1. Forward particle production in proton-nucleus collisions Cyrille Marquet Institut de Physique Théorique – CEA/Saclay C. Marquet, Nucl. Phys. B705 (2005) 319 C. Marquet, Nucl. Phys. A796 (2007) 41 C. Marquet and J. Albacete, in preparation + work in progress

2. The hadron wavefunction in QCD non-perturbative regime: soft QCD relevant for instance for the total cross-section in hadron-hadron collisions perturbative regime, dilute system of partons: hard QCD (leading-twist approximation) relevant for instance for top quark production Three types of states:  S (k T ) << 1 weakly-coupled regime, effective coupling constant: dense system of partons mainly gluons (small-x gluons): the saturation regime of QCD not relevant for experiments until the mid 90’s with HERA and RHIC: recent gain of interest for saturation physics

3. The dilute regime The dilute (leading-twist) regime: hadron =a dilute system of partons which interact incoherently for instance, the total cross-section in DIS partonic cross-sectionparton density leading-twist regime 1/k T ~ parton transverse size as k T increases, the hadron gets more dilute Dokshitzer Gribov Lipatov Altarelli Parisi transverse view of the hadron

4. The saturation regime The saturation regime of QCD: the weakly-coupled regime that describes the collective behavior of quarks and gluons inside a high-energy hadron The saturation regime: hadron =a dense system of partons, responsible for collective phenomena the separation between the dilute and dense regimes is caracterized by a momentum scale: the saturation scale Q s (x) Balitsky Fadin Kuraev Lipatov as x decreases, the hadron gets more dense

5. deep inelastic scattering at small x Bj : particle production at forward rapidities y : When is saturation relevant ? In processes that are sensitive to the small-x part of the hadron wavefunction in DIS small x corresponds to high energy saturation relevant for inclusive, diffractive, exclusive events p T, y in particle production, small x corresponds to high energy and forward rapidities saturation relevant for the production of jets, pions, heavy flavours, dileptons at HERA, x Bj ~10 -4 for Q² = 10 GeV² at RHIC, x 2 ~10 -4 for p T ² = 10 GeV²

6. Geometric scaling in DIS geometric scaling can be easily understood as a consequence of large parton densities the hadron in the (Q², x) plane:  0.3 Stasto, Golec-Biernat and Kwiecinski (2001) x < 10 -2 lines parallel to the saturation line are lines of constant densities along which scattering is constant

7. Contents The Color Glass Condensate formalism - effective description of the small-x gluons - the JIMWLK evolution equation - scattering off the CGC and n-point functions Single particle production at forward rapidities - probes the two-point functions - inclusive spectra and modification factors at RHIC - from qualitative to quantitative CGC description Two-particle production at forward rapidities - probes more information about the CGC - comparisons with recent RHIC data

8. The CGC formalism

9. 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

10. 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

11. 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

12. 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 Balitsky (1996), Kovchegov (1999)

13. 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 the NLO-CGC era 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)

14. Single particle production

15. Forward particle production k T, y transverse momentum k T, rapidity y > 0 the large-x hadron should be described by standard leading-twist parton distributions the small-x hadron/nucleus should be described by all-twist parton distributions values of x probed in the process: the cross-section: single gluon production probes only the unintegrated gluon distribution (2-point function) Kovner and Wiedemann (2001), Kovchegov and Tuchin (2002), Dumitru and McLerran (2002) Blaizot, Gélis and Venugopalan (2004), Marquet (2005), Gélis and Mehtar-Tani (2006) if the emitted particle is a (valence) quark, involves if the emitted particle is a gluon, involves

16. The suppression of R dA 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 we learned if forward rapidity data are included in npdfs fit, the resulting gluon distribution is over suppressed forward rapidities are needed to see the suppression

17. R dA and forward pion spectrum first comparisons to data: Kharzeev, Kovchegov and Tuchin (2004) Kharzeev, Levin and Nardi (2005) Dumitru, Hayashigaki and Jalilian-Marian (2006) more recent work: from qualitative to quantitative agreement shows the importance of both evolutions: x A (CGC) and x d (DGLAP) shows the dominance of the valence quarks R dA p T - spectrum

18. New NLO-BK description 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 the CGC to describe the (small-x) proton also works Albacete and C.M, in preparation 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 now predicted

19. Two particles at forward rapidities

20. 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 the modification factor were studied - my calculation: two-particle production at forward rapidities - 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 next d-Au run d Au → h 1 h 2 X I computed C. Marquet, NPA 796 (2007) 41 (probes up to a 6-point function)

21. Central/forward correlations first measurements of azinuthal correlations signal STAR, PRL 97 (2006) 152302 PHENIX, PRL 96 (2006) 222301 coincidence probability difficult to make robust predictions - the fragmentation of low energy particles is not well known (fragmentation functions are not constrained at low z) - the values of x A are at the limit of the CGC applicability (trigger at central rapidity  high x) a measurement sensitive to possible modifications of the back-to-back emission pattern in a hard process

22. moderate values of x d, typically 0.5 dominant partonic process : Two particles at forward rapidities feasible in d-Au collisions at RHIC (or p-Pb at LHC, but then x p ~ 0.1, and or important) |k 1 |, |k 2 | >>  QCD  collinear factorization of the quark density h+T  h 1 +h 2 +X y 1 ~ y 2 ~ 3 : both h 1 and h 2 in forward hemisphere very low values of x A, typically < 10 -4 need CGC resummation of large logarithms α S ln(1/x A ) ~ 1 and large g S A ~ 1 the CGC cannot be described by a single gluon distribution

23. 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 comp. conj. amplitude x’: gluon in the comp. 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 ) Nikolaev, Schäfer, Zakharov and Zoller (2005) I obtain a formula similar to that of

24. 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

25. 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)

26. 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 →

27. Final expression quark density in dilute hadron unintegrated gluon density of CGC (Fourier transform of 2-point function) the final expression for the cross-section can be decomposed into three pieces: modified q → qg vertex due to multiple scattering : pQCD q → qg wavefunction in momentum space with zero quark masses, I reduces to with goal: study the CGC evolution  try to avoid the competition between the x d (DGLAP) evolution ofand the small x A evolution of and

28. Forward/forward correlations the focus is on the away-side peak where non-linearities have the biggest effect p T dependence the away-side peak is restored at higher p T typical coincidence probability to calculate the near-side peak, one needs di-pion fragmentation functions suppressed away-side peak

29. Centrality dependence comparison with data for central collisions there is a very good agreement with STAR data (an offset is needed to account for the background) the centrality dependence this shows the qualitative behavior of the correlation for a given impact parameter, the initial saturation scale used is

30. Conclusions Forward particle production in d+Au collisions - the suppressed production at forward rapidities was predicted - there is a good agreement with CGC calculations - now that NLO-BK is known, one should stop using models Two-particle correlations at forward rapidities - probe the theory deeper than single particle measurements - forward/forward correlations probe x as small as in the R dA measurement - jet quenching seen in central d+Au collisions - first theory(CGC)/data comparison successful, more coming