Forward particle production in d+Au collisions in the CGC framework Cyrille Marquet Institut de Physique Théorique, CEA/Saclay

the spectrum and Motivation - after the first d+Au run at RHIC, there was a lot of new results on single inclusive particle production at forward rapidities the suppressed production (R dA < 1) was predicted in the Color Glass Condensate picture of the high-energy nucleus d Au → h X y increases the modification factor were studied - but single particle production probes limited information about the CGC (only the 2-point function) to strengthen the evidence, we need to study more complex observables to be measured with the new d+Au run - the experimental focus has been on I dA a correlation measurement sensitive to possible modifications of the back-to-back emission pattern in a hard process d Au → h 1 h 2 X

Outline Saturation and the Color Glass Condensate the unintegrated gluon distribution and the BK equation multi-parton distributions in the nuclear wave function Single particle production at forward rapidities different parametrizations of the unintegrated gluon distribution R dA and the success of the CGC running coupling corrections to the BK equation Probing small x with two-particle correlations the ideal final-state kinematics correlations in azimuthal angle and I dA some results of CGC calculations

Saturation and the Color Glass Condensate

Gluon saturation x : parton longitudinal momentum fraction k T : parton transverse momentum the distribution of partons as a function of x and k T : dilute/dense separation characterized by the saturation scale Q s (x) QCD linear evolutions: DGLAP evolution to larger k T (and a more dilute hadron) BFKL evolution to smaller x (and denser hadron) QCD non-linear evolution:meaning recombination cross-section gluon density per unit area it grows with decreasing x recombinations important when the saturation regime: for with this regime is non-linear yet weakly coupled

The Color Glass Condensate the idea of the CGC is to describe the saturation regime with strong classical fields McLerran and Venugopalan (1994) lifetime of the fluctuations in the wave function ~ high-x partons ≡ static sources low-x partons ≡ dynamical fields  small x gluons as radiation field valence partons as static random color source separation between the long-lived high-x partons and the short-lived low-x gluons CGC wave function classical Yang-Mills equations an effective theory to describe the saturation regime  from, one can obtain the unintegrated gluon distribution, as well as any n-parton distributions in the A + =0 gauge

The small-x evolution the solution gives the evolution of with x is a renormalization-group equation for a given value of k², the saturation regime in a nuclear wave function extends to a higher value of x compared to a hadronic wave function the JIMWLK equation is mainly non-perturbative, but its evolution is known Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner the energy evolution of cross-sections is encoded in the evolution of in the CGC framework, any cross-section is determined by colorless combinations of Wilson lines, averaged over the CGC wave function Observables

Scattering off the CGC scattering of a quark: this is described by Wilson lines dependence kept implicit in the following 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 it is used in many CGC calculations without precaution when only the two-point function enters in the formulation of a cross-section, the so-called k T -factorization is applicable more complicated correlators for less inclusive observables

The Balitsky-Kovchegov equation 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  modeling the unintegrated gluon distribution the numerical solution of the BK equation is not useful for phenomenology, because this is a leading-order calculation instead, CGC-inspired parameterizations are used for, with a few parameters adjusted to reproduce the data

Single particle production at forward rapidities

Forward particle production k T, y transverse momentum k T, rapidity y > 0 forward rapidities probe small values of x 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 values of x probed in the process: the cross-section: single gluon production probes only the unintegrated gluon distribution (2-point function)

The KKT parametrization build to be used as an unintegrated gluon distribution the idea is to play with the saturation exponent Kovchegov, Kharzeev and Tuchin (2004) 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 practiceis always replaced by before the Fourier transformation KKT modified to better account for geometric scaling violations

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

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

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

Probing small x with two-particle correlations

Final-state kinematics the best situation probes 2-, 4- and 6- point functions final state : one can test more information about the CGC compared to single particle production at forward rapidities in order to probe small x two hadrons close in rapidity both in the same forward direction x p ~ 1, x A << 1 x p ~ 1, x A ~ 1 BFKL evolution ? this increases x A a lot (~ a factor 20) probes initial condition, not evolution a large rapidity separation between the two particles ? this does not probe the nuclear wavefunction at small-x - doesn’t probe large parton densities - as much effect in pp as in d+Au - we know from Tevatron that for  y < 5 there is no effect C. Marquet, NPA 796 (2007) 41

RHIC d+Au measurements PHENIXSTAR central/forward correlation trigger at central rapidity : high-x correlation functioncoincidence probability conditional yield signal STAR, PRL 97 (2006) PHENIX, PRL 96 (2006) trigger at forward rapidity : low-x transverse momentum range includes the region need to do forward/forward correlation first measurments for x > 0.01 problems to calculate the pp baseline

Status of CGC calculation the d+Au part results at parton level ready but problems with pdf’s and fragmentation functions at low p T (meaning p T < 1.5 GeV, which includes most experimental bins) the p+p part needed for I dA to be computed in NLOQCD framework potential problems for low p T bins results at hadron level ready at high-p T not yet ready to put numbers on this plot, but hopefully soon

Conclusions Forward particle production in d+Au collisions - the suppressed production at forward rapidities was predicted - there is a good agreement with CGC calculations What we learned from single particle production - both d and Au should not be described by a CGC, the deuteron pdf is important - this only tests limited information about the CGC: 2-point function ~ gluon density - now that NLO-BK is known, one should stop using models for - if the suppression is due to (small)large-x effects, there will be (more)less suppression at the LHC Two-particle correlations - probe more than the 2-point function - no large rapidity interval is needed between the two particles, in fact this wouldn’t probe large parton densities - only forward/forward correlations will probe x as small as in the R dA measurement - CGC predictions almost ready