Charles Gale
This text is meant as an introduction to the theoretical physics of photon emission in hot and dense strongly interacting matter, the principal application being relativistic nuclear collisions. We shall cover some of the results and techniques appropriate for studies at SPS, RHIC, and LHC energies
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I review some properties of hot and/or dense releativistic matter. This review is aimed at a general audience of particle physicists.
We study the propagation of leptons in hot and dense media and estimate the background corrections to the purely leptonic processes in the early universe and in the stellar cores.
This talk summarizes some of the theoretical issues currently most debated in the field of hot and dense QCD matter and ultra-relativistic heavy ion collisions.
The photoproduction rate of pentaquark $Θ^+$ is calculated in a hot and dense medium. At high temperature and density, due to the restoration of chiral symmetry, photoproduction energy threshold is increased. Above the thresold the production cross section is strongly enhanced.
We evaluate thermodynamical quantities and the transport coefficients of a dense and hot hadronic matter based on the event generator URASiMA (Ultra-Relativistic AA collision Simulator based on Multiple Scattering Algorithm) with periodic boundary conditions. As the simplest example of the transport coefficients we investigate the temperature dependence and the chemical potential dependence of the baryon diffusion constant of a dense and hot hadronic matter.
We study the behavior of the $π^0$ width as a function of temperature and density. We provide simple expressions for the neutral pion width in a hot and dense medium based on a renormalized version of the microscopic Nambu Jona Lasinio model. Then we consider the two cases where the pion mass is finite or vanishes at the critical temperature and discuss the phenomenological consequences of both cases.
We present a relativistic three-body equation to investigate three-quark clusters in hot and dense quark matter. To derive such an equation we use the Dyson equation approach. The equation systematically includes the Pauli blocking factors as well as the self energy corrections of quarks. Special relativity is realized through the light front form. Presently we use a zero-range force and investigate the Mott transition.
The one-particle electron spectrum is found for hot and dense QED and its properties are investigated in comparison with the collective spectrum. It is shown that the one-particle spectrum (in any case its zero momentum limit) is gauge invariant, but the collective spectrum, being qualitatively different, is always gauge dependent. The exception is the case $m,μ=0$ for which the collective spectrum long wavelength limit demonstrates the gauge invariance as well.
We study the properties of an electromagnetically interacting medium in the presence of high concentration of electrons at extremely high temperatures and chemical potentials. We show that the electromagnetic properties of a medium such as the electric permittivity, magnetic permeability, magnetic moments and the propagation speed of electromagnetic waves as well as the corresponding particle processes depend on temperature and density of the medium. Electromagnetic properties of neutrinos are significantly modified due to their interactions with electrons when they propagate through such a me…
Photons, as quanta of electromagnetic fields, determine the electromagnetic properties of an extremely hot and dense medium. Considering the properties of photons in the interacting medium of charged particles, we explicitly calculate the electromagnetic properties such as the electric permittivity, magnetic permeability, refractive index and the propagation speed of electromagnetic signals in extremely hot and dense background in cosmos. Photons acquire dynamically generated mass in a medium. The screening mass of photon, Debye shielding length and the plasma frequency are calculated as funct…
We generate the statistical ensembles in equilibrium with fixed temperature and chemical potential by imposing periodic boundary condition to the simulation of URASiMA(Ultra-Relativistic AA collision Simulator based on Multiple Scattering Algorithm). By using the generated ensembles, we investigate the temperature dependence and the chemical potential dependence of the nucleon diffusion constant of a dense and hot hadronic matter.
We evaluate charge diffusion constant of dense and hot hadronic matter based on the molecular dynamical method by using a hadronic collision generator which describes nuclear collisions at energies 10 < E < 100 GeV/A and satisfies detailed balance at low temperatures (T < 200 MeV). For the hot and dense hadronic matter of the temperature range, 100 < T < 200 MeV and baryon number density, 0.16 < nB < 0.32 fm^-3, charge diffusion constant D gradually increases from 0.5 fm c to 2 fm c with temperature and is almost independent of baryon number density. Based on the obtained diffusion constant we…
The Fermi excitations in hot and dense quark-gluon plasma are studied in the Feynman gauge using the temperature Green function technique. We find the four well-separated branches for the case $m=0$ and establish the additional splitting between them (the four different masses) when $m\ne 0$. The long wavelength limit of these excitations is found in the general case of the massive fermions at finite temperature and densities to give the exact one-loop spectrum. Simultaneously the many known results are reproduces as its different limits.
Some features of hot and dense gas of quarks which are considered as the quasi-particles of the model Hamiltonian with four-fermion interaction are studied. Being adapted to the Nambu-Jona-Lasinio model this approach allows us to accommodate a phase transition similar to the nuclear liquid-gas one at the proper scale. It allows us to argue an existence of the mixed phase of vacuum and baryonic matter (even at zero temperature) as a plausible scenario of chiral symmetry (partial) restoration.
We investigate the phase structure of hot and/or dense QCD with massless 2-flavors using the Schwinger-Dyson equation (SDE) with the improved ladder approximation in the Landau gauge. We examine the effect of the antiquark contribution and find that setting the antiquark Majorana mass equal to the quark one is a good approximation in the medium density region. The imaginary part of the Dirac mass has an important influence on the chiral phase transition, in particular on the tricritical point.
The one-loop dispersion equation which defines the collective excitations of the massive Dirac particles in hot and dense quark-gluon medium is obtained in the high temperature limit for the case $m<<T$ and solved explicitly for all $|\q|$ when $μ=0$. Four well-separated spectrum branches (quasi-particle and quasi-hole excitations) are found and their behaviors for the small and large $|\q|$ are investigated. All calculations are performed using the temperature Green function technique and fixing the Feynman gauge. The gauge dependency of the spectra found are briefly discussed.
Hot and dense pQCD in a very strong magnetic background
该研究利用pQCD在有限温度、强磁场及物理夸克质量下计算两圈阶的压强等物理量，并探讨冷密夸克物质与夸克磁星约束，拓展了强磁场下热密QCD的研究。
We present the first complete calculation of the soft photon self-energy to the next-to-leading order in a hot and/or dense ultrarelativistic plasma in Quantum Electrodynamics (QED). The calculation is performed within the real-time formalism utilizing dimensional regularization in $4-2ε$ dimensions, while the result is reported including explicit $O(ε)$ terms in the zero-temperature limit. This information is required to extend the perturbative calculation of the pressure of cold and dense QED matter to partial next-to-next-to-next-to-leading order in a weak-coupling expansion, reported in a …
The one-loop Fermi spectra (one-particle and collective ones) are found for all momenta in the $T^2$-approximation and their gauge invariance in hot and dense Abelian and non-Abelian theories is studied. It is shown that the one-particle spectrum, if the calculation accuracy is kept strictly, is gauge invariant for all momenta and has two branches as the bare one. The collective spectrum always has four branches which are gauge dependent including also their $|\q|=0$ limit. The exception is the case $m,μ=0$ for which this spectrum is gauge invariant for all momenta as well.
Using the standard Green-Kubo formalism, we determine the shear viscosity $η$ of a hot and dense Yukawa-Fermi gas. In particular, we study the effect of particle and plasmino excitations on thermal properties of the fermionic part of the shear viscosity, and explore the effects of thermal corrections to particle masses on bosonic and fermionic shear viscosities, $η_b$ and $η_f$. It turns out that the effects of plasminos on $η_f$ become negligible with increasing (decreasing) temperature (chemical potential).
I offer some computational details and useful and concise formulae to calculate the effective potential for a general abelian supersymmetric model at high temperature and density. It will be shown that such cases are very good candidates for symmetry nonrestoration at high temperature, providing large densities are present.
Power corrections to the photon polarization tensor in a hot and dense medium of massive fermions
本文在硬热圈近似和实时形式体系下计算热密有质量费米子介质中光子极化张量的 $\mathcal{O}(k^2)$ 质量修正，揭示其温度依赖并用于电极化率与磁极化率计算。
We present recent results on bulk observables and electromagnetic probes obtained using a hybrid approach based on the Ultrarelativistic Quantum Molecular Dynamics transport model with an intermediate hydrodynamic stage for the description of heavy-ion collisions at AGS, SPS and RHIC energies. After briefly reviewing the main results for particle multiplicities, elliptic flow, transverse momentum and rapidity spectra, we focus on photon and dilepton emission from hot and dense hadronic matter.
Photon and electron spectra in hot and dense QED are found in the high temperature limit for all $|\q|$ using the Feynman gauge and the one-loop self-energy. All spectra are split by the medium and their branches develop the gap (the dynamical mass) at zero momentum. The photon spectrum has two branches (longitudinal and transverse) with the common mass; but electron spectrum is split on four branches which are well-separated for any $|\q|$ including their $|\q|=0$ limits (their effective masses). These masses and the photon thermal mass are calculated explicitly and the different limits of sp…
The behavior of $η$ and $η'$ in hot strange quark matter in weak equilibrium with temperature, is investigated within the SU(3) Nambu-Jona-Lasinio [NJL] model. Possible manifestations of restoration of symmetries, by temperature or density, in the behavior of $η$ and $η'$ are discussed. The role played by the combined effect of temperature and density in the nature of the phase transition and meson behavior is also analyzed.
We study phase transitions and the behavior of kaons in hot and dense matter, giving special attention to the role of strange quarks. At T=0, it is found that the fraction of the strange valence quarks affects the energy per particle of the system, without changing the nature of the phase transition, and, on the other side, it has meaningful effects on the behavior of kaons and antikaons masses. The phase behavior of kaons in the $T-ρ$ plane is analyzed in connection with the chiral phase transition.
We review recent results on properties of the meson gas relevant for Heavy Ion Collision and Nuclear Matter experiments, within the framework of chiral lagrangians. In particular, we describe the temperature and density evolution of the $σ$ and $ρ$ poles and its connection with chiral symmetry restoration, as well as the chemical nonequilibrated phase and transport coefficients.
A full (3+1)-dimensional calculation using the Lagrangian hydrodynamics is proposed for relativistic nuclear collisions. The calculation enables us to evaluate anisotropic flow of hadronic matter which appears in non-central and/or asymmetrical relativistic nuclear collisions. Applying hydrodynamical calculations to the deformed uranium collisions at AGS energy region, we discuss the nature of space-time structure and particle distributions in detail.
We discuss the chiral phase transition of hot and dense quark matter. We illustrate that the first-order phase transition is generally favored at high baryon density and the repulsive vector-vector interaction weakens the first-order phase transition. We use the Nambu--Jona-Lasinio model with the Polyakov loop coupling for concreteness. We locate the QCD critical surface on the quark mass plane for various values of the vector coupling constant. We find that, with increasing quark chemical potential, the first-order region in the quark mass plane could shrink for sufficiently large vector coup…
We study the neutrino interaction rates in hot matter at high densities in the presence of uniform magnetic field. The neutrino cross-sections involving both the charged current absorption and neutral current scattering reactions on baryons and leptons have been considered. We have in particular considered the interesting case when the magnetic field is strong enough to completely polarise the protons and electrons in supernovae and neutron stars. The opacity in such a situation is considerably modified and the cross-section develops anisotropy. This has implications for phenomenon invoked in …
An important role of the scalar isoscalar sigma-meson in the low-energy physics is discussed. The behavior of the sigma-meson in the hot and dense medium is studied. It is shown that in the vicinity of critical values of temperature(T) and chemical potential(m) the sigma-meson can become a sharp resonance. This effect can lead to a strong enhancement of the processes pi pi -> gamma gamma and pi pi-> pi pi near the two-pion threshold. Experimental observation of this phenomenon can be interpreted as a signal of approaching the domain where the chiral symmetry restoration and phase transition of…
We investigate $J/ψ$ suppression in ultrarelativistic heavy ion collisions within a generalized GLAUBER model and compare results of a hadronic comover scenario with those of a quark plasma scenario where conditions for MOTT dissociation of charmonium are fulfilled locally at the short time scales before hadronization. We study possible consequences for the theoretical description to be drawn from the observation of ``anomalous'' thresholds in the $J/ψ$ suppression pattern by the NA50 collaboration.
For Dirac neutrinos with magnetic moment, we compute the production rate for right-handed neutrinos in a hot and dense QED plasma containing an initial population of left-handed neutrinos thermally distributed. The most important mechanisms for $ν_L$ depolarization, or production of right-handed neutrinos, are the $ν_L \to ν_R$ chirality flip and the plasmon decay to $\barν_L + ν_R$. The rates for these processes are computed in terms of a resummed photon propagator which consistently incorporates the background effects to leading order. Applying the results to the cases of supernovae core col…
The behavior of neutral pseudoscalar mesons $π^0, η$ and $η'$ in hot and dense matter is investigated, in the framework of the three flavor Nambu-Jona-Lasinio model. Three different scenarios are considered: zero density and finite temperature, zero temperature and finite density in a flavor asymmetric medium with and without strange valence quarks, and finite temperature and density. The behavior of mesons is analyzed in connection with possible signatures of restoration of symmetries. In the high density region and at zero temperature it is found that the mass of the $η'$ increases, the devi…
We investigate vector meson spectral functions at finite temperature and density through the soft wall model, a bottom-up holographic approach to QCD. We find narrow resonances at small values of the parameters, becoming broader as temperature and density increase. We study dissociation of such states, occurring when no peak can be distinguished in the spectral function. We also find a decreasing of the mass of vector mesons at increasing temperature and density. Finally, a discussion of these results is presented.
We summarize recent developments in our understanding of low-mass quark-antiquark excitations in hadronic matter under various different conditions. This includes the thermodynamics of the chiral condensate, pions as Goldstone bosons in normal nuclear matter, and excursions into extreme territory of the QCD phase diagram: lepton pair production from a fireball expanding through the transition boundary between the quark-gluon and hadron pha ses of QCD.
It is pointed out that the hadron spectroscopy should be a study of the structure of the QCD vacuum, low-energy elementary excitations on top of which are hadrons. Concentrating on the dynamical breaking of the chiral symmetry in the QCD vacuum, we emphasize the importance to clarify what is going on with mesons in the $I=J=0$-channel, i.e., the sigma meson channel, because it is connected to the quantum fluctuations of the chiral order parameter. After summarizing the significance of the sigma meson in QCD and low-energy hadron phenomenology, we give a review on some theoretical and experimen…
In this paper, quarkonium dissociation is investigated in an anisotropic plasma in the hot and dense media. For that purpose, the multidimensional Schrodinger equation is solved analytically by Nikiforov-Uvarov (NU) method for the real part of the potential in an anisotropic medium. The binding energy and dissociation temperature are calculated. In comparison with an isotropic medium, the binding energy of quarkonium is enhanced in the presence of an anisotropic medium. The present results show that the dissociation temperature increases with increasing anisotropic parameter for 1S state of th…
The leading-order weak-coupling shear viscosity of QCD was computed almost 20 years ago, and the extension to next-to-leading order is 4 years old. But these results have never been applied at finite baryon chemical potential $μ$, despite the fact that intermediate-energy heavy ion collisions and merging neutron stars may explore the Quark-Gluon Plasma in a regime where baryon chemical potentials are large. Here we extend the leading-log shear viscosity calculation to finite $μ$, and we argue that the convergence of the weak-coupling expansion, while questionable for achievable plasmas, should…
A thermodynamically consistent excluded volume model is proposed to account for the particle multiplicities obtained from lowest SIS energies to the highest RHIC energies. The chemical freeze-out volumes lying in a slice of one unit of rapidity for pions and kaons are separately inferred from this analysis and the results are compared with the corresponding thermal freeze-out volumes obtained from the Hanbury-Brown Twiss (HBT) pion interferometry. Furthermore, we extract the variations of freeze-out number densities for pions and nucleons with the center-of-mass energy in our model and compare…
Using the unification of the chiral SU(3) model and QCD sum rules, we deduce the in-medium properties of $K^\pm_1$ meson. Within the chiral SU(3) model, medium modified gluon and quark condensates are evaluated through their interactions with the scalar fields ($σ$, $ζ$, $δ$, and $χ$). These condensates are further used as input in the Borel transformed equations of QCD sum rules to evaluate the in-medium mass of strange $K^\pm_1$ meson. The in-medium property of the above meson can be used to study the restoration of chiral symmetry in nuclear matter.
One of the important perturbative ("hard") probes of hot and dense QCD matter is the medium-induced energy loss of energetic partons, so called "jet quenching", which is predicted to be very different in cold nuclear matter and in QGP, and leads to a number of phenomena which are already seen in the RHIC data on the qualitative level. The inclusion of jet quenching and other important collective effects, such as radial and elliptic flows, in the existing Monte-Carlo models of relativistic heavy ion collisions is discussed. Some issues on the corresponding physical observables at RHIC and LHC e…
Phase transitions in hot and dense matter and the in--medium behavior of pseudoscalar mesons ($π^{\pm}, π^0, K^{\pm}, K^0 ,\bar K^0,η{and} η' $) are investigated, in the framework of the three flavor Nambu--Jona-Lasinio model, including the 't Hooft interaction, which breaks the $U_A(1)$ symmetry. Three different scenarios are considered: zero density and finite temperature, zero temperature and finite density in quark matter with different degrees of strangeness, and finite temperature and density. At T=0, the role of strange valence quarks in the medium is discussed, in connection with the p…
We investigate chiral symmetry breaking in strong magnetic fields at finite temperature and densities in a 3 flavor Nambu Jona Lasinio (NJL) model including the Kobayashi Maskawa t-Hooft (KMT) determinant term, using an explicit structure for the ground state in terms of quark antiquark condensates. The mass gap equations are solved self consistently and are used to compute the thermodynamic potential. We also derive the equation of state for strange quark matter in the presence of strong magnetic fields which could be relevant for proto-neutron stars. ~
Using a real-time formalism of equilibrium and nonequilibrium quantum-field theory, we derive the reaction-rate formula for neutrino-conversion ($ν\to ν'$) process and $ν\barν'$ annihilation process, which take place in a hot and dense QED plasma with background (anti)neutrinos out of equilibrium. Also derived is the formula for the inverse processes to the above ones. Using the hard-thermal-loop resummation scheme, we include the contribution from the coherent processes. The decay/production of a neutrino causes an evolution of its spatial distribution. A scheme for dealing with this evolutio…
We conjecture that the confinement- deconfinement phase transition in QCD at large number of colors $N$ and $N_f\ll N$ at $T\neq 0$ and $μ\neq 0$ is triggered by the drastic change in $θ$ behavior. The conjecture is motivated by the holographic model of QCD where confinement -deconfinement phase transition indeed happens precisely at $T=T_c$ where $θ$ dependence experiences a sudden change in behavior. The conjecture is also supported by quantum field theory arguments when the instanton calculations (which trigger the $θ$ dependence) are under complete theoretical control for $T>T_c$, suddenly…
One of the fundamental objectives of experiments with ultrarelativistic heavy ions is to explore strongly interacting matter at high density and high temperature. In this investigation we study in particular the information which can be obtained by analyzing baryonic and mesonic resonances. The decay products of these resonances carry information on the resonances properties at the space time point of their decay. We especially investigate the percentage of reconstructable resonances as a function of density for heavy ion collisions in the energy range between $E_{lab}$ = 30 AGeV and $\sqrt{s}…
We estimate the electrical and thermal conductivities of hot and dense hadronic matter in the relaxation time approximation of the Boltzmann equation. We estimate the thermodynamical quantities of hot and dense hadronic matter within the ambit of the excluded volume hadron resonance gas model. The relaxation time for all the hadrons is estimated assuming the constant cross section with uniform as well as mass dependent hard-core radius. We compare our results with various existing results. Finally we give an estimate of electrical and thermal conductivities in the context of heavy ion collisio…
The vector manifestation (VM) was proposed as a novel manifestation of chiral symmetry in which the massless vector meson becomes the chiral partner of pion. In this write-up, I briefly summarize the following main ingredients to formulate the VM in hot and/or dense matter: Effective field theory (EFT) based on the hidden local symmetry; Wilsonian matching between the EFT and QCD; Intrinsic thermal and/or dense effects.
Pions may remain stable under certain conditions in a dense media at zero temperature in the normal phase (non pion superfluid state). The stability condition is achieved when the in-media pion width vanishes. However, thermal fluctuations will change this stable regime. For low temperature pions will remain in a metastable state. Here we discuss the different possible scenarios for leptonic pion decays at finite temperature, taking into account all the different chemical potentials involved. The neutrino emission due to pions in a hot-dense media is calculated, as well as the coolig rate of a…
The dispersion relation of $ρ$ meson in both timelike and spacelike regimes in hot and dense nuclear medium is analyzed and compared with $σ$ meson based on the quantum hadrodynamics model. The pole and screening masses of $ρ$ and $σ$ are discussed. The behavior of screening mass of $ρ$ is different from that of $σ$ due to different Dirac- and Fermi-sea contributions at finite temperature and density.
Chiral restoration phase transition in hot and/or dense hadronic matter is discussed in terms of the BR scaling based on chiral symmetry and scale anomaly of QCD. The precise connection between the scalar field that figures in the trace anomaly and the sigma field that figures in the linear $σ$ model is established. It is suggested that in hot and/or dense medium, the nonlinear $σ$ model linearizes with the help of a dilaton to a linear $σ$ model with medium-renormalized constants. The relevance of Georgi's vector symmetry and/or Weinberg's ``mended symmetry" in chiral restoration is pointed o…
In this talk I summarize main features of the vector manifestation (VM) which was recently proposed as a novel manifestation of the Wigner realization of chiral symmetry in which the symmetry is restored at the critical point by the massless degenerate pion (and its flavor partners) and the rho meson (and its flavor partners) as the chiral partner. I show how the VM is realized in hot and dense QCD using the effective field theory of QCD based on the hidden local symmetry.
Electric conductivity of hot and dense nuclear matter
本研究基于矢量主导模型与强子多体理论，通过电磁谱函数零能极限计算高温高密强子物质电导率，分析了其随温度和重子化学势的变化及相变线上的取值。
We discuss the thermoelectric effect of hot and dense hadron gas within the framework of the hadron resonance gas model. Using the relativistic Boltzmann equation within the relaxation time approximation we estimate the Seebeck coefficient of the hot and dense hadronic medium with a gradient in temperature and baryon chemical potential. The hadronic medium in this calculation is modeled by the hadron resonance gas (HRG) model with hadrons and their resonances up to a mass cutoff $Λ\sim 2.6$ GeV. We also extend the formalism of the thermoelectric effect for a nonvanishing magnetic field. The pr…
We review the proposal to resum the physics of hard thermal loops in the thermodynamics of the quark-gluon plasma through nonperturbative expressions for entropy and density obtained from a Phi-derivable two-loop approximation. A comparison with the recently solved large-N_f limit of hot QCD is performed, and some updates, in particular on quark number susceptibilities, are made.
Different types of non-Abelian vortex-strings appear in dense or hot QCD, both of which possess non-Abelian internal orientation zero modes. We calculate the interaction between them and find the universal repulsion for dense QCD (color superconductivity) and the dependence on the orientations for hot QCD (chirally broken phase). This is a review article based on our papers arXiv:0708.4092 and arXiv:0708.4096.
We calculate the scattering rate of low energy neutrinos in hot and dense neutron matter encountered in neutrons stars and supernova in the hydrodynamic regime. We find that the Brillouin peak, associated with the sound mode, and the Rayleigh peak, associated with the thermal diffusion mode, dominate the dynamic structure factor. Although the total scattering cross section is constrained by the compressibility sum rule, the differential cross-section calculated using the hydrodynamic response function differs from results obtained in approximate treatments often used in astrophysics such as ra…
Due to their penetrating nature, electromagnetic probes, i.e., lepton-antilepton pairs (dileptons) and photons are unique tools to gain insight into the nature of the hot and dense medium of strongly-interacting particles created in relativistic heavy-ion collisions, including hints to the nature of the restoration of chiral symmetry of QCD. Of particular interest are the spectral properties of the electromagnetic current-correlation function of these particles within the dense and/or hot medium. The related theoretical investigations of the in-medium properties of the involved particles in bo…
Starting from the Kubo formula and the the QCD low energy theorem, we study the the bulk viscosity of hot dense quark matter in the PNJL model from the equation of state . We show that the bulk viscosity has a sharp peak near the chiral phase transition, and the ratio of bulk viscosity over entropy rises dramatically in the vicinity of the phase transition. These results agrees with that from lattice and other model calculations. In addition, we show that the increase of chemical potential raises the bulk viscosity.
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