STAR azimuthal correlations of forward di-pions in d+Au collisions in the Color Glass Condensate 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 - I will focus on di-hadron azimuthal correlations a measurement sensitive to possible modifications of the back-to-back emission pattern in a hard process d Au → h 1 h 2 X

Outline Introduction to parton saturation - the hadronic/nuclear wave function at small-x - non-linear parton evolution in QCD - the saturation scale and the unintegrated gluon distribution Di-hadron correlation measurements - at high-p T /central rapidities in p+p collisions : high-x physics - at low-p T /forward rapidities in p+p collisions : small-x physics - at low-p T /forward rapidities in d+Au collisions : saturation physics Comparing d+Au data with CGC predictions - parameters fixed with single particle spectra (Javier’s talk, last meeting) - forward di-pion correlations : monojets are produced in central d+Au

Parton 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

Di-hadron correlation measurements

Di-hadron final-state kinematics final state : forward rapidities probe small x x p ~ 1, x A << 1 azimuthal correlations scanning the wave-function high p T ’s probe large x x p ~ x A < 1 - but are very sensitive to possible non-linear effects (modification of the back-to-back emission pattern in a hard process) - are only a small part of the information contained in

Dijets in standard (linear) pQCD this is supported by Tevatron data in pQCD calculations based on collinear factorization, dijets are back-to-back  transverse view peak narrower with higher p T

Azimuthal correlations in p+p typical measurement in p+p collisions at RHIC: coincidence probability this is probing small-x, but not quite the saturation regime rather one is sensitive to the growth of the gluon distribution  (near side)  (away side) (rad) at RHIC this is done with low-p T pions

Azimuthal correlations in d+Au the evidence for parton saturation: d+Au central  (near side)  (away side) (rad) p+p  transverse view

Comparison with CGC predictions

Forward particle production k T, y transverse momentum k T, rapidity y > 0 forward rapidities probe small values of x 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 a Color Glass Condensate the cross-section: single gluon production probes only the (unintegrated) gluon distribution

NLO-BK description of d+Au data this fixes the two parameters of the theory: - the value of x at which one starts to trust (and therefore use) the CGC description - and the saturation scale at that value of x in very forward particle production in p+p collisions at RHIC (where NLO DGLAP fails), using this formalism to describe the (small-x) proton also works Albacete and C.M. (2010) Betemps, Goncalves, de Santana Amaral (2009) the shapes and normalizations are well reproduced, except the  0 normalization the speed of the x evolution and of the p T decrease are predicted

Forward di-hadron production the CGC cannot be described by a single gluon distribution involves 2-, 4- and 6- point functions no k T factorization is sensitive to multi-parton distributions, and not only to the gluon distribution the saturation regime is better probed compared to single particle production a good test for the theory C. M. (2007)

The two-particle spectrum collinear factorization of quark density in deuteron Fourier transform k ┴ and q ┴ into transverse coordinates pQCD q → qg wavefunction b: quark in the amplitude x: gluon in the amplitude b’: quark in the conj. amplitude x’: gluon in the conj. amplitude interaction with hadron 2 / CGC n-point functions that resums the powers of g S A and the powers of α S ln(1/x A ) computed with JIMWLK evolution at NLO (in the large-Nc limit), and MV initial conditionsno parameters

Monojets in central d+Au in central collisions where Qs is the biggest there is a very good agreement of the saturation predictions with STAR data suppressed away-side peak an offset is needed to account for the background the focus is on the away-side peak where non-linearities have the biggest effect to calculate the near-side peak, one needs di-pion fragmentation functions standard (DGLAP-like) QCD calculations cannot reproduce this

The centrality dependence it can be estimated by modifying the initial condition for NLO-BK evolution for a given impact parameter, the initial saturation scale used is no data yet, but hopefully soon peripheral collisions are like p+p collisions the away-side peak is reappearing when decreasing the centrality

with higher p T, one goes away from the saturation regime the away-side peak is restored at higher p T The p T dependence so far, only p+p data have been shown

Conclusions New d+Au RHIC data show evidence for parton saturation Single particle production at forward rapidities - the suppressed production at forward rapidities was predicted - there is a good agreement with NLO-BK calculations Two-particle correlations at forward rapidities - probe the theory deeper than single particle measurements - mono-jets were predicted and are now seen in central d+Au collisions - first theory(CGC)/data comparison successful, more coming

Back-up slides

The non-linear QCD evolution this is a leading-order equation in which the coupling doesn’t run BK equation in coordinate space the unintegrated gluon distribution Balitsky-Kovchegov x evolution BK evolution at NLO has been calculated one should obtain from the evolution equation 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, saturation models are used for (with a few parameters adjusted to reproduce the data) before now Balitsky-Chirilli (2008)

BK evolution at NLO running coupling (RC) corrections to the BK equation taken into account by the substitution Kovchegov Weigert Balitsky RC corrections represent most of the NLO contribution (2007) the begining of saturation phenomenology at NLO first numerical solution first phenomenological implementation Albacete and Kovchegov (2007) to successfully describe the proton structure function F 2 at small x Albacete, Armesto, Milhano and Salgado (2009)

2- 4- and 6-point functions the scattering off the CGC is expressed through the following correlators of Wilson lines: if the gluon is emitted before the interaction, four partons scatter off the CGC if the gluon is emitted after the interaction, only the quarks interact with the CGC interference terms, the gluon interacts in the amplitude only (or c.c. amplitude only) Blaizot, Gélis and Venugopalan (2004) need more than the 2-point function: no k T factorization same conclusions in sea quark production and two-gluon production using Fierz identities that relate W A and W F, we recover the z → 0 (soft gluon) limit Jalilian-Marian and Kovchegov (2004) Baier, Kovner, Nardi and Wiedemann (2005) we will now include the x A evolution

Performing the CGC average characterizes the density of color charges along the projectile’s path with this model for the CGC wavefunction squared, it is possible to compute n-point functions a Gaussian distribution of color sources is the two-dimensional massless propagator applying Wick’s theorem when expandingin powers of α and averaging, all the field correlators can be expressed in terms of the difficulty is to deal with the color structure Fujii, Gelis and Venugopalan (2006)

MV model and BK evolution in the large-Nc limit is related to in the following way With this model for the CGC wavefunction squared, it is possible to compute the n-point functions: Blaizot, Gélis and Venugopalan (2004) and obeys the BK equation: we will use the MV initial condition: McLerran and Venugopalan (1994) withthe initial saturation scale →