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 July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider Structure Functions k k’ New Results/fits New results Not relevant at small x Transverse resolution Momentum fraction Inelasticity July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider 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 July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

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 July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Recent development: combined ZEUS and H1 Data sets/fits July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

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 2 for fits). Need better data to test whether our parton densities are reasonable. The structure function FL will provide an important test. July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider Brand New : FL from HERA Need to measure differential cross section at two beam energies (at least). small Q2 LO pQCD Expected to dominate at small-x 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 1 y2/Y+ July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Reduced Cross Sections FL expected to produce turnover at small-x (assuming F2 continues as x-λ) July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider 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. July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Hadron-Hadron Cross Section HERA: total photoproduction cross section ZEUS prel.   (W2) e July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider The rise at small x revisited Look in proton rest frame Parameterize: D 2P BH July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider Data Sets for Fitting Bayesian analysis based on Markov Chain Monte Carlo Hep-ph 0802.0769 July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider Fixed Target July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider ZEUS Summary: 2P gives best fits D also OK BH does not fit July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider Slope of the cross section with l increases with Q Extrapolation of the cross section with the D parameterization: July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider 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 ? July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider 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). July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

The second HERA surprise rapidity Color-neutral object July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider 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 July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider Diffractive PDF’s where July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider 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 July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Forward neutron production - electron - pion scattering Same x dependence as inclusive July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider 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. July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Ratio of diffractive to total cross section versus scale Logarithmic decrease of diffractive cross section at fixed W, MX July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

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. July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

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. July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider Exclusive Processes e p ,VM A long list of processes have been measured: N is low mass system and QCD July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider Data can be parameterized as smooth function of July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider The dependence of R on W is not the expected one (much less W dependence than initially expected). Maybe due to wavefunction effects. July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider The Upsilon is now seen with 5 sigma with the full HERA data. July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider DVCS has also been measured – consistent interpretation withing the CDM (see talk by H. Kowalski) July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Forward Jet Production in DIS 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) July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider 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 July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider Inclusive Forward Jet • Lepto too low • Ariadne “default “ too high • Ariadne “tuned”(by H1) is fine CASCADE has problem with shape of distributions July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

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. July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider

Structure of hadrons and nuclei at an electron-ion collider 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 ? July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider