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Forward particle production in proton-nucleus collisions

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. perturbative regime,

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Forward particle production in proton-nucleus collisions

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

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

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

  5. When is saturation relevant ? In processes that are sensitive to the small-x part of the hadron wavefunction • deep inelastic scattering at small xBj : • particle production at forward rapidities y : at HERA, xBj ~10-4 for Q² = 10 GeV² in DIS small xcorresponds to high energy saturation relevant for inclusive, diffractive, exclusive events at RHIC, x2 ~10-4 for pT ² = 10 GeV² pT , y in particle production, small xcorresponds to high energy and forward rapidities saturation relevant for the production of jets, pions, heavy flavours, dileptons

  6. Stasto, Golec-Biernat and Kwiecinski (2001) x < 10-2  0.3 Geometric scaling in DIS geometric scaling can be easily understood as a consequence of large parton densities the hadron in the (Q², x) plane: 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. 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 ~ 

  10. 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

  11. 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

  12. 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 Balitsky (1996), Kovchegov (1999) the BK equation is a closed equation for obtained by assuming robust only for impact-parameter independent solutions r = dipole size

  13. the begining of the NLO-CGC era 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

  14. Single particle production

  15. if the emitted particle is a (valence) quark, involves if the emitted particle is a gluon, involves Kovner and Wiedemann (2001), Kovchegov and Tuchin (2002), Dumitru and McLerran (2002) Blaizot, Gélis and Venugopalan (2004), Marquet (2005), Gélis and Mehtar-Tani (2006) Forward particle production 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 all-twist parton distributions the cross-section: single gluon production probes only the unintegrated gluon distribution (2-point function)

  16. what we learned forward rapidities are needed to see the suppression xA decreases (y increases) if forward rapidity data are included in npdfs fit, the resulting gluon distribution is over suppressed The suppression of RdA • the suppression of RdA was predicted in the absence of nuclear effects, meaning if the gluons in the nucleus interact incoherently like in A protons

  17. 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

  18. New NLO-BK description Albacete and C.M, in preparation the shapes and normalizations are well reproduced, except the 0 normalization the speed of the x evolution and of the pT decrease are now 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 the CGC to describe the (small-x) proton also works Betemps, Goncalves, de Santana Amaral (2009)

  19. Two particles at forward rapidities

  20. - 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 next 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 up to a 6-point function) 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 the suppressed production (RdA < 1) was predicted in the Color Glass Condensate picture of the high-energy nucleus

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

  22. the CGC cannot be described by a single gluon distribution very low values of xA, typically < 10-4 need CGC resummation of large logarithmsαS ln(1/xA) ~ 1and large gS A ~ 1 Two particles at forward rapidities 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 h+T  h1+h2+X feasible in d-Au collisions at RHIC (or p-Pb at LHC, but then xp ~ 0.1, and or important)

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

  24. 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)

  25. 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

  26. 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

  27. modifiedq → qgvertex 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 xd (DGLAP) evolution of and the small xA evolution of and Final expression the final expression for the cross-section can be decomposed into three pieces: quark density in dilute hadron unintegrated gluon density of CGC (Fourier transform of 2-point function)

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

  29. the centrality dependence for a given impact parameter, the initial saturation scale used is this shows the qualitative behavior of the correlation 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)

  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 RdA measurement - jet quenching seen in central d+Au collisions - first theory(CGC)/data comparison successful, more coming

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