Azimuthal correlations of forward dijets in d+Au collisions

1. Azimuthal correlations of forward dijets in d+Au collisions Cyrille Marquet Columbia University & RIKEN BNL Research Center

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 - my calculation: two-particle production at forward rapidities d Au → h1 h2 X I computed C. Marquet, NPA 796 (2007) 41 probes more information about the CGC (up to a 6-point function) Outline 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 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. Measurements at RHIC with d-Au trustable theory difficult when the two particles are separated by a large interval in rapidity a first attempt: Kharzeev, Levin and McLerran (2005) qualitative features : OK, quantitative results : NO it is a simpler problem when the two particles have similar rapidities

4. QCD non-linear evolution: meaning CGC evolution into the saturation regime there the hadron is dressed with many gluons responsible for a large color field which can be treated as a classical field and one can use an effective theory McLerran and Venugopalan (1994)  Gluon saturation and the CGC 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 dilute hadron) BFKL evolution to smaller x (and a dense hadron) dilute/dense separation characterized by the saturation scale Qs(x) weakly-coupled regime

5. - the most common average is the 2-point function- it is often called the dipole scattering amplitude - (at large Nc) it obeys the Balitsky-Kovchegov (BK) equation when only the two-point function enters in the formulation of a cross-section, the so-called kT-factorization is applicable (it is used in many CGC calculations without precaution) The CGC wavefunction - obeys the JIMWLK equation: a functional equation for the small-x evolution of Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner - is used to compute physical observables: the x evolution of the cross-sections is encoded in the x evolution of functions of Wilson lines, describing the scattering of partons off the CGC we will use this formalism to compute forward particle production

6. the suppression of RdA was predicted x2 decreases (y increases) Baier, Kovner and Wiedemann (2003), Kharzeev, Kovchegov and Tuchin (2003) Iancu, Itakura and Triantafyllopoulos (2004), Albacete, Armesto, Kovner, Salgado and Wiedemann, (2004) Single inclusive particle production final state: transverse momentum k and rapidity y and the partons probed in the process have high energies and forward rapidities are needed to probe small values of x involves

7. RdA and forward pion spectrum RdA first comparisons to data: Kharzeev, Kovchegov and Tuchin (2004) Kharzeev, Levin and Nardi (2005) more recent work: from qualitative to quantitative agreement Dumitru, Hayashigaki and Jalilian-Marian (2006) pT - spectrum shows the importance of both evolutions: xA (CGC) and xd (DGLAP) shows the dominance of the valence quarks of the deuteron

8. very low values of xA, typically < 10-4 the CGC cannot be described by a single gluon distribution no kT factorization involves 2-, 4- and 6- point functions Two particles at forward rapidities final state moderate values of xd, typically 0.5 dominant partonic process : |k1|, |k2| >>QCD  collinear factorization of the quark density y1 ~ y2 ~ 3 : both h1 and h2 in forward hemisphere d+Au  h1+h2+X feasible in d-Au collisions at RHIC A

9. to compute the correlators, and include the small-x QCD evolution: - use a Gaussian CGC wavefunction: at large Nc, one can obtain from the BK equation Fujii, Gélis and Venugopalan (2006) the 6-point function is a new result 2- 4- and 6-point functions the scattering off the CGC is expressed through the following correlators of Wilson lines: need more than the 2-point function: no kT factorization same conclusions in heavy-quark production and two-gluon production Blaizot, Gélis and Venugopalan (2004) Jalilian-Marian and Kovchegov (2004)

10. some results for (1/σ) dσ/dΔΦ: k2 is varied from 1.5 to 3 GeV as k2 decreases, it gets closer to QS and the correlation in azimuthal angle is suppressed - in practice I use the McLerran-Venugopalan initial condition at : the initial saturation scale with for these kinematics, the spectrum does not get completely flat MV model +BK evolution - then I evolve the correlators to the value of needed using BK evolution - finally I can compute the cross-section

11. xA xA xp xd RHIC vs LHC the CGC picture would be even better tested: value of xA at LHC << RHIC but at RHIC, one has xh ~ 0.5, and the dominant partonic process is RHIC LHC the value of xdat the LHC is slightly smaller than at RHIC including the gluon-initiated processes and in the calculation will be needed

12. Conclusions and Outlook • I obtained CGC predictions (MV model + BK evolution) for the two-particle spectrum, when both particles are produced at forward rapidities  need to include hadron fragmentation for final results  need comparison with standard NLOQCD calculations - the predictions for the fully differential spectrum are not directly comparable with the data (unless fully differential spectra can be measured)  need integrations over the experimental y and pT ranges future measurements: - at RHIC with the new d+Au run data - at the LHC with p+Pb collisions ?