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

Proton b – impact p. Dipole Saturation Models T(b) - proton shape Glauber Mueller GBW KT BGBK DGLAP IIM Model with BFKL & CG evolution

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 S 2 -probability that a dipole does not suffer an inelastic interaction passing through the entire proton <= Landau-Lifschitz Uncorrelated scatterings NOTE: the assumption of uncorrelated scatterings is not valid for BK and JIMWLK equations Correlations from evolution  IIM Dipole fit GM Dipole + DGLAP mimics full evolution

Parameters fitted to HERA DIS data:  2 /N ~ 1  0 = 23 mb  = 0.29 x 0 = Data precision is essential to the progress of understanding GBW GBW

Smaller dipoles  steeper rise Large spread of eff characteristic for Impact Parameter Dipole Models (KT) universal rate of rise of all hadronic cross-sections GBW =0.29

BGBK KT In IP Saturation Model (KT) change of with Q 2 is mainly due to evolution effects GBW In GBW Model change of with Q 2 is due to saturation effects In BGBK Model change of with Q 2 is due to saturation and evolution effects Analysis of data within Dipole Models Theory (RV): evolution leads to saturation - Balitzki- Kovchegov and JIMWLK GBW =0.29

GBW BGBK ___________________________________ - numerical evaluation x = x = x = x = Evolution increases gluon density => smaller dipoles scatter stronger, gluons move to higher virtualities Fourier transform In Color-Glass gluons occupy higher momentum states

A glimpse into nuclei Naïve assumption for T(b): Wood-Saxon like, homogeneous, distribution of nuclear matter

Smooth Gluon Cloud Q 2 (GeV 2 ) C Ca

Lumpy Gluon Cloud Q 2 (GeV 2 ) C Ca

Saturation Scale at RHIC

Diffractive production of a qq pair _

Diffractive production of a qqg system

Inclusive Diffraction

Non-Diffraction Diffraction Select diffractive events by requirement of no forward energy deposition called  max cut Q: what is the probability that a non-diff event has no forward energy deposition? e =><=p

pp  Y log W 2 detector log M X 2 M X Method Non-Diffractive Event Diffractive Event   * p-CMS  Y non-diff events are characterized by uniform, uncorrelated particle emission along the whole rapidity axis => probability to see a gap  Y is ~ exp(-  Y) – Gap Suppression Coefficient since  Y ~ log(W 2 /M 2 X ) –  0 dN/dlogM 2 X ~exp(  log(M 2 X )) diff events are characterized by exponentially non-suppressed rapidity gap  Y dN/ dM 2 X ~ 1/ M 2 X => dN/dlogM 2 X ~ const YY YY

Non- diff M X Method Non- diff Non- diff Non-Diffraction dN/dM 2 X ~exp(  log(M 2 X )) Gap suppression coefficient independent of Q 2 and W 2 for Q 2 > 4 GeV 2 Diffraction dN/dlog M 2 X ~ const

Gap Suppression in Non-Diff MC ---- Generator Level CDM ---- Detector Level CDM dN/dM 2 X ~exp( log(M 2 X )) In MC independent of Q 2 and W 2 ~ 2 in MC  in data Detector effects cancel in Gap Suppression !

Physical meaning of the Gap Suppression Coefficient Uncorrelated Particle Emission (Longitudinal Phase Space Model)  – particle multiplicity per unit of rapidity Feynman (~1970):  depends on the quantum numbers carried by the gap  2 for the exchange of pion q.n.   for the exchange of rho q.n   for the exchange of pomeron q.n   is well measurable provided good calorimeter coverage exp(-  Y ) = exp(- log(W 2 /M 2 X )= (W 2 /M 2 X )  from Regge point of view ~ (W 2 ) 

SR = SATRAP: MC based on the Saturated Dipole Saturation Model

~ H1 approach

A. Martin M. Ryskin G. Watt

 BEKW A. Martin M. Ryskin G. Watt

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

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

Absorptive correction to F 2 from AGK rules Example in Dipole Model F 2 ~ - Single inclusive pure DGLAP Diffraction A.Martin M. Ryskin G. Watt

A. Martin M. Ryskin G. Watt

AGK Rules The cross-section for k-cut pomerons: Abramovski, Gribov, Kancheli Sov.,J., Nucl. Phys. 18, p308 (1974) 1-cut 2-cut QCD Pomeron F (m) – amplitude for the exchange of m Pomerons

Color singlet dominates over octet in the 2-gluon exchange amplitude at high energies 3-gluon exchange amplitude is suppressed at high energies 2-gluon pairs in color singlet (Pomerons) dominate the multi-gluon QCD amplitudes at high energies Pomeron in QCD t-channel picture

2-Pomeron exchange in QCD Final States (naïve picture) 0-cut 1-cut 2-cut p   * p-CMS  YY detector p   * p-CMS  p  detector Diffraction

0-cut 1-cut 2-cut 3-cut

AGK Rules in the Dipole Model Total cross section Mueller-Salam (NP B475, 293) Dipole cross section Amplitude for the exchange of m pomerons in the dipole model KT model

AGK rules Dipole model Diffraction from AGK rules very simple but not quite right

Q 2 ~1/r 2 exp(-m q r)

All quarks Charmed quark

Note: AGK rules underestimate the amount of diffraction in DIS

Conclusions We are developing a very good understanding of inclusive and diffractive  * p interactions: F 2, F 2 D(3), F 2 c, Vector Mesons (J/Psi)…. Observation of diffraction indicates multi-pomeron interaction effects at HERA HERA measurements suggests presence of Saturation phenomena Saturation scale determined at HERA agrees with the RHIC one Saturation effects in ep are considerably increased in nuclei

Thoughts after CTEQ School George Sterman: Parton Model Picture (in Infinite Momentum Frame) is in essence probabilistic, non-QM. It is summing probabilities and not amplitudes F 2 =  f e 2 f x q(x,Q 2 ) Parton Model Picture is extremely successful, it easily carries information from process to process, e.g. we get jet cross-sections in pp from parton densities detemined in ep Dipole Models (Proton rest Frame) are very successful carrying information from process to process within ep. They are in essence QM, main objects are amplitudes: In DM Picture diffraction is a shadow of F 2. Many other multi-pomeron effects should be present

Several attempts are underway to build a bridge over the gap between Infinite Momentum Frame and Proton Rest Frame Pictures Jochen Bartels, Lipatov & Co: Feynman diagrams for multi-pomeron processes… Raju Venogopulan & Co, Diffraction from Wilson loops, fluctuations from JIMWLK… ……………………………………..

A new detector to study strong interaction physics e p Hadronic Calorimeter EM Calorimeter Si tracking stations Compact – fits in dipole magnet with inner radius of 80 cm. Long - |z|  5 m

e 27 GeV p 920 GeV Forward Detector

Increase of kinematic range by over 4 order of magnitude in x at moderate Q 2 and 6 order of magnitude in Q 2 HERA Interactions Collisions of e + (e - ) of 27.5 GeV with p of 920 GeV