LLearning about the QCD medium using electromagneticand weak probes
Gojko Vujanovic a , ∗ a Wayne State University, 666 W Hancock St, Detroit, Michigan 48201, USA
E-mail: [email protected]
Recent theoretical developments concerning radiation of electromagnetic and weak probes inultra-relativistic heavy-ion collisions is overviewed. These proceedings focus on electromagneticprobes and briefly cover weak probes. An outlook regarding the future use of electromagneticprobes is formulated whereby a quantitative Bayesian comparison, simultaneously employingelectromagnetic and hadronic calculations of experimental observables against data, is highlightedas a path towards a better understanding of the properties of the QCD medium.
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 ] A ug earning about the QCD medium using electromagnetic and weak probes Gojko Vujanovic
1. Introduction and overview
Ultra-relativisitc heavy-ion collisions (URHIC) produce a novel state of matter composedof deconfined quarks and gluons known as the quark gluon plasma (QGP). Characterizing theproperties of the QGP is one of the main goals for modern URHIC experiments, such as thosecurrently running at the Relativistic Heavy-Ion Collider (RHIC) and the Large Hadron Collider(LHC). Electroweak (EW) probes are key in this regard as they can separate initial state information,following the onset of a heavy-ion collision, from later dynamical evolution of the QGP, given howsmall EW coupling is compared to strong coupling (at energy scales probed by RHIC or the LHC).Given their large masses, weak probes, composed of W ± and Z gauge bosons, are preferentiallyproduced near the onset of a heavy-ion collision, and thus are sensitive to the modifications of theparton distribution functions (PDFs) inside the nucleus (see e.g. [1] for a recent results about Z production). Compared to W ± and Z , electromagnetic (EM) probes are typically much lighter(be it real photons or virtual photons decaying into leptons pairs, i.e. dileptons), and are notonly emitted at the early stages of the collision, but also throughout the entire evolution of theQGP. Furthermore, as soon as EM probes are created in the QGP, they escape it with negligiblerescattering, thus giving precise information about that state of the QGP at their production point.Thus, EM radiation has been considered as “clean” probe of the QGP. As these proceeding arefocusing on the properties of the QCD medium, discussion about EM probes will take center stage.Among electromagnetic probes, i.e. photons and dileptons, the latter have additional degreeof freedom, the center of mass energy of the lepton pair, or the invariant mass ( M ) of the virtualphoton, which allows for a separation between different sources of radiation from the QCD medium.In the low invariant mass region ( M (cid:46) ρ , ω , and φ ), while atintermediate invariant masses (1 (cid:46) M (cid:46) . M . Another way to detect radiation directly from the QCD medium, compared to dilepton sources thatexit in p-p collisions, is via a sizable dilepton v , which has not been observed in p-p collisions.In particular for dileptons, measuring v at intermediate invariant masses would confirm that thehigh temperature medium expands anisotropically, which can be used to narrow down the speed ofsound in that region (see Ref. [3]), provided experimentally “confounding” sources are removed.Dilepton radiation in 1 (cid:46) M (cid:46) . M region is interesting in and of itself, as willbe highlighted below. However, distinguishing between dileptons coming semi-leptonic of openheavy (anti)flavor pairs and those from the QGP allows to study the latter directly , especially through Prompt photons and Drell-Yan (DY) dileptons are most directly sensitive to nuclear modifications to the PDFs. The transverse momentum ( p T ) spectrum of EM probes is rather featureless, thus it is difficult to distinguish betweenthe HM and QGP sources using p T spectrum alone. earning about the QCD medium using electromagnetic and weak probes Gojko Vujanovicits v at intermediate invariant masses [4]. There are sources to dilepton production coming fromdecays of heavy quarkonia contributing M (cid:38) .
2. Electromagnetic radiation from the QCD medium
The production rate of EM probes, in thermal equilibrium, is given by: d R (cid:96) + (cid:96) − d q = − α E M π M Im [ Π E M ( M , q ; T , µ i )] e p · u / T − q d R γ d q = − α E M π Im [ Π E M ( M = , q ; T , µ i )] e p · u / T − , (1)where M = (cid:0) q (cid:1) − | q | , T is the temperature, and Im [ Π E M ] = Im (cid:2) g µν Π µν E M (cid:3) is the EM spectralfunction. A dedicated effort has been invested in recent years towards studying the in-equilibriumelectromagnetic spectral function using both perturbative and non-perturbative techniques. Inparallel to these developments, an equally important endeavor was the inclusion of non-equilibriumeffects, through viscous corrections ( δ R ) added to the thermal rates in Eq. (1), accounting fornon-equilibrium deviations owing to, for example, shear and bulk viscosity of the QCD medium,in both partonic and hadronic sectors. Using perturbative QCD (pQCD), the electromagnetic spectral function has been calculated atnext-to-leading order (NLO) for both photons [6, 7] and dileptons [8–10]. These efforts ultimatelyculminated in the results found in Refs. [11, 12] where using the NLO pQCD EM spectral functionwas devised combining results both above and below the light cone, as well as employing longitu-dinal and transverse channels with respect to spatial momentum. Using these new developments,Ref. [12] shows an unprecedented agreement between NLO pQCD EM spectral function and latticeQCD results of Ref. [13, 14], for both quenched and unquenched lattice calculations; thus usheringa new era of precision calculations of EM spectral functions.In the hadronic sector, many-body effective Lagrangians are used to describe hadronic inter-actions in the QCD medium, while the inclusion of the EM interaction is achieved through thecoupling to vector mesons, well described by the vector meson dominance (VDM). The leadingcontribution to the EM spectral function stems from tree-level scattering matrix elements, whichcan also be used in a Boltzmann description of the hadronic scattering rates. More specifically, the Note that heavy flavor is not produced within the QGP in practice, given the temperatures accessible to RHIC andLHC collisions. earning about the QCD medium using electromagnetic and weak probes Gojko Vujanovicmesonic contribution to photon production using SU(3) Massive Yang-Mills theory was discussedin [15], while tree-level scattering-based approach for dileptons in a medium composed of pionsand nucleons, is discussed in [16–18]. In addition to tree-level hadronic interactions, higher ordercorrection to the EM spectral function have also been included [19] (see also [20] for a more recentreview). The baryonic contribution to the photon production rates are also included in EM thespectral function of Refs. [19, 20], while parametrizations of photon production rate from bothsources can be found in Refs. [15, 21]. On the dilepton side, additional baryonic interactionsincluded in Refs. [19, 20] compared to [16–18] were found to be important contributors to vectormeson spectral functions. These findings have recently been extended to the chiral partner of the ρ meson — the a — thus opening the possibility to study the axial vector spectral function of the a .As the ( ρ, a ) constitutes a chiral partner pair, a study of the vector-axial vector spectral function[22] as temperature increases shows that the ρ and a start to overlap at temperature T =
170 MeV.This is one of the first signs of chiral symmetry restoration appearing in hadronic Lagrangians.Another promising approach to studying chiral symmetry restoration relies on the non-perturbativefunctional renormalization group (FRG) [23]. Using FRG, it was found that the ρ and a spectralfunction overlap at T =
300 MeV. However, the calculation of Ref. [23] is lacking baryonic degreesof freedom, which may bring the overlap temperature closer to the pseudo-critical temperature T = ± . Modern hydrodynamical modeling of the QCD medium involve dissipative phenomena such asviscosity, thus requiring modifications to the equilibrated EM rates. Introducing dissipative degreesof freedom to electromagnetic production has been done for all tree-level matrix elements throughtheir Boltzmann kinetic theory representation. Indeed, under the Boltzmann approximation, thethermal photon rates are: d R γ d q = ∫ d p p ( π ) d p p ( π ) d p p ( π ) ( π ) δ ( ) ( p + p − p − q ) f p f p |M | q ( π ) ( ± f p ) , (2)where f p i are the equilibrium distributions of scattering particles. To obtain dissipative corrections,Refs. [25–27] use the Chapman-Enskog/14-moment approximations as ansätze, which results into f → f + δ f . The effects of both bulk and shear viscous corrections are encapsulated δ f . Theviscous correction δ R to the rate is obtained by expanding to linear order in δ f to the deviationfrom the equilibrium distribution f [25–27]. Going beyond the tree-level interactions, in particularincluding the Landau-Pomeranchuck-Migdal effect, was only done for pQCD photon rates [28],though the implications for phenomenology of such rates have yet to be explored in full.As far as dilepton rates are concerned, the effects of the above-mentioned δ f viscous correctionwas done in the leading density expansion [16–18] presented in Refs. [2, 4, 29].
3. Selected phenomenology of electromagnetic probes
Except the NLO pQCD EM rates of Ref. [12], the above-mentioned EM production rates havebeen used in many dynamical models, and compared against experimental data. At top RHIC orLHC energies, these are ranging from early-time dynamics modeled by e.g. effective kinetic theory4 earning about the QCD medium using electromagnetic and weak probes
Gojko Vujanovic[30], to late-time dynamics modeled by hadronic transport [31–34], with hydrodynamics used todescribe the evolution between these extremes. Alternative dynamical modeling schemes to the onejust outlined consist, for instance, of Parton-Hadron-String Dynamics (PHSD) [35, 36], Boltzmannapproach to multiparton scatterings (BAMPS) [37] and so on. The comparison of such simulationsagainst experimental data is very useful to learn about, and even constrain, various properties of theQCD medium, such as its viscous transport coefficients. Doing so in the hydrodynamical contexthas shown that the penetrating nature of EM probes allows them to be quite sensitive to transportcoefficients. For example, dileptons are can be more sensitive to the temperature-dependent specificshear viscosity η s ( T ) than hadrons are. This is displayed in Fig. 1 using a quadratic form of the η s ( T ) (for details see Ref. [4]). This result is particularly important in light of the recent Bayesian analysis v c h p T [GeV] PHENIX (20%-40%) η /s=1/4 πη /s=0.1986(T/T tr -1) +1/4 πη /s=0.4513(T/T tr -1) +1/4 π v γ * ( M ) ( H M + QG P ) M [GeV] η /s=1/4 πη /s=0.1986(T/T tr -1) +1/4 πη /s=0.4513(T/T tr -1) +1/4 π Figure 1:
Charged hadron v ch2 and dilepton v ( M ) within a 20 −
40% centrality at top RHIC collision energytaken from [4]. This dilepton calculation includes sources from the HM and the QGP. The same underlyinghydrodynamical simulations are used for both observables. [38] where η s ( T ) is poorly constrained at high temperatures. For this sensitivity of dileptons to befully exploited however, accurate measurements of dilepton v , such as those being planned in Ref.[39], are needed. Electromagnetic probes are also sensitive to other viscous transport coefficients,such as shear relaxation time [40] or bulk viscosity [2, 27] of the hydrodynamical medium, thususing EM probes together with hadrons in a Bayesian analysis should be considered in the pathtowards increased constraints on transport coefficients of QCD media.There are other sources of EM probes, beyond those produced hydrodynamically, that need to beincluded as well. For purposes of extracting properties of the QGP, an important source of photonsemission stems from pre-hydrodynamical simulations. On the dilepton side, the semi-leptonicdecays of open heavy (anti-)flavor pairs contribute for 1 (cid:46) M (cid:46) . q or η D . Describing the evolution of the heavy quark within the QGPis best achieved using an agnostic framework that allows for different models to be used (andalso compared) depending on the kinematic regime. This is currently being pursued inside theJETSCAPE Collaboration [41, 42]. Following hadronization, the dilepton signal originates from At lower beam energies, hadronic transport can and, in fact, is used to describe much of the evolution of the system,leaving little room for hydrodynamics or other effective kinetic theories at those lower energies. ˆ q measures the amount of momentum diffusion, while η D measures instead the amount of momentum drag. earning about the QCD medium using electromagnetic and weak probes Gojko Vujanovicthe decay of the open heavy (anti-)flavor pair and is thus different from other semi-leptonic decaymeasurements that do not consider open heavy flavors as a pair. The heavy quark energy/momentuminteraction with the QGP also generates dilepton v [29]. Thus, measuring dilepton v in theintermediate mass region is crucial as it gives novel information about ˆ q or η D from open heavyflavor decay pairs, while direct radiation from the QGP gives better access to bulk properties suchas viscosities. p T ( GeV )10 d N / d y p T dp T ( G e V ) Direct photonsDirect photonsw/ suppression at early timeDirect photonsno pre-eq. photonsALICE 2015 p T ( GeV )0.000.050.100.150.200.250.300.350.40 v Direct photonsDirect photonsw/ suppression at early timeDirect photonsno pre-eq. photonsALICE 2018
Figure 2:
Direct photon yield and v within a 20 −
40% centrality for √ s N N = .
76 TeV Pb-Pb collisionscarried out at the LHC [5].
Starting from studies on prompt and hydrodynamical photons [27], novel studies includephotons production from a pre-hydrodynamical evolution [5, 30]. These pre-hydordynamicalsimulations not only provide a non-trivial initial condition for hydrodynamics, but also possessimportant physics processes for photon production, notably dynamical quark generation. Indeed, adynamical quark production bridges the gap between the gluon-dominated PDF sampled/created atthe onset of high energy collisions, and the hydrodynamically evolved QGP, that assumes thermallyequilibrated quarks. From that perspective, KøMPøST is an interesting effective kinetic theory asit provides a mechanism to dynamically generate quarks. Figure 2 is showing the sensitivity ofdirect photon production to the EM radiation before hydrodynamics, and thus to the dynamicallygenerated quarks. The effects of photon production during KøMPøST in Fig. 2 are strong enough toaffect total direct photons spectra and v . This is promising avenue to explore further in the future.
4. Conclusion and outlook
As all of the major ingredients regarding photon/dilepton production calculation are largely inplace, more focus should now be directed towards combining these different calculations together,while gearing towards a comprehensive/simultaneous understanding of EM probes and hadronicobservables. Of course, theoretical improvements pertaining to the production rates (via e.g. viscouscorrection prescription used), or enhancements in the dynamical modeling (e.g. pre-hydrodynamicalevolution/EM production) should happen in parallel. Those theoretical advancements are usefulboth in improving the understanding of EM production, and serve as a source of theoreticaluncertainty to the already available sources to be used within a future Bayesian analysis. A6 earning about the QCD medium using electromagnetic and weak probes
Gojko Vujanoviccombined calculation within a Bayesian model-to-data comparison will not only allow for a betterconstrains on transport coefficients, such as ˆ q or η s ( T ) , but also be employed to give more credenceto certain models. For instance, one can use Bayesian model selection on a dilepton calculationthat contain chiral symmetry restoration effects compared to the one without, to ascertain whetherexperimental data favors either calculation. Bayesian analyses could also help devise whether bettermeasurements are needed in certain areas (see e.g. Ref. [43]). A precision measurement of dilepton v is thus crucially needed, such as that being planned in Ref. [39]. Acknowledgements : This work was supported by the Natural Sciences and EngineeringResearch Council of Canada, and by the National Science Foundation (in the framework of theJETSCAPE Collaboration) through award No. ACI-1550300.
References [1] ALICE, S. Acharya et al. , Phys. Lett. B , 372 (2018).[2] G. Vujanovic et al. , Phys. Rev. C , 044904 (2020).[3] S. Pratt, E. Sangaline, P. Sorensen, and H. Wang, Phys. Rev. Lett. , 202301 (2015).[4] G. Vujanovic, G. S. Denicol, M. Luzum, S. Jeon, and C. Gale, Phys. Rev.
C98 , 014902 (2018).[5] C. Gale, J.-F. Paquet, B. Schenke, and C. Shen, Probing Early-Time Dynamics and Quark-Gluon Plasma Transport Properties with Photons and Hadrons, in , 2020, 2002.05191.[6] J. Ghiglieri et al. , JHEP , 010 (2013).[7] J. Ghiglieri, O. Kaczmarek, M. Laine, and F. Meyer, Phys. Rev. D94 , 016005 (2016).[8] M. Laine, JHEP , 120 (2013).[9] I. Ghisoiu and M. Laine, JHEP , 83 (2014).[10] J. Ghiglieri and G. D. Moore, JHEP , 029 (2014).[11] G. Jackson, Phys. Rev. D , 116019 (2019).[12] G. Jackson and M. Laine, JHEP , 144 (2019).[13] B. B. Brandt, A. Francis, T. Harris, H. B. Meyer, and A. Steinberg, EPJ Web Conf. , 07044(2018).[14] B. B. Brandt et al. , Lattice QCD estimate of the quark-gluon plasma photon emission rate, in , 2019, 1912.00292.[15] S. Turbide, R. Rapp, and C. Gale, Phys. Rev. C , 014903 (2004).[16] V. L. Eletsky, M. Belkacem, P. J. Ellis, and J. I. Kapusta, Phys. Rev. C64 , 035202 (2001).[17] A. T. Martell and P. J. Ellis, Phys. Rev.
C69 , 065206 (2004).7 earning about the QCD medium using electromagnetic and weak probes
Gojko Vujanovic[18] G. Vujanovic, J. Ruppert, and C. Gale, Phys. Rev.
C80 , 044907 (2009).[19] R. Rapp and J. Wambach, Adv.Nucl.Phys. , 1 (2000).[20] R. Rapp, J. Wambach, and H. van Hees, Landolt-Bornstein , 134 (2010).[21] M. Heffernan, P. Hohler, and R. Rapp, Phys. Rev. C , 027902 (2015).[22] P. M. Hohler and R. Rapp, Phys. Lett. B , 103 (2014).[23] R.-A. Tripolt, B.-J. Schaefer, L. von Smekal, and J. Wambach, Phys. Rev. D , 034022(2018).[24] HotQCD, A. Bazavov et al. , Phys. Lett. B , 15 (2019).[25] M. Dion et al. , Phys. Rev. C , 064901 (2011).[26] C. Shen, J.-F. Paquet, U. Heinz, and C. Gale, Phys. Rev. C91 , 014908 (2015).[27] J.-F. Paquet et al. , Phys. Rev.
C93 , 044906 (2016).[28] S. Hauksson, S. Jeon, and C. Gale, Phys. Rev.
C97 , 014901 (2018).[29] G. Vujanovic et al. , Phys. Rev.
C89 , 034904 (2014).[30] J.-F. Paquet, C. Shen, B. Schenke, and C. Gale, in these proceedings (2020).[31] S. Endres, H. van Hees, and M. Bleicher, Phys. Rev. C , 054901 (2016).[32] S. Endres, H. van Hees, and M. Bleicher, Phys. Rev. C , 024912 (2016).[33] J. Staudenmaier, J. Weil, V. Steinberg, S. Endres, and H. Petersen, Phys. Rev. C98 , 054908(2018).[34] A. Schäfer et al. , Phys. Rev. D , 114021 (2019).[35] T. Song, W. Cassing, P. Moreau, and E. Bratkovskaya, Phys. Rev. C97 , 064907 (2018).[36] E. Bratkovskaya, in these proceedings (2020).[37] M. Greif et al. , Phys. Rev. C , 054903 (2017).[38] https://indico.cern.ch/event/792436/contributions/3535670/.[39] Z. Citron et al. , CERN Yellow Rep. Monogr. , 1159 (2019).[40] G. Vujanovic et al. , Phys. Rev. C94 , 014904 (2016).[41] JETSCAPE, G. Vujanovic et al. , Multi-stage evolution of heavy quarks in the quark-gluonplasma, in ,2020, 2002.06643.[42] W. Fan, in these proceedings (2020).[43] E. Sangaline and S. Pratt, Phys. Rev. C93