HERA KINEMATIC PLANE

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2. HERAKINEMATICPLANE • Accessible Kinematic Plane now almost completely covered • Measurements extend to cover high y, high x and very high Q2 • Probe distances to ~ 1/1000th of proton size AramKotzinian

3. Q2 = xys Tevatron COMPASS AramKotzinian

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8. The data show that F2 depends more and more steeply on Q2 as x falls. These logarithmic scaling violations are predicted by QCD. The driver is gluon emission from the quark lines - the gluons in turn spilt into quark-antiquark pairs, which in turn radiate gluons - and so on, ad infinitum. At each branching, the energy is shared, so the result is to throw more and more partons to lower and lower x - the “steep rise in F2” which is one of the most significant discoveries of HERA. AramKotzinian

9. 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 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 AramKotzinian

10. 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 AramKotzinian

11. 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 AramKotzinian

12. 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 AramKotzinian

13. 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 AramKotzinian

14. 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… AramKotzinian

15. Several groups perform global fits CTEQ: currently CTEQ6 MRS: currently MRST2001 GRV: currently GRV98 Experiments: H1, ZEUS Overall good agreement between fits Despite some different 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 AramKotzinian

16. 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 AramKotzinian

17. 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? AramKotzinian

18. 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 AramKotzinian

19. 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 AramKotzinian

20. Longitudinal Structure Function FL from NC DIS Need to vary y, keeping x, Q2 fixed → vary s Disentangle F2(x,Q2) and FL(x,Q2) Data from SLAC and CERN: e/μ scattering on fixed targets with different beam energies Measurement of R(x,Q2): Ratio of longitudinal and transverse cross section AramKotzinian

21. 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 AramKotzinian