Electromagnetic Probes Theory and Experiment

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Electromagnetic Probes: Theory and Experiment

Ralf-Arno Tripolta,b,∗, Frank Geurtsc

aInstitut für Theoretische Physik, Justus-Liebig-Universität, Heinrich-Buﬀ-Ring 16, 35392 Giessen, Germany

bHelmholtz Research Academy Hesse for FAIR (HFHF), Campus Giessen, 35392 Giessen, Germany

cDepartment of Physics & Astronomy, Rice University, Houston TX 77005, USA

Abstract

We review the current state of research on electromagnetic probes in the context of heavy-ion collisions. The focus is on

thermal photons and dileptons which provide unique insights into the properties of the created hot and dense matter.

This review is intended to provide an introductory overview of the topic as well as a discussion of recent theoretical and

experimental results. In particular, we discuss the role of vector-meson spectral functions in the calculation of photon and

dilepton rates and present recent results obtained from diﬀerent frameworks. Furthermore, we will highlight the special

role of photons and dileptons to provide information on observables such as the temperature, the lifetime, the polarization

and the electrical conductivity of the produced medium as well as their use to learn about chiral symmetry restoration

and phase transitions.

Keywords: electromagnetic probes, photons, dileptons, heavy-ion collisions, QCD phase diagram

∗Corresponding author

Email address: Ralf-Arno.Tripolt@theo.physik.uni-giessen.de (Ralf-Arno Tripolt)

Preprint submitted to Progress in Particle and Nuclear Physics November 1, 2022

arXiv:2210.01622v2 [hep-ph] 31 Oct 2022

Contents

1 Introduction 3

2 Experimental aspects of photon and dilepton measurements 6

2.1 Heavy-ion collision process ............................................. 6

2.2 Electromagnetic Spectroscopy ........................................... 9

3 Theoretical aspects of electromagnetic probes 13

3.1 QCD phase diagram and symmetries ....................................... 13

3.2 Photon and dilepton production rates ...................................... 16

3.3 Electromagnetic spectral function and Vector Meson Dominance ....................... 18

4 Vector mesons in medium 21

4.1 Low-density expansions and chiral mixing .................................... 21

4.2 Lattice QCD .................................................... 22

4.3 Chiral and QCD sum rules ............................................ 24

4.4 Massive Yang Mills and hadronic many-body theory .............................. 25

5 Vector mesons with the analytically-continued FRG (aFRG) method 29

5.1 Flow equations and analytic continuation .................................... 29

5.2 Mass generation of nucleons and the parity-doublet model ........................... 31

5.3 Results for the parity-doublet model ....................................... 32

6 Thermal photon and dilepton rates 37

6.1 Thermal photons from the QGP ......................................... 37

6.2 Thermal photons from hadrons .......................................... 38

6.3 Thermal dilepton rates ............................................... 40

7 Photons in heavy-ion collisions 43

7.1 Classiﬁcation and production channels ...................................... 43

7.2 Interpretation of photon spectra ......................................... 44

7.3 Recent experimental results ............................................ 47

8 Dileptons in heavy-ion collisions 49

8.1 Classiﬁcation and production channels ...................................... 49

8.2 Interpretation of dilepton spectra ......................................... 49

8.3 Recent experimental results ............................................ 56

9 Conclusions and Outlook 60

1. Introduction

The investigation of matter under extreme conditions in temperature and density as prevailing in the aftermath of the

Big Bang is one of the central aims of present theoretical as well as experimental research eﬀorts in high-energy particle

physics. Nowadays, such an extreme state of matter may occur naturally in the core of compact stellar objects like

neutron stars or during neutron star merger events. In a laboratory environment, extreme temperatures and densities can

be created in relativistic collisions of heavy particles, see for example [1,2,3,4,5] for reviews. Such heavy-ion collisions are

furthermore the only means by which bulk properties of a non-Abelian gauge theory, such as Quantum Chromodynamics

(QCD), can be assessed experimentally. Heavy-ion collision experiments are currently performed at the Large Hadron

Collider (LHC) at CERN, the Relativistic Heavy Ion Collider (RHIC) at BNL, the Schwer-Ionen-Synchrotron (SIS) at

GSI and planned at future facilities such as the Facility for Antiproton and Ion Research (FAIR), the Nuclotron-based

Ion Collider fAcility (NICA), the High Intensity heavy ion Accelerator Facility (HIAF), and the heavy-ion program at

the Japan Proton Accelerator Complex (J-PARC).

Electromagnetic (EM) probes, i.e. photons and dileptons, have proven to be exceptionally versatile and useful probes

to study the properties of the hot and dense medium created in such collisions, see for example [6,7,8,9,10] for

reviews. This is due to the fact that they don’t (directly) interact ‘strongly’ with the surrounding medium, i.e. not via the

strong interaction as described by QCD, but predominantly via the electromagnetic interaction as described by Quantum

Electrodynamics (QED). Since the electromagnetic interaction is considerably weaker than the strong interaction, as for

example evident by comparing the EM coupling strength αEM ≈1/137 with the strong coupling αswhich is of the order

O(10−1)−O(1), photons and dileptons have a mean-free path that is larger than the extent of the created ﬁreball. They

can thus traverse the medium almost undisturbed and carry information from their production point to the detector.

The smallness of the EM coupling, however, also entails that photons and dileptons are produced very rarely compared

to strongly-interacting particles such as pions. For example, the decay of the ρ(770) vector meson into dileptons, i.e. into

an electron-positron pair or into a muon-antimuon pair, is suppressed by a factor of ∼5·10−5as compared to the decay

into pions, see for example the corresponding experimental branching ratios [5].

Another important feature of photons and dileptons is that they are produced at all stages of the collision process. In

principle, they can thus be used to obtain information on all phases of the ﬁreball evolution, from initial hard scattering

processes over the pre-equilibrium phase and the Quark-Gluon Plasma (QGP) phase to the hadron gas phase. This

information is, however, convoluted with the space-time evolution of the medium which makes extracting information on

a particular phase, such as the thermally-equilibrated QGP or the hadron-gas phase, very challenging. A good theoretical

understanding of the underlying dilepton production rates within the various phases as well as of the space-time evolution

of the collision process is therefore imperative for a robust interpretation of photon and dilepton spectra.

In this review, we will focus in particular on the theoretical description and experimental results concerning the

soft thermal radiation from the QGP and the hadron gas phase. Those regimes are of particular interest since they

correspond to the extreme state of matter that ﬁlled our Universe shortly after the Big Bang and since they allow to

study fundamental properties of QCD such as conﬁnement and chiral symmetry breaking. Color conﬁnement, which

describes the fact that no color-neutral objects have been observed in an isolated state, is expected to disappear at high

enough temperatures and/or densities. Chiral symmetry, on the other hand, is a symmetry of the QCD Lagrangian for

massless quarks that is spontaneously broken in the vacuum, i.e. at zero temperature and density, but eventually gets

restored at high temperatures and/or densities. Mapping out the corresponding QCD phase diagram is one of the central

Figure 1.1: Sketch of the QCD phase diagram. Figure adapted from [11].

goals in high-energy physics, see also Fig. 1.1 which shows an illustration of the QCD phase diagram as well as of the

approximate regimes1where heavy-ion collision experiments can be used for its investigation, see for example [12,13] for

reviews. EM probes, and in particular dileptons, can indeed be useful to learn about certain aspects of the QCD phase

diagram such as the location of ﬁrst-order phase transitions and the conjectured critical endpoint.

A special role in the theoretical description of thermal photon and dilepton spectra is played by the light vector

mesons. This is due to the fact that vector mesons carry the same quantum numbers as the photon and can therefore

directly transform into a real or virtual photon, where the virtual photon can subsequently decay into a lepton-antilepton

pair, i.e. a dilepton. The light vector mesons ρ(770),ω(782), and φ(1020), therefore, act as an intermediary between the

hadronic strong-interaction regime and the emitted electromagnetic particles. In fact, the resulting thermal EM spectra

can almost exclusively be described by the decay of light vector mesons, with the largest contribution stemming from the

ρ(770) vector meson. This phenomenological result is known as Vector Meson Dominance (VMD) and will be discussed

in more detail in the following.

One of the main challenges for a realistic description of thermal photon and dilepton rates is therefore the computation

of in-medium vector-meson spectral functions. This can be achieved using diﬀerent frameworks such as hadronic many-

body theory (HMBT), QCD sum rules, the Massive Yang Mills (MYM) framework, or the Functional Renormalization

Group (FRG) approach, see Secs. 4and 5. In particular, the Rapp-Wambach spectral functions as obtained from hadronic

many-body theory have proven to be very successful for the description of experimental data and are still widely used.

More recently, also in-medium spectral functions from the FRG have become available for diﬀerent eﬀective theories. The

FRG approach, for example, allows to take the eﬀects of ﬂuctuations into account and to incorporate important aspects

of chiral symmetry and its breaking pattern. In particular, recent results concerning the in-medium spectral function of

the ρ(770) vector meson and of its chiral partner, the a1(1260) axial-vector meson, will be discussed in this review.

The resulting thermal photon and dilepton rates can then be combined with suitable descriptions of the space-time

evolution of the heavy-ion collision process in order to obtain the measured spectra, see Fig. 1.2 for an example of a

1We note that the experimental regimes shown in Fig. 1.1 are merely for illustrative purposes and should of course also extend into the

hadron gas phase.

Figure 1.2: Excess dimuon invariant-mass spectrum as measured in In-In collisions at √sN N = 17.3GeV by the NA60 collaboration at the

SPS [14,15] together with theoretical results based on hadronic many-body theory [16]. Figure adapted from [16].

dilepton spectrum measured with high precision and the excellent agreement with theoretical predictions. For central

heavy-ion collisions at high collision energies, ideal or viscous relativistic hydrodynamics is frequently used to describe

the dynamics of the produced medium, while at lower collision energies transport descriptions, sometimes in combination

with a coarse-graining procedure, have proven to be successful. The obtained results on spectra and other observables

can then be used to learn about the properties of the produced medium and thus about the properties of hot and dense

strong-interaction matter in general. In particular, we will discuss the connection to the temperature and the lifetime of

the produced medium, the degree of collectivity, the underlying spectral functions and chiral symmetry, phase transitions,

changes in degrees of freedom, and to transport coeﬃcients such as the electrical conductivity.

We close this introduction by giving an overview of the structure of the remaining parts of this review. In Sec. 2we

discuss general aspects of experimental photon and dilepton measurements which includes a presentation of the heavy-ion

collision process and an introduction to electromagnetic spectroscopy. In Sec. 3we discuss general theoretical aspects

of electromagnetic probes. This includes a short introduction to QCD, its phase diagram and symmetries, as well as a

discussion on the theoretical computation of photon and dilepton rates, the EM spectral function and the idea of VMD.

In Sec. 4we give a more detailed account of the theoretical approaches to describe vector mesons in a thermal medium

which include low-density expansions and chiral mixing, lattice QCD, chiral and QCD sum rules, as well as Massive Yang

Mills and hadronic many-body theory. In Sec. 5we focus on a more recent theoretical framework for the computation

of in-medium spectral functions, i.e. the analytically-continued FRG (aFRG) method, and present results on vector and

axial-vector mesons as obtained for nuclear matter. In Sec. 6we discuss diﬀerent theoretical results obtained for thermal

photon and dilepton rates while experimental results on photon and dilepton spectra in heavy-ion collisions are discussed

in Secs. 7and 8, respectively. In the latter sections, a particular emphasis is on the interpretation of photon and dilepton

spectra and what kind of information one can extract from them, such as on the temperature or the lifetime of the

produced ﬁreball. Finally, in Sec. 9we conclude and provide an outlook on the future of electromagnetic probes in

heavy-ion collisions.

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ElectromagneticProbes:TheoryandExperimentRalf-ArnoTripolta,b,,FrankGeurtscaInstitutfürTheoretischePhysik,Justus-Liebig-Universität,Heinrich-Bu-Ring16,35392Giessen,GermanybHelmholtzResearchAcademyHesseforFAIR(HFHF),CampusGiessen,35392Giessen,GermanycDepartmentofPhysics&Astronomy,RiceUniversity,Hous...

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