Small-x Physics and Diffraction: HERA Results Allen Caldwell, Max Planck Institute for Physics

1. Small-x Physics and Diffraction: HERA Results Allen Caldwell, Max Planck Institute for Physics Munich, Germany Topics: Inclusive measurements (structure functions, photon-proton cross sections) Fits to inclusive cross sections Diffraction (‘inclusive’, VM production, DVCS) Factorization in diffraction Forward jets Structure of hadrons and nuclei at an electron-ion collider

2. Structure Functions k k’ New Results/fits New results Not relevant at small x Transverse resolution Momentum fraction Inelasticity Structure of hadrons and nuclei at an electron-ion collider

3. Small-x F2 x- HERA Discovery! The rise of the parton densities (and of F2) with decreasing x is strongly dependent on Q2. Implies very large density of partons in the proton when probe at high energies ! Small fraction of HERA data Typically define small x as x<0.01 Structure of hadrons and nuclei at an electron-ion collider

4. A classic HERA plot: the dependence of the rise of F2 on Q2 Parametrize: Below Q20.5 GeV2, see same x (energy) dependence as observed in hadronic interactions. Start to resolve the (constituent) quarks and see the partons at larger Q2. I will show an update of this plot later Structure of hadrons and nuclei at an electron-ion collider

5. Recent development: combined ZEUS and H1 Data sets/fits Structure of hadrons and nuclei at an electron-ion collider

6. Range of validity of DGLAP not clear all is not well … There are signs that DGLAP (Q2 evolution) may be in trouble at small x (negative gluons, high 2for fits). Need better data to test whether our parton densities are reasonable. The structure function FL will provide an important test. Structure of hadrons and nuclei at an electron-ion collider

7. Brand New : FL from HERA Expected to dominate at small-x Need to measure differential cross section at two beam energies (at least). small Q2 LO pQCD F2 Available luminosity (pb-1) HER Ep=920 GeV e+p >300 e-p >200 MER Ep=575 GeV e+p 8 LER Ep=460 GeV e+p 14 r F2-FL 0 1 y2/Y+ Structure of hadrons and nuclei at an electron-ion collider

8. Reduced Cross Sections FL expected to produce turnover at small-x (assuming F2 continues as x-λ) Structure of hadrons and nuclei at an electron-ion collider

9. Preliminary results just out … H1 results consistent with NLO pQCD expectations from H1 fits, ZEUS data somewhat lower. H1 results now published, ZEUS still preliminary. Structure of hadrons and nuclei at an electron-ion collider

10. Hadron-Hadron Cross Section HERA: total photoproduction cross section   (W2) ZEUS prel.   s0.08 e Structure of hadrons and nuclei at an electron-ion collider

11. The rise at small x revisited Look in proton rest frame Parameterize: D 2P BH Structure of hadrons and nuclei at an electron-ion collider

12. Data Sets for Fitting Bayesian analysis based on Markov Chain Monte Carlo Hep-ph 0802.0769 Structure of hadrons and nuclei at an electron-ion collider

13. Fixed Target Structure of hadrons and nuclei at an electron-ion collider

14. H1 Structure of hadrons and nuclei at an electron-ion collider

15. ZEUS Summary: 2P gives best fits D also OK BH does not fit Structure of hadrons and nuclei at an electron-ion collider

16. Slope of the cross section with l increases with Q Extrapolation of the cross section with the D parameterization: Structure of hadrons and nuclei at an electron-ion collider

17. Data extrapolated with this form indicates a merging of cross sections. Crossing is unphysical, eventually expect all cross sections to behave similarly at large l, independent of the starting scale. Is the distance scale meaningful ? Structure of hadrons and nuclei at an electron-ion collider

18. Look at the effective slope with all available data. See indications of a turnover at the highest Q. The data prefers the 2P parameterization. In this case, there is a saturation of the growth of the cross section with Q (so there would not be a unique l for crossing as could happen in the D parameterization). Structure of hadrons and nuclei at an electron-ion collider

19. The second HERA surprise E rapidity Color-neutral object Structure of hadrons and nuclei at an electron-ion collider

20. Evidence of Hard Diffraction at HERA 10% of events have large rapidity gap ! Implies scattering on color neutral cluster: at least two gluons. Nearly constant ratio of diffraction to total as a function of W for fixed MX,Q2 Structure of hadrons and nuclei at an electron-ion collider

21. Diffractive PDF’s where Structure of hadrons and nuclei at an electron-ion collider

22. The ‘inclusive’ diffractive cross section has the same x dependence as the total cross section. There is an indication of universal behavior: Similar at small x Structure of hadrons and nuclei at an electron-ion collider

23. Forward neutron production - electron - pion scattering Same x dependence as inclusive Structure of hadrons and nuclei at an electron-ion collider

24. Small x partons Message: at small-x, data suggests that source of partons (photon, pion, proton, pomeron) is not critical – the gluon density is a universal quantity. Fundamental aspect of matter at small distances. Structure of hadrons and nuclei at an electron-ion collider

25. Ratio of diffractive to total cross section versus scale Logarithmic decrease of diffractive cross section at fixed W, MX Structure of hadrons and nuclei at an electron-ion collider

26. Factorization in Diffractive Scattering Factorization has been proven for Diffractive DIS and exclusive hard diffraction (Collins, Berera&Soper, Trentadue&Veneziano). However, factorization is not expected to hold for diffractive hadron-hadron scattering. The cross sections for large rapidity gap events at the Tevatron are well below expectations based on HERA diffractive pdfs. What about diffractive photoproduction ? The photon can behave both as a point particle and as a composite (hadronic) particle. The ratio of dijet measurement to NLO prediction is photoproduction is a factor 0.5+-0.1 smaller than the same ratio in DIS. However, no dependence on xgamma found. Structure of hadrons and nuclei at an electron-ion collider

27. Factorization in Diffractive Scattering • ZEUS also sees some evidence of suppression of dijets in diffractive photoproduction, but less than H1. Could be related to higher ET. • Summary: • Diffractive charm – no hint of factorization breaking observed • Diffractive dijets – in photoproduction, data favor a global suppression relative to NLO QCD diff pdfs. Factorization breaking observed at low ET but no xgamma dependence. Structure of hadrons and nuclei at an electron-ion collider

28. Exclusive Processes e p ,VM A long list of processes have been measured: N is low mass system and QCD Structure of hadrons and nuclei at an electron-ion collider

29. Data can be parameterized as smooth function of Structure of hadrons and nuclei at an electron-ion collider

30. The dependence of R on W is not the expected one (much less W dependence than initially expected). Maybe due to wavefunction effects. Structure of hadrons and nuclei at an electron-ion collider

31. The Upsilon is now seen with 5 sigma with the full HERA data. Structure of hadrons and nuclei at an electron-ion collider

32. DVCS has also been measured – consistent interpretation withing the CDM (see talk by H. Kowalski) Structure of hadrons and nuclei at an electron-ion collider

33. Forward Jet Production in DIS Forward Jet High x Small x Idea (A. Mueller): selection of events with large rapidity interval visible in the detector – laboratory for studying QCD radiation. NLOJET++: Fixed order QCD partonic cross section, on mass shell ME + DGLAP , (collinear factorisation) Structure of hadrons and nuclei at an electron-ion collider

34. MC Models LEPTO: LO ME on mass shell + PS in DGLAP Strong ordering in kT CASCADE: LO off mass shell ME + PS based on kT factorized CCFM evolution At small xBj no ordering in kT ARIADNE: implementation of Color Dipole Model (CDM) Random walk in kT like in BFKL Structure of hadrons and nuclei at an electron-ion collider

35. Inclusive Forward Jet • Lepto too low • Ariadne “default “ too high • Ariadne “tuned”(by H1) is fine CASCADE has problem with shape of distributions Structure of hadrons and nuclei at an electron-ion collider

36. Trijet with Forward Jet NLOJET++ is below the data – more partons needed. LEPTO also too low, default ARIADNE too high, tuned ARIADNE OK. Summary: Only CDM (ARIADNE MC), with BFKL-like kT parton cascade, can describe all data on forward jets. However, parameter tuning was necessary. Structure of hadrons and nuclei at an electron-ion collider

37. Summary • Understanding the small-x physics is still a work in progress, but: • new data from HERA still coming in (FL, VM updates, total photoproduction cross section) • The data has simple features • indications of universality in small-x behavior • at small enough x, forget the source – gluons are fundamental aspect of nature • Phenomenological studies can give insight • need for new round of experiments, e.g., EIC. What will it bring for the small-x aspects of QCD ? Structure of hadrons and nuclei at an electron-ion collider