Multiple parton interactions in heavy-ion collisions Cyrille Marquet Columbia University

High-energy heavy-ion collisions relativistic heavy ion collisions  multiple partonic interactions (MPI) what can be described with QCD at weak coupling (1st principle calculation)? maybe the early stages of the collision space-time picture of heavy-ion collisions 5. Individual hadrons freeze out 4. Hadron gas cooling with expansion 3. Quark Gluon Plasma thermalization, expansion 2. Pre-equilibrium state collision 1. Nuclei (initial condition)  Glasma  CGC MPI at weak coupling  the saturation scale

Outline The saturation scale in the Color Glass Condensate the nuclear wave function at small-x the saturation phenomenon The saturation scale in the Glasma multiple partonic interactions particle production in AA collisions The saturation scale in the quark-gluon plasma medium-induced energy loss and pT broadening weakly-coupled vs strongly-coupled plasma

The saturation scale in the nuclear wave function Color Glass Condensate

The hadron wave function in QCD one can distinguish three regimes S (kT ) << 1 perturbative regime, dilute system of partons: hard QCD (leading-twist approximation) weakly-coupled regime, dense system of partons (gluons) non linear QCD the saturation regime non-perturbative regime: soft QCD relevant for instance for the total cross-section in hadron-hadron collisions relevant for instance for top quark production not relevant to experiments until the mid 90’s with HERA and RHIC: recent gain of interest for saturation physics

The dilute regime hadron = a dilute system of partons transverse view of the hadron hadron = a dilute system of partons 1/kT ~ parton transverse size evolution: as kT increases, the hadron gets more dilute leading-twist regime Dokshitzer Gribov Lipatov Altarelli Parisi the partons interact incoherently for instance, the total cross-section in DIS partonic cross-section parton density higher twist not valid if x is too small when the hadron becomes a dense system of partons

The saturation regime the saturation scale Qs(x) the separation between the dilute and dense regimes is caracterized by a momentum scale: the saturation scale Qs(x) in the saturation regime, higher-twists are important: Balitsky Fadin Kuraev Lipatov hadron = a dense system of partons the saturation regime of QCD: - non-linear yet weakly-coupled - describes the collective behavior of partons in the nuclear wave function evolution: as x decreases, the hadron gets more dense in the saturation regime, the evolution becomes non linear the partons interact coherently

The saturation scale and MPI gluon recombination in the hadronic wave function gluon density per unit area it grows with decreasing x recombination cross-section recombinations important when gluon kinematics the saturation regime: for with occupation numbers are large multiple scattering parton saturation is as important as MPI, to be consistent, both should be included so far I only discussed the nuclear wave function, multiple scatterings occur during the collision, when

The Color Glass Condensate the idea in the CGC is to take into account saturation via strong classical fields the CGC: an effective theory to describe the saturation regime McLerran and Venugopalan (1994) lifetime of the fluctuations in the wave function ~ high-x partons ≡ static sources low-x partons ≡ dynamical fields   the solution gives 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 the evolution of with x is a renormalization group equation classical Yang-Mills equations Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner (1997-2002)

The saturation scale in the Glasma

Collision of two CGCs the initial condition for the time evolution in heavy-ion collisions before the collision: the distributions of ρ contain the small-x evolution of the nuclear wave function r1 r2 after the collision compute the gluon field in the forward light-cone express cross-sections in terms of the field the fields decay, once they are not strong (classical) anymore, a particle description is again appropriate this is where multiple partonic interactions should be included

Particle production in the Glasma single scattering factorization theorems in pQCD answer this question multiple scatterings this is what happens in heavy-ion collisions one needs to reformulate quantum field theories to address the problem Gelis, Lappi and Venugopalan (2006-now) one needs to understand how strong color fields decay into particles the time scale is possible application to pp collisions: a first principle calculation of the underlying event

Total multiplicity in AA predictions including NLO evolution Albacete (2007) the extrapolation from RHIC to LHC is driven by the small-x evolution yellow band: uncertainties due to the starting point of the small-x evolution and the initial saturation scale caveat: kT factorization is assumed, meaning MPI are not treated properly the focus was the correct NLO evolution, however numbers are similar with an exact numerical treatment of MPI (but an approximate treatment of the evolution) Lappi (2008) day-1 measurement ~ 1400 charged particles is a robust prediction, if one gets <1000 or >2500, this rules out the CGC

The saturation scale in the QCD plasma Quark-Gluon Plasma

The heavy quark wave function consider a heavy quark of mass M and energy E the heavy quark wave function at lowest order the energy of the gluon is denoted its transverse momentum is denoted the virtuality of the fluctuations is measured by their lifetime or coherence time short-lived fluctuations are highly virtual the probability of this fluctuation is Lorentz factor of the heavy quark the dead cone effect compared to massless quarks, the fluctuation with are suppressed  absence of radiation in a forward cone Dokshitzer and Kharzeev (2001)

Medium induced gluon radiation Baier, Dokshitzer, Mueller, Peigne, Schiff (1997) multiple scattering of the radiated gluon this is how the virtual gluon in the heavy quark wave function is put on shell it becomes emitted radiation if it picks up enough transverse momentum the accumulated transverse momentum picked up by a gluon of coherence time average pT picked up in each scattering only property of the medium needed mean free path only the fluctuations which pick up enough transverse momentum are freed this discussion is also valid for light quarks the saturation scale of the pQCD plasma 

Heavy quark energy loss the case of infinite extend matter for heavy quarks, the radiated gluons which dominate the energy loss have and this allows to express Qs in terms of T and E/M only  and and the heavy quark energy loss is the relevant fluctuations in the wave function have a smaller energy the case of finite extend matter of length the maximum transverse momentum that gluons can pick-up is the radiated gluons which dominate the energy loss have

Indications from RHIC data light-quark energy loss comparisons between models and data indicate the need for however, for a weakly-coupled pQCD plasma we expect heavy-quark energy loss STAR, PRL 192301 (2007) PHENIX, PRL 172301 (2007) suppression similar to light hadron suppression at high pT

Energy-loss at strong coupling? it is unclear if the perturbative QCD approach can describe the suppression of high-pT particles in Au+Au collisions at RHIC, in particular for heavy-quark energy loss: high-pT electrons from c and b decays indicate similar suppression for light and heavy quarks, while the dead-cone effect in pQCD implies a weaker suppression for heavier quarks  this motivates to think about a strongly-coupled plasma for the N=4 SYM theory, the AdS/CFT correspondence allows to investigate the strong coupling regime limited tools to address the QCD dynamics at strong coupling  the results for SYM may provide insight on strongly-coupled gauge theories, some aspects may be universal main result: one can also identify a momentum scale which controls what fluctuations become emitted radiation

Energy loss and Qs results for energy loss infinite matter or Dominguez, C.M., Mueller, Wu and Xiao (2008) infinite matter or finite matter with QCD at weak coupling SYM at strong coupling heavy-quark energy loss results for energy loss coherence time - same parametric form for the energy loss in pQCD and SYM at strong coupling ! - first estimate of the plasma length dependence of heavy quark energy loss

Conclusions MPI in heavy-ion collisions - are not only important but crucial (HIC probe non-linear QCD) - are at the origin of the interesting phenomena MPI at weak coupling - are characterized by the saturation scale Qs - at RHIC, Qs may be hard enough to justify using weak coupling - CGC & Glasma : first-principle description of the early stages - parton saturation & MPI equally important MPI in the quark-gluon plasma - are responsible for the energy loss and pT-broadening of hard probes - the corresponding saturation scale is related to - at strong coupling, MPI can be also described in terms of a saturation scale