Forward particle production in d+Au collisions in the CGC framework

1. Forward particle productionin d+Au collisionsin the CGC framework Cyrille Marquet Institut de Physique Théorique, CEA/Saclay

2. - but single particle production probes limited information about the CGC (only the 2-point function) to strengthen the evidence, we need to studymore complex observables to be measured with the new d+Au run - the experimental focus has been on IdA a correlation measurement sensitive to possible modificationsof the back-to-back emission pattern in a hard process d Au → h1 h2 X Motivation - after the first d+Au run at RHIC, there was a lot of new results on single inclusive particle production at forward rapidities d Au → h X the spectrum and the modification factor were studied y increases the suppressed production (RdA < 1) was predicted in the Color Glass Condensate picture of the high-energy nucleus

3. 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 parametrizationsof the unintegrated gluon distribution RdA 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 IdA some results of CGC calculations

4. Saturation and theColor Glass Condensate

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

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

7. Observables in the CGC framework, any cross-section is determined by colorless combinations of Wilson lines , averaged over the CGC wave function the energy evolution of cross-sections is encoded in the evolution of The small-x evolution is mainly non-perturbative, but its evolution is known • the JIMWLK equation Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner the evolution of with x is a renormalization-group equation the solution gives 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

8. the 2-point function or dipole amplitude • more complicated correlators for less inclusive observables the dipole scattering amplitude: x: quark space transverse coordinate y: antiquark space transverse coordinate when only the two-point function enters in the formulation of a cross-section, the so-called kT-factorization is applicable this is the most common average for instance it determines deep inelastic scattering it is used in many CGC calculations without precaution Scattering off the CGC • this is described by Wilson lines scattering of a quark: dependence kept implicit in the following

9. 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 The Balitsky-Kovchegov equation • the BK equation the BK equation is a closed equation for obtained by assuming robust only for impact-parameter independent solutions r = dipole size

10. Single particle productionat forward rapidities

11. 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)

12. the DHJ version Dumitru, Hayashigaki and Jalilian-Marian (2006) KKT modified to better account for geometric scaling violations • the BUW version Boer, Utermann and Wessels (2008) KKT modified to feature exact geometric scaling in practice is always replaced by before the Fourier transformation 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

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

14. both initial particles should not be described by a CGC, only the small-x hadron • suppression of RdA due to large-x effects? it has been proposed as an alternative explanation pA collisions at the LHC would answer that 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

15. 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 Running coupling corrections • running coupling corrections to the BK equation taken into account by the substitution Kovchegov Weigert Balitsky

16. Probing small x withtwo-particle correlations

17. a large rapidity separation between the two particles ? this does not probe the nuclear wavefunction at small-x xp ~ 1, xA ~ 1 BFKL evolution ? - 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 this increases xA a lot (~ a factor 20) probes initial condition, not evolution Final-state kinematics final state : • the best situation two hadrons close in rapidity both in the same forward direction at forward rapidities in order to probe small x xp ~ 1, xA << 1 probes 2-, 4- and 6- point functions C. Marquet, NPA 796 (2007) 41 one can test more information about the CGC compared to single particle production

18. transverse momentum range includes the region first measurments for x > 0.01 problems to calculate the pp baseline • need to do forward/forward correlation RHIC d+Au measurements • central/forward correlation PHENIX, PRL 96 (2006) 222301 STAR, PRL 97 (2006) 152302 PHENIX STAR correlation function coincidence probability conditional yield trigger at forward rapidity : low-x signal trigger at central rapidity : high-x

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

20. 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 - onlyforward/forward correlations will probe x as small as in the RdA measurement - CGC predictions almost ready