Small-x and Diffraction in DIS at HERA I Henri Kowalski DESY 12th CTEQ Summer School Madison - Wisconsin June 2004

H1 detector ZEUS detector Ep = 920 GeV, Ee = 27.5 GeV, # bunches = 189 Ip = 110 mA, Ie = 40 mA Linst= 2 x 1031 cm-2 s-1

ZEUS detector Q2 ~ 2 –100 GeV2 Q2 ~ 0.05-0.6 GeV2 Q2 - virtuality of the incoming photon W - CMS energy of the incoming photon-proton system x - Fraction of the proton momentum carried by struck quark x ~ Q2/W2

Infinite momentum frame Proton looks like a cloud of y – inelasticity Q2 = sxy Infinite momentum frame Proton looks like a cloud of noninteracting quarks and gluons F2 measures parton density in proton at scale Q2 F2 = f e2f x q(x,Q2)

there is a change of slope at small-x, near Q2 = 1 GeV2

Gluon density Gluon density dominates F2 for x < 0.01

Gluon density known with good precision at larger Q2. For Q2 ~1 GeV2 gluons tends to go negative. NLO, so not impossible BUT – cross sections such as L also negative !

MX - invariant mass of all particles seen in the central detector t - momentum transfer to the diffractively scattered proton

Diffractive Signature DY ~ log(W2 / M 2X) diff Non- diff Non-Diffraction Diffraction - Rapidity uniform, uncorrelated particle emission along the rapidity axis => probability to see a gap DY is ~ exp(-<n>DY) <n> - average multiplicity per unit of rapidity dN/ dM 2X ~ 1/ M 2X => dN/dlog M 2X ~ const

Slow Proton Frame incoming virtual photon fluctuates into a quark-antiquark pair which in turn emits a cascade-like cloud of gluons Transverse size of the quark-antiquark cloud is determined by r ~ 1/Q ~ 2 10-14cm/ Q (GeV) Diffraction is similar to the elastic scattering: replace the outgoing photon by the diffractive final state r , J/Y or X = two quarks Rise of sgptot with W is a measure of radiation intensity

Radiation process emission of gluons is ordered in rapidities QCD Toy Model: integrals over transverse momenta are independent of each other Rise of sgptot with W is a measure of radiation intensity

Dipole description of DIS

Q2~1/r2 exp(-mq r)

GBW Model K. Golec-Biernat, M. Wuesthoff Scaling in Geometrical Scaling A. Stasto & Golec-Biernat J. Kwiecinski Parameters fitted to DIS F2 data: s0 = 23 mb l = 0.29 x0 = 0.0003

Parameters fitted to HERA DIS data: c2 /N ~ 1 s0 = 23 mb l = 0.29 x0 = 0.0003

Saturation Model Predictions for Diffraction

Geometrical Scaling A. Stasto & Golec-Biernat J. Kwiecinski

GBW model, in spite of its compelling success has some obvious shortcomings: The treatment of QCD evolution is only rudimentary remedy => incorporate DGLAP into dipole cross-section J. Bartels, K. Golec-Biernat, H. Kowalski The dipole cross section is integrated over the transverse coordinate although the gluon density is expected to be a strongly varying function of the impact parameter. Recently: BFKL motivated Ansatz proposed by Iancu, Itakura, Munier

Impact Parameter Dipole Saturation Model H. Kowalski D. Teaney hep-ph/0304189 Proton b – impact parameter well motivated: Glauber Mueller Levin Capella Kaidalov T(b) - proton shape

Derivation of the GM dipole cross section probability that a dipole at b does not suffer an inelastic interaction passing through one slice of a proton S2 -probability that a dipole does not suffer an inelastic interaction passing through the entire proton <= Landau-Lifschitz

t-dependence of the diffractive cross sections determines the b distribution

mu = 0.05 GeV Q02 = 0.8 GeV2 c2/N = 0.8 x < 10-2 Q2 > 0.25 GeV2 mc = 1.30 GeV Fit parameters lg = -0.12 C= 4.0 Q02 = 0.8 GeV2 c2/N = 0.8 x < 10-2

GBW Model IP Saturation Model

Smaller dipoles  steeper rise Large spread of leff characteristic for ----- universal rate of rise of all hadronic cross-sections Smaller dipoles  steeper rise Large spread of leff characteristic for Impact Parameter Dipole Models

Saturation region -------------------------------------------------------------------------------------------------------

All quarks Charmed quark

Gluon density Charm structure function

Photo-production of Vector Mesons

Absolute values of cross sections are strongly dependent on mc

Absorptive correction to F2 from AGK rules Martin M. Ryskin G. Watt Example in Dipole Model F2 ~ - Single inclusive pure DGLAP Diffraction

Fit to diffractive data using MRST Structure Functions A. Martin M. Ryskin G. Watt

A. Martin M. Ryskin G. Watt

rS - dipole size for which proton consists of one int. length Density profile grows with diminishing x and r approaches a constant value Saturated State - Color Glass Condensate S2 -probability that a dipole does not suffer an inelastic interaction passing through the entire proton Saturated state = = high interaction probability S2 => 0 multiple scattering rS - dipole size for which proton consists of one int. length

Saturation scale = Density profile at the saturation radius rS lS = 0.25 lS = 0.15

Saturation in the un-integrated gluon distribution kT factorisation formula dipole formula

GBW - - - - - - - - - - - - - - - - - - - - - x = 10-6 BGBK ___________________________________ x = 10-2 GBW - - - - - - - - - - - - - - - - - - - - - x = 10-4 BGBK ___________________________________ x = 10-2 - numerical evaluation

Diffractive production of a qq pair _ Diffractive production of a qq pair

Inclusive Diffraction LPS - Method

END of Part I