Forward particle production in the presence of saturation Cyrille Marquet Columbia University

Outline Saturation and the Color Glass Condensate the BK equation and the unintegrated gluon distribution Forward particle production in pA collisions single particle production and the success of the CGC Some predictions for the LHC in pp, pA and AA Mueller-Navelet jets in pp azimuthal correlations in pA particle multiplicity in AA

Saturation and the Color Glass Condensate

The saturation phenomenon gluon recombination in the hadronic wave function gluon density per unit area it grows with decreasing x recombination cross-section recombinations important when gluon kinematics this regime is non-linear yet weakly coupled the saturation regime: for with the idea of the CGC is to take into account this effect via strong classical fields McLerran and Venugopalan (1994) the CGC: an effective theory to describe the saturation regime lifetime of the fluctuations in the wave function ~ high-x partons ≡ static sources low-x partons ≡ dynamical fields 

Scattering off the CGC this is described by Wilson lines scattering of a quark: dependence kept implicit in the following in the CGC framework, any cross-section is determined by colorless combinations of Wilson lines , averaged over the CGC wave function x : quark space transverse coordinate y : antiquark space transverse coordinate the dipole scattering amplitude: this is the most common average for instance it determines deep inelastic scattering the 2-point function or dipole amplitude for 2-particle correlations more complicated correlators for instance

Evolution of the wave function the JIMWLK equation Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner the energy evolution of cross-sections is encoded in the evolution of this wave function is mainly non-perturbative, but its evolution is known  Balitsky hierarchy for Wilson lines correlators sums both and the BK equation is a closed equation for obtained by assuming robust only for impact-parameter independent solutions the BK equation r = dipole size the unintegrated gluon distribution 

When is saturation relevant ? in processes that are sensitive to the small-x part of the hadron wavefunction deep inelastic scattering at small xBj : particle production at forward rapidities y : at HERA, xBj ~10-4 for Q² = 10 GeV² in DIS small x corresponds to high energy saturation relevant for inclusive, diffractive, exclusive events at RHIC, x2 ~10-4 for pT ² = 10 GeV² pT , y in particle production, small x corresponds to high energy and forward rapidities saturation relevant for the production of jets, pions, heavy flavors, photons

Forward particle production in pA collisions

Forward particle production forward rapidities probe small values of x kT , y transverse momentum kT, rapidity y > 0 values of x probed in the process: the large-x hadron should be described by standard leading-twist parton distributions the small-x hadron/nucleus should be described by CGC-averaged correlators the cross-section: single gluon production probes only the unintegrated gluon distribution (2-point function)

RHIC vs LHC typical values of x being probed at forward rapidities (y~3) xA xp xd RHIC deuteron dominated by valence quarks nucleus dominated by early CGC evolution LHC the proton description should include both quarks and gluons on the nucleus side, the CGC picture would be better tested RHIC LHC if the emitted particle is a quark, involves if the emitted particle is a gluon, involves how the CGC is being probed

Running coupling corrections running coupling corrections to the BK equation taken into account by the substitution Kovchegov Weigert Balitsky consequences similar to those first obtained by the simpler substitution running coupling corrections slow down the increase of Qs with energy also confirmed by numerical simulations, however this asymptotic regime is reached for larger rapidities

The KKT parametrization build to be used as an unintegrated gluon distribution Kovchegov, Kharzeev and Tuchin (2004) the idea is to play with the saturation exponent the DHJ version the BUW version KKT modified to feature exact geometric scaling Dumitru, Hayashigaki and Jalilian-Marian (2006) Boer, Utermann and Wessels (2008) in practice is always replaced by before the Fourier transformation KKT modified to better account for geometric scaling violations

RdA and forward pion spectrum the suppression of RdA was predicted xA decreases (y increases) in the absence of nuclear effects, meaning if the gluons in the nucleus interact incoherently like in A protons first comparison to data RdA Kharzeev, Kovchegov and Tuchin (2004) qualitative agreement with KKT parametrization

What about the large-x hadron? getting a quantitative agreement requires correct treatment Dumitru, Hayashigaki and Jalilian-Marian (2006) for the pT – spectrum with the DHJ model shows the importance of both evolutions: xA (CGC) and xd (DGLAP) shows the dominance of the valence quarks it has been proposed as an alternative explanation pA collisions at the LHC would answer that suppression of RdA due to large-x effects? both initial particles should not be described by a CGC, only the small-x hadron

Some predictions for the LHC

Mueller-Navelet jets in pp Mueller and Navelet (1994) moderate values of x1, x2, typically 0.05 k1, k2 >> QCD  collinear factorization of large rapidity interval Δη ~ 8 pQCD: need ressumation of powers of αS Δη ~ 1 in the partonic cross-section gg → JXJ azimuthal correlation predictions for future measurements at CDF and LHC C.M. and Royon, Sabio-Vera and Schwenssen (2007) NLL-BFKL studies Iancu, Kugeratski and Triantafyllopoulos (2008) geometric scaling predictions for ordered transverse momenta

2-particle correlations in pA inclusive two-particle production at forward rapidities in order to probe small x final state : probes 2-, 4- and 6- point functions one can test more information about the CGC compared to single particle production as k2 decreases, it gets closer to QS and the correlation in azimuthal angle is suppressed some results for azimuthal correlations obtained by solving BK, not from model k2 is varied from 1.5 to 3 GeV C.M. (2007)

Total multiplicity in AA Albacete (2007) predictions including running coupling the extrapolation from RHIC to LHC is driven by the small-x evolution yellow band: uncertainties due to the starting point of the small-x evolution and the initial saturation scale caveat: kT factorization is assumed day-1 measurement ~ 1400 charged particles is a robust prediction, if one gets <1000 or >2500, this rules out the CGC

Conclusions Forward particle production in d+Au collisions - the suppressed production at forward rapidities was predicted - there is a quantitative agreement with CGC predictions  this is often claimed as evidence for the CGC picture Something we learned from RHIC - in d+Au, both p and A should not be described by a CGC - the proton pdf is important, uncertainties should be minimal What observables should be looked at next ? - we only tested limited information about the CGC: 2-point function ~ gluon density - correlations should be investigated, this will be done at RHIC What theorists are looking at now ? - predictions for LHC, A+A collisions, NLO corrections…