Small-x and Diffraction at HERA and LHC Henri Kowalski DESY EDS Château de Blois 2005

ZEUSH1 Q 2 - virtuality of the incoming photon W - CMS energy of the incoming photon-proton system x - Fraction of the proton momentum carried by the struck quark x ~ Q 2 /W 2 Liquid Argon Calorimeter Uranium-Scintillator Calorimeter e 27 GeV p 920 GeV HERA – ep Collider

y – inelasticity Q 2 = sxy Infinite momentum frame Proton looks like a cloud of non-interacting quarks and gluons F 2 measures parton density in the proton at a scale Q 2

Gluon density Gluon density dominates F 2 for x < 0.01

Diffractive Scattering Non-Diffractive Event ZEUS detector Diffractive Event M X - invariant mass of all particles seen in the central detector t - momentum transfer to the diffractively scattered proton t - conjugate variable to the impact parameter

Dipole description of DIS equivalent to Parton Picture in perturbative region GBW – first Dipole Model only rudimentary evolution BGBK – DM with DGLAP Iancu, Itakura, Mounier (IIM) - CGC motivated ansatz Forshaw, Shaw (FS) - Regge type ansatz with saturation, CGC-inspired Mueller, Nikolaev, Zakharov  r  Q 2 ~1/r 2 Optical T

Comparison with Data FS model with/without saturation and IIM CGC model hep-ph/ Fit F 2 and predict x IP F 2 D(3 ) F2F2 F2F2 FS(nosat) x CGC FS(sat)

Diffractive contribution of the total cross section  For larger M X,  diff has the similar W and Q 2 dependences as  tot. For the highest W bin (200<W<245 GeV),  diff (0.28<M X <35 GeV, M N <2.3 GeV) /  tot

Proton b – impact parameter Impact Parameter Dipole Saturation Model T(b) - proton shape Glauber-Mueller, Levin, Capella, Kaidalov… Kowalski Teaney

x < universal rate of rise of all hadronic cross-sections Total  * p cross-section

Dipole cross section determined by fit to F 2 Simultaneous description of many reactions Gluon density test? Teubner  * p -> J/  p IP-Dipole Model F 2 C IP-Dipole Model

GBW Model IP Dipole Model less saturation (due to IP and charm) strong saturation

Saturation scale HERA RHIC Q S RHIC ~ Q S HERA

Saturated state is partially perturbative   p cross-section exhibits the universal rate of growth

Absorptive correction to F 2 Example in Dipole Model F 2 ~ - Single inclusive pure DGLAP Diffraction

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 Feynman diagrams QCD amplitudes J. Bartels A. Sabio-Vera H. K.

Note: AGK rules underestimate the amount of diffraction in DIS AGK rules in the Dipole Model

HERA Result Unintegrated Gluon Density Dipole Model Example from dipole model - BGBK Another approach (KMR) Active field of study at HERA: UGD in heavy quark production, new result expected from high luminosity running in 2005, 2006, 2007

Exclusive Double Diffractive Reactions at LHC  Diff = hard X-section × Gluon Luminosity factorization !!! f g – unintegrated gluon densities gg Jet+Jet gg Higgs low x QCD reactions : pp => pp + g Jet g Jet  ~ 1 nb for E T > 20 GeV, M(jj) ~ 50 GeV   ~ 0.5 pb for E T > 60 GeV, M(jj) ~ 200 GeV  JET | < 2 KMR Eur. Phys J. C23, p 311 x IP =  p/p, p T x IP ~ % pp => pp + Higgs   3) fb SM ~ O(100) fb MSSM 1 event/sec x IP =  p/p, p T x IP ~ %

t – distributions at HERA t – distributions at LHC with the cross-sections of the O(1) nb and L ~ 1 nb -1 s -1 => O(10 7 ) events/year are expected. For hard diffraction this allows to follow the t – distribution to t max ~ 4 GeV 2 For soft diffraction t max ~ 2 GeV 2 Saturated gluons Non-Saturated gluons t-distribution of hard processes should be sensitive to the evolution and/or saturation effects see: Al Mueller dipole evolution, BK equation, and the impact parameter saturation model for HERA data

Dipole form double eikonal single eikonal Khoze Martin Ryskin t – distributions at LHC Effects of soft proton absorption modulate the hard t – distributions t-measurement will allow to disentangle the effects of soft absorption from hard behavior Survival Probability S 2 Soft Elastic Opacity

L. Motyka, HK preliminary Gluon Luminosity Q T 2 (GeV 2 ) Dipole Model F2F2 Exclusive Double Diffraction

Conclusions We are developing a very good understanding of inclusive and diffractive g * p interactions: F 2, F 2 D(3), F 2 c, Vector Mesons (J/Psi)…. Observation of diffraction indicates multi-gluon interaction effects at HERA HERA measurements suggests presence of Saturation phenomena Saturation scale determined at HERA agrees with RHIC HERA determined properties of the Gluon Cloud Diffractive LHC ~ pure Gluon Collider => investigations of properties of the gluon cloud in the new region Gluon Cloud is a fundamental QCD object - SOLVE QCD!!!!

Smaller dipoles  steeper rise Large spread of eff characteristic for IP Dipole Models universal rate of rise of all hadronic cross-sections The behavior of the rise with Q 2

GBW Model KT-IP Dipole Model less saturation (due to charm) strong saturation

Unintegrated Gluon Densities Exclusive Double Diffraction Note: xg(x,.) and P gg drive the rise of F 2 at HERA and Gluon Luminosity decrease at LHC Dipole Model

Saturation Model Predictions for Diffraction

Absorptive correction to F 2 Example in Dipole Model F 2 ~ - 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

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

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 Feynman diagrams QCD amplitudes J. Bartels A. Sabio-Vera H. K.

Probability of k-cut in HERA data Dipole Model

Problem of DGLAP QCD fits to F 2 CTEQ, MRST, …., IP-Dipole Model at small x valence like gluon structure function ? Remedy: Absorptive corrections? MRW Different evolution? BFKL, CCSS, ABFT

BFKL from Gavin Salam - Paris2004 LO DGLAP --- at low x Next to leading logs NLLx -----

from Gavin Salam - Paris 2004 Ciafalloni, Colferai, Salam, Stasto Similar results by Altarelli, Ball Forte, Thorn

Density profile grows with diminishing x and r approaches a constant value Saturated State - Color Glass Condensate multiple scattering S – Matrix => interaction probability Saturated state = high interaction probability S 2 => 0 r S - dipole size for which proton consists of one int. length

Saturation scale = Density profile at the saturation radius r S S = 0.15 S = 0.25

Saturated state is partially perturbative cross-sectiom exhibits the universal rate of growth

RHIC

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-gluon interaction effects at HERA Open problems: valence-like gluon density? absorptive corrections low-x QCD-evolution HERA measurements suggests presence of Saturation phenomena Saturation scale determined at HERA agrees with the RHIC one HERA+NMC data => Saturation effects are considerably increased in nuclei

Diffractive Scattering Non-Diffractive Event ZEUS detector Diffractive Event M X - invariant mass of all particles seen in the central detector t - momentum transfer to the diffractively scattered proton t - conjugate variable to the impact parameter

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

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