywhere! → no significant deviations Evolution with Q2: 5 orders of magnitude QCDs greatest success!!! No deviations at high Q2: → no new physics: no contact interactions no leptoquarks Fit includes data with low Q2: αS(Q2) large → surprise → expected to work only for Q2 ≥ 10 GeV2 J Repond - DIS

34. Results of fits II Gluon density Quark and gluon densities Inferred from QCD fit not probed directly by γ Errors of order 4% at Q2 = 200 GeV2 CTEQ6 Valence quarks Strong coupling constant Based on NLO pQCD including terms of αS2 Scale error reduced with NNLO not yet available J Repond - DIS

35. Universality of Parton Density Functions Determined with DIS data and pQCD fits Can now be used to calculate any process involving protons W±Production at the Tevatron Higgs production at LHC And yet another success of pQCD… Jet production at HERA J Repond - DIS

36. Other interpretations DGLAP formalism Standard approach: Equations to NLO Include all terms O(αS2) Calculation of NNLO corrections First results by the MRST group Effects seem small, but will reduce uncertainties Collinear Factorization DGLAP also resums terms proportional (αS log Q2)n corresponds to gluon ladder with kT ordered gluons kT,n >> kT,n-1 … >> kT,0 struck parton collinear with incoming proton Does not resum terms proportional to (αS log 1/x)n → Is this ok at small x? J Repond - DIS

37. BFKL formalism Q2 Y Balitskii, V Fadin, L Lipatov, E Kuraev Resums terms proportional to (αs log 1/x)n gluons in ladder not kT ordered, but ordered in x x1 >> x2 … >> xn Predicts x, but not Q2dependence kT Factorization results in kT unintegrated gluon distributions g(x,kT2,Q2) DGLAP CCFM BFKL x CCFM formalism S Catani, M Ciafaloni, F Fiorani, G Marchesini Resums terms proportional to (αs log 1/x)n and (αs log 1/(1-x))n gluons in ladder now ordered in angle kT Factorization results in kT unintegrated gluon distributions g(x,kT2,Q2) Easier to implement in MC programs, e.g. CASCADE Low x: approaches BFKL High x: approaches DGLAP J Repond - DIS

38. Asymmetric sea FNAL fixed target experiment E-866 Measurement of Drell-Yan production with H2 and D2 targets p N →μ+ μ- X …with x = x1 – x2 Sea not flavor symmetric!!! Explanations: Meson clouds Chiral model Instantons More data to come: P-906 at the Main Injector J Repond - DIS

39. Longitudinal Structure Function FL from NC DIS …ignore xF3 at lower Q2 Disentangle F2(x,Q2) and FL(x,Q2) Need to vary y, keeping x, Q2 fixed → vary s lower Ep to say 920 → 450 GeV Involves large effort - Machine tuning - Detector acceptance for lower Ee’ - Large statistics needed Not yet done at HERA J Repond - DIS

40. H1 Analysis Determine PDFs using only low y data contribution from FL negligible Evolve PDFs to high y region according to DGLAP equations Subtract prediction of F2 from measurements at high y → FL Yellow line: Result of DGLAP fit including FL Points: Subtraction technique ZEUS: No comparable analysis Circularity? At small x: Fit at low y already determines FL J Repond - DIS

41. Low Energy Results Data from SLAC and CERN Electron/μ scattering on fixed targets with different beam energies Measurement of R(x,Q2) Ratio of longitudinal and transverse cross section J Repond - DIS

42. Measurements at high x > 0.1 but low Q2 < 80 GeV2 Curves Rfit … fit to empirical function RQCD … prediction based on PDFs from F2data RQCD+TM … same as above, corrected for target mass effects Differences between data and QCD higher twist effects? decrease as 1/Q2 g Important to measure at HERA!!! J Repond - DIS

43. xF3 Structure Function from NC DIS Cross section for scattering of Left, Right – handed electrons FL(x,Q^2) … ignored (small at high Q2) Parity conserving Parity violating … sum over all q and q …sum over the 2 valence distributions At high Q2: weak terms non-negligible interference electromagnetic pure weak interference pure weak J Repond - DIS

44. Up to now: no longitudinal polarization for H1/ZEUS → How to measure xF3(x,Q2) ??? Consider Parity and CP Operations CP conserved in DIS xF3(x,Q2) can be measured using difference of Clear difference at high Q2 J Repond - DIS

45. First measurement on proton No nuclear corrections Agrees with expectations based on PDFs from F2 fits Clearly needs more statistics → HERA II program J Repond - DIS

46. Charm contribution to F2 Events with charm identified through Identify e± with dE/dx of central drift chamber Mass plot of Δm = m(Kππ) – m(Kπ) Sharp peak at Δm = mD* - mD = 145 MeV J Repond - DIS

47. Charm production mechanisms Variable Flavor Number Scheme VFNS - Charm treated as extra flavor c(x,Q2) in proton (mass ignored) - c(x,Q2) assumed to be zero for scales μ < mc - c(x,Q2) evolved to higher scales using DGLAP → this also resums (log(Q/mc)2)n - Expect good description at large Q2 where log’s might be large - Expect problems at Q ~ mc γ, Z0 c γ, Z0 Fixed Flavor Number Scheme FFNS - no heavy quarks inside proton, only u, d, s quarks - Charm produced via Boson-gluon fusion process (including masses) - Expect good description for μ ~ mc - Expect problems at large Q2, since log’s not resummed c c g Mixed Flavor Scheme MFS - Uses best of both J Repond - DIS

48. Determination of Fc(x,Q2) 2 Charmed production measured in limited phase space e.g. 1.5 < pT(D*) < 15 GeV |η(D*)| < 1.5 Extrapolation to full (pT,η) phase space model dependent! ignored Nice agreement with FFNS based on xg(x) from F2 fits J Repond - DIS

49. Comparison of Schemes Some differences at 3 < Q2 < 32 GeV2 Data can not distinguish → HERA II FFNS VFNS VFNS Agreement between schemes at large Q2 → (log(Q/mc)2)n not important? Plots from A Chuvakin, B Harris and J Smith J Repond - DIS

50. Charm Fraction of Inclusive F2 Fraction increases with increasing Q2 → as large as 30% !!! Reproduced by FFNS calculations based on xg(x,Q2) from fits to inclusive F2 J Repond - DIS