STAR azimuthal correlations of forward di-pions in d+Au collisions in the Color Glass Condensate

1. STAR azimuthal correlations of forward di-pions ind+Au collisions in theColor Glass Condensate 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 - I will focus on di-hadron azimuthal correlations a 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 • 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-pT/central rapidities in p+p collisions : high-x physics - at low-pT/forward rapidities in p+p collisions : small-x physics - at low-pT/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

4. 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 Parton 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

5. Di-hadron correlation measurements

6. Di-hadron final-state kinematics final state : • scanning the wave-function xp ~ 1, xA << 1 xp ~ xA < 1 forward rapidities probe small x high pT’s probe large x • azimuthal correlations - are only a small part of the information contained in - but are very sensitive to possible non-linear effects (modification of the back-to-back emission pattern in a hard process)

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

8. Df=0 (near side) Df=p (away side) (rad) Azimuthal correlations in p+p typical measurement in p+p collisions at RHIC: coincidence probability at RHIC this is done with low-pT pions this is probing small-x, but not quite the saturation regime rather one is sensitive to the growth of the gluon distribution

9. Df=0 (near side) Df=p (away side) (rad) ~p Azimuthal correlations in d+Au the evidence for parton saturation: p+p d+Au central transverse view

10. Comparison with CGC predictions

11. 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 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:

12. NLO-BK description of d+Au data Albacete and C.M. (2010) the shapes and normalizations are well reproduced, except the 0 normalization the speed of the x evolution and of the pT decrease are predicted 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 Betemps, Goncalves, de Santana Amaral (2009)

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

14. Fourier transform k┴ andq┴ into transverse coordinates collinear factorization of quark density in deuteron pQCD q→ qg wavefunction interaction with hadron 2 / CGC n-point functions that resums the powers ofgS A and the powers ofαS ln(1/xA) computed with JIMWLK evolution at NLO (in the large-Nc limit), and MV initial conditions no parameters The two-particle spectrum b: quark in the amplitude x: gluon in the amplitude b’: quark in the conj. amplitude x’: gluon in the conj. amplitude

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

16. 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 peripheral collisions are like p+p collisions the away-side peak is reappearing when decreasing the centrality no data yet, but hopefully soon

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

18. 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

19. Back-up slides

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

21. the begining of saturation phenomenology at NLO first numerical solution Albacete and Kovchegov (2007) first phenomenological implementation Albacete, Armesto, Milhano and Salgado (2009) to successfully describe the proton structure function F2 at small x BK evolution at NLO • running coupling (RC) corrections to the BK equation taken into account by the substitution Kovchegov Weigert (2007) Balitsky RC corrections represent most of the NLO contribution

22. need more than the 2-point function: no kT factorization same conclusions in sea quark production and two-gluon production Blaizot, Gélis and Venugopalan (2004) Jalilian-Marian and Kovchegov (2004) using Fierz identities that relate WA and WF, we recover the z→ 0 (soft gluon) limit Baier, Kovner, Nardi and Wiedemann (2005) we will now include the xA evolution 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)

23. applying Wick’s theorem Fujii, Gelis and Venugopalan (2006) when expanding in powers of α and averaging, all the field correlators can be expressed in terms of is the two-dimensional massless propagator the difficulty is to deal with the color structure Performing the CGC average • a Gaussian distribution of color sources 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

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