Event-plane decorrelation of photons produced in the early stage of heavy-ion collisions
Charles Gale, Jean-François Paquet, Björn Schenke, Chun Shen
EEvent-plane decorrelation of photons produced in theearly stage of heavy-ion collisions
Charles Gale, a Jean-François Paquet, b, ∗ Björn Schenke c and Chun Shen d a Department of Physics, 3600 University Street, Montréal, QC, H3A 2T8, Canada b Department of Physics, Duke University, Durham, NC 27708, USA c Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USA d Department of Physics and Astronomy, Wayne State University, Detroit, MI 48201, USARIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973, USA
E-mail: [email protected], [email protected],[email protected], [email protected]
We study photon production in the early stage of heavy-ion collisions using a multistage modelcombining IP-Glasma, KøMPøST and relativistic hydrodynamics. We discuss the small mo-mentum anisotropy of these photons, highlighting the role of the photon-hadron event-planedecorrelation. We comment that this singular characteristic of early photons could be used toprovide dynamical information on the complex pre-hydrodynamics phase of heavy-ion collisions.
HardProbes20201-6 June 2020Austin, Texas ∗ Speaker © Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/ a r X i v : . [ nu c l - t h ] S e p vent-plane decorrelation of early photons in heavy-ion collisions Jean-François Paquet
Introduction
Relativistic collisions of heavy nuclei produce a short-lived medium of deconfinednuclear matter. Shortly after the impact of the nuclei, the local energy density of this deconfinedmedium can reach hundreds of GeV/fm . An illustration of such an energy density profile is shownin Fig. 1, as a function of time and a direction transverse to the collision axis. At high densities,the deconfined medium takes the form of a complex excited state of strongly-interacting coloureddegrees of freedom. This matter expands rapidly in the vacuum of the collider’s beam pipe, passingthrough the QCD crossover as it becomes more dilute and finally reconfining into hadrons. −1 (fm) −7.5−5.0−2.50.02.55.07.5 T r a n s v e r s e d i r e c t i o n ( f m ) DeconfinedQCDmatter QCDcrossover Hadronicmatter E n e r g y d e n s i t y ( G e V / f m ) Figure 1:
Illustration of the energy density in the transverse plane, as a function of time. This example is fora single Au-Au collision at √ s NN = 200 GeV. The shaded grey area labeled “QCD crossover” correspondsto energy densities between 0.234 and 1.77 GeV/fm (temperatures 150–200 MeV for an equilibrium QCDplasma). The evolution of the medium produced in heavy-ion collisions is governed by the strong nuclearinteraction. Yet a large number of degrees of freedom produced in the collisions carry an electriccharge, leading to continuous photon emission throughout the collision. In this work, we discussphotons emitted in the early stages of the plasma. We focus on a distinguishing feature of theirmomentum distribution: the decorrelation of their event plane with that of soft hadrons.
Spacetime description of heavy-ion collisions
It is likely that the deconfined and crossover phaseof the collision — the darker shades in Fig. 1 ( τ (cid:46) − fm) — do not admit a general quasi-particle picture, a consequence of the strongly-interacting nature of the medium. More commonly,the deconfined medium is described in terms of macroscopic quantities, such as the energy density(depicted in Fig. 1) and the flow velocity profile of the medium. For times larger than O (1 fm),there is good evidence that the spacetime evolution of the energy density and fluid velocity can bedescribed with relativistic hydrodynamics [1]. This hydrodynamics description cannot be extendedto arbitrarily early times, and the “pre-hydrodynamics” stage of heavy-ion collisions contains richphysics that must be modelled independently from hydrodynamics.In this work, we model the “pre-hydrodynamics” stage with IP-Glasma [2, 3] and KøMPøST [4,5]. We first use IP-Glasma to describe the incoming nuclei using the Color-Glass-Condensate2 vent-plane decorrelation of early photons in heavy-ion collisions Jean-François Paqueteffective theory and subsequently evolve the deconfined matter for up to τ = 0 . fm by solvingthe Yang-Mills equations. The energy-momentum tensor of IP-Glasma at τ = 0 . fm is thenused to initialize the KøMPøST framework, which evolves it up to τ = 0 . fm. In KøMPøST,the energy-momentum tensor is divided into a uniform background — defined locally from thecausal circle around this point — and linearised fluctuations atop this background. The evolutionof this background follows a simple scaling relation [4, 5, 6]. Fluctuations are propagated withresponse functions that have been calculated in QCD kinetic theory [4, 5]. At τ = 0 . fm, theenergy-momentum tensor from KøMPøST is used to initialize the relativistic viscous hydrodynamicsimulation, which includes both shear and bulk viscosities, as described in Ref. [7]. The energydensity profile from Fig. 1 is the result of the KøMPøST and hydrodynamic evolution. Evaluating photon emission
Photon emission at lower energy densities — the lighter shades inFig. 1 — is relatively well understood, since the medium takes the form of an interacting gas ofhadrons. A number of hadronic channels lead to the production of photons, many of which havebeen calculated using hadronic effective theory (e.g. Ref. [8]). A source of uncertainty originatesfrom the exact mapping between the energy-momentum tensor of hydrodynamics and the hadronicmomentum distribution, an uncertainty that propagates to the calculation of photon emission in theform of “viscous corrections” to the thermal photon emission rates. In this work, we use the samehadronic photon emission rates and the same viscous correction as in Ref. [9].Photon emission at higher energy densities is more challenging to calculate because of thestrongly-interacting nature of the deconfined medium. Intuition originates in part from our under-standing of weakly-coupled deconfined nuclear matter. In a weakly-coupled quark-gluon plasma,photons are produced through elementary processes such as Compton scattering ( qg → qγ ) andquark-antiquark annihilation ( q ¯ q → gγ ), along with more complex channels through bremsstrahlungand inelastic pair annihilation [10]. These channels can be used to calculate photon emission ratesfor deconfined nuclear plasma. Strictly speaking, these rates are only valid for energy densitiesasymptotically higher than those encountered in heavy-ion collisions, where the strong couplingconstant g s is small. Moreover these rates are only known for plasmas relatively close to localthermal equilibrium. The challenge presented by the higher density regions of Fig. 1 is twofold:(i) the higher density regions, while more weakly coupled, also tend to deviate more significantlyfrom thermal equilibrium; while (ii) the intermediate density regions are thought to be closer toequilibrium, but are also more strongly coupled. In this work, we follow previous studies such asRef. [9]: we calculate photon production in the deconfined phase with photon emission rates cal-culated in the weakly-coupled limit and then extrapolated to g s = 2 . Corrections due to deviationsfrom thermal equilibrium are also treated as in Ref [9], for both shear and bulk viscosity. We usethe exact same approach to compute photons in the KøMPøST and hydrodynamic phases. Othersources of photons, such as prompt photons, are left out at the moment. Early photon emission and photon-hadron correlations
The spectra of photons produced atdifferent time intervals in KøMPøST and the hydrodynamics is shown in Fig. 2(a). The correspond-ing photon momentum anisotropy is shown in Fig. 2(b). As a general feature, photons producedin the earlier stage of the collision contribute predominantly at higher p T . They also have a smallmomentum anisotropy. Recall that the momentum anisotropy of hadrons originates from the devel-3 vent-plane decorrelation of early photons in heavy-ion collisions Jean-François Paquet p T (GeV) −6 −4 −2 / ( p T ) d N / dp T ( G e V ) Au-Au s NN = 200 GeV
20 40 % KøMPøST ( fm)Hydro ( fm)Hydro ( fm)Hydro ( > 2 fm) (a) p T (GeV) v { S P } Au-Au s NN = 200 GeV
20 40 % KøMPøST ( fm)Hydro ( fm)Hydro ( fm)Hydro ( > 2 fm) (b)
Figure 2: (a) Spectra and (b) v { SP } (Eq. 2) of photons produced at different time intervals. opment of an anisotropic flow velocity, itself a consequence of an asymmetry in the spatial energydeposition after the nuclei’s impact. This flow velocity anisotropy takes time to build; we see onFig. 2(b) that photons emitted earlier in the collision do have a smaller momentum anisotropy. p T ( GeV ) c o s ( ( ( p T ) h )) Au-Au s NN = 200 GeV
20 40 % KøMPøST ( fm)Hydro ( fm)Hydro ( fm)Hydro ( > 2 fm)
Figure 3:
Correlation between the hadron and photonevent plane, as quantified by cos(2(Ψ γ − Ψ h )) . The anisotropy in the flow velocity duringthe pre-hydrodynamics phase is considerablysmaller than that developed in the hydrodynam-ics phase. Moreover the angular distribution ofthe flow velocity in the IP-Glasma phase is ef-fectively uncorrelated with that developed in thehydrodynamic phase. This can be quantified bycomparing the event plane angle of soft hadronswith that of photons produced at different stagesof the collision. Recall that the measured pho-ton anisotropy is a photon-hadron correlationgiven by v n { SP } ( p γT ) = (cid:104) v γn ( p γT ) v hn cos( n (Ψ γn ( p γT ) − Ψ hn )) (cid:105) (cid:112) (cid:104) ( v hn ) (cid:105) (1)with v n ( p T ) e in Ψ n ( p T ) = (cid:20)(cid:90) dydφ (cid:18) p d Nd p (cid:19) e inφ (cid:21) (cid:46) (cid:20)(cid:90) dydφ (cid:18) p d Nd p (cid:19)(cid:21) (2)where p T is the transverse momentum, y the momentum rapidity and φ the transverse azimuthalangle, and p d N h/γ /d p is the momentum distribution of photons or hadrons for a single collisionevent. The hadronic v hn and Ψ hn are integrated over p T . The event plane Ψ h/γn of photons or hadronsenters in v n { SP } through cos( n (Ψ γn − Ψ hn )) . This factor is plotted in Fig. 3 for photons emitted atdifferent times in the medium. At higher p T , where photons emitted at early times tend to dominate,the value of cos(2(Ψ γ − Ψ h )) is around . . This decorrelation of the photon and hadron eventplanes, combined with the overall small v of these early stage photons, results in the very small v { SP } seen in Fig. 2(b). 4 vent-plane decorrelation of early photons in heavy-ion collisions Jean-François Paquet
Summary
Evaluating photon emission from the early stages of heavy-ion collisions is currently adeveloping field of inquiry. While uncertainties are still significant, there is accumulating evidencethat photons produced at the earlier stage of heavy-ion collisions have a small v and an eventplane that is decorrelated with that of soft hadrons. Unless a mechanism can be found to producesimultaneously a larger v and a stronger correlation with soft hadrons, these photons are unlikelyto provide a solution to the “direct photon puzzle”. Yet these same characteristics can be an asset,distinguishing them from the larger number of photons produced in the later stages of the collisions,and providing an additional probe of the complex early stage of heavy-ion collisions. Acknowledgments
This work was supported by the U.S. Department of Energy (DOE) undergrant numbers DE-FG02-05ER41367, DE-SC0012704, and DE-SC0013460, by National ScienceFoundation (NSF) under grant number PHY-2012922, and by the Natural Sciences and EngineeringResearch Council of Canada. This research used resources of the National Energy ResearchScientific Computing Center (NERSC), a U.S. DOE Office of Science User Facility operated undergrant number DE-AC02-05CH11231.
References [1] C. Gale, S. Jeon and B. Schenke,
Hydrodynamic Modeling of Heavy-Ion Collisions , Int. J.Mod. Phys. A (2013) 1340011 [ ].[2] B. Schenke, P. Tribedy and R. Venugopalan, Fluctuating Glasma initial conditions and flowin heavy ion collisions , Phys. Rev. Lett. (2012) 252301 [ ].[3] B. Schenke, P. Tribedy and R. Venugopalan,
Event-by-event gluon multiplicity, energydensity, and eccentricities in ultrarelativistic heavy-ion collisions , Phys. Rev. C (2012)034908 [ ].[4] A. Kurkela, A. Mazeliauskas, J.-F. Paquet, S. Schlichting and D. Teaney, Matching theNonequilibrium Initial Stage of Heavy Ion Collisions to Hydrodynamics with QCD KineticTheory , Phys. Rev. Lett. (2019) 122302 [ ].[5] A. Kurkela, A. Mazeliauskas, J.-F. Paquet, S. Schlichting and D. Teaney,
Effective kineticdescription of event-by-event pre-equilibrium dynamics in high-energy heavy-ion collisions , Phys. Rev. C (2019) 034910 [ ].[6] G. Giacalone, A. Mazeliauskas and S. Schlichting, Hydrodynamic attractors, initial stateenergy and particle production in relativistic nuclear collisions , Phys. Rev. Lett. (2019)262301 [ ].[7] C. Gale, J.-F. Paquet, B. Schenke and C. Shen,
Probing Early-Time Dynamics andQuark-Gluon Plasma Transport Properties with Photons and Hadrons , in , 2, 2020 [ ].[8] S. Turbide, R. Rapp and C. Gale,
Hadronic production of thermal photons , Phys. Rev. C (2004) 014903 [ hep-ph/0308085 ].[9] J.-F. Paquet, C. Shen, G.S. Denicol, M. Luzum, B. Schenke, S. Jeon et al., Production ofphotons in relativistic heavy-ion collisions , Phys. Rev. C (2016) 044906 [ ].[10] P.B. Arnold, G.D. Moore and L.G. Yaffe, Photon emission from quark gluon plasma:Complete leading order results , JHEP (2001) 009 [ hep-ph/0111107hep-ph/0111107