Sourendu Gupta, Rishi Sharma
We present an effective field theory model for QCD at finite temperature with quarks. We discuss the mean field theory, the fixing of parameters, and a prediction for the curvature of the critical line. We proceed to write down a pionic theory of fluctuations around the mean field, and discuss how the parameters of this pionic effective theory descend from the model with quarks.
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I review recent developments in QCD thermodynamics and collective excitations from the hard-thermal-loop effective theory. I begin by motivating the discussion with open questions from heavy-ion collisions. I then discuss a finite-temperature and -density calculation of QCD thermodynamics at NNLO from the hard-thermal-loop perturbation theory. Finally I discuss a recent exploration of generalizing the hard-thermal-loop framework to the (chromo)magnetic scale $g^2T$, from which a novel massless mode is uncovered.
Thermal monopoles, identified after Abelian projection as magnetic currents wrapping non-trivially around the thermal circle, are studied in $N_f = 2+1$ QCD at the physical point. The distribution in the number of wrappings, which in pure gauge theories points to a condensation temperature coinciding with deconfinement, points in this case to around 275 MeV, almost twice the QCD crossover temperature $T_c$; similar indications emerge looking for the formation of a percolating current cluster. The possible relation with other non-perturbative phenomena observed above $T_c$ is discussed.
We present results of modeling the temperature dependence of the spatial string tension and thermal phase transition in a five-dimensional framework nowadays known as AdS/QCD. For temperatures close to the critical one we find a behaviour remarkably consistent with the lattice results.
We study QCD at finite temperature in the presence of imaginary electric fields. In particular, we determine the electric susceptibility, the leading coefficient in the expansion of the QCD pressure in the imaginary field. Unlike for magnetic fields, at nonzero temperature this coefficient requires a non-trivial separation of genuine electric field-related effects and spurious effects related to the chemical potential, which becomes an unphysical gauge parameter in this setting. Our results are based on lattice simulations with stout improved dynamical staggered quarks at physical quark masses…
In mean field approximation, the grand canonical potential of SU(3) Polyakov linear-$σ$ model (PLSM) is analysed for chiral phase-transition, $σ_l$ and $σ_s$ and for deconfinement order-parameters, $ϕ$ and $ϕ^*$ of light- and strange-quarks, respectively. Various PLSM parameters are determined from the assumption of global minimization of the real part of the potential. Then, we have calculated the subtracted condensates ($Δ_{l,s}$). All these results are compared with recent lattice QCD simulations. Accordingly, essential PLSM parameters are determined. The modelling of the relaxation time is…
We present lattice non-relativistic QCD calculations of bottomonium correlation functions at temperatures $T \simeq 150-350$ MeV. The correlation functions were computed using extended bottomonium operators, and on background gauge-field configurations for 2+1-flavor QCD having physical kaon and nearly-physical pion masses. We analyzed these correlation functions based on simple theoretically-motivated parameterizations of the corresponding spectral functions. The results of our analyses are compatible with significant in-medium thermal broadening of the ground state S- and P-wave bottomonia.
We present results for correlators and spectral functions of open charm mesons using 2+1 flavours of clover fermions on anisotropic lattices. The D mesons are found to dissociate close to the deconfinement crossover temperature Tc. Our preliminary results suggest a shift in the thermal D meson mass below Tc. Mesons containing strange quarks exhibit smaller thermal modifications than those containing light quarks.
We present results from numerical studies of the NJL model with two massless quarks at nonzero temperature. We show that the model undergoes a second order chiral phase transition which belongs to the 3d O(4) spin model universality class.
Thermal QCD phase transition with dynamical chiral fermions
本文通过overlap费米子格点模拟研究有限温度下QCD的性质，该离散化在有限格距下保持手征对称性，并给出了格点公式细节、手征可观测量初步结果及系统在手征热相变附近的行为。
We study properties of the thermal transition in QCD, using anisotropic, fixed-scale lattice simulations with $N_f = 2+1$ flavours of Wilson fermion. Observables are compared for two values of the pion mass, focusing on chiral properties. Results are presented for the Polyakov loop, various susceptibilities, the chiral condensate and its susceptibility, and the onset of parity doubling in the light and strange baryonic sector.
We discuss information on thermal modifications of hadron properties which can be extracted from the structure of Euclidean correlation functions of hadronic currents as well as more direct information obtained through the reconstruction of the spectral functions based on the Maximum Entropy Method.
We present a lattice QCD calculation with two dynamical flavors of the isovector vector correlator in the high-temperature phase. We analyze the correlator in terms of the associated spectral function, for which we review the theoretical expectations. In our main analysis, we perform a fit for the difference of the thermal and vacuum spectral functions, and we use an exact sum rule that constrains this difference. We also perform a direct fit for the thermal spectral function, and obtain good agreement between the two analyses for frequencies below the two-pion threshold. Under the assumption …
The effective action for hard thermal loops in QCD is related to a gauged WZNW theory. Some of the technical issues of this approach are clarified and the Hamiltonian formulation is presented. The two-point correlation function for the induced current in QCD is obtained; some simplifications of the dynamics of the longitudinal modes are also pointed out.
Thermal Field Theory in the Presence of a Background Magnetic Field and its Application to QCD
本文探讨了背景磁场下热场论的理论框架及其在QCD等离子体中的应用，分析了热磁QCD介质的热力学特性与动态行为。
The infamous sign problem makes it impossible to probe dense (baryon density $μ_B>0$) QCD at temperatures near or below the deconfinement threshold. As a workaround, one can explore QCD-like theories such as two-colour QCD (QC2D) which don't suffer from this sign problem but are qualitively similar to real QCD. Previous studies on smaller lattice volumes have investigated deconfinement and colour superfluid to normal matter transitions. In this study we look at a larger lattice volume $N_s=24$ in an attempt to disentangle finite volume and finite temperature effects. We also fit to a larger nu…
Chiral and deconfinement thermal transitions at finite quark spin polarization in lattice QCD simulations
本文利用格点QCD模拟研究有限夸克自旋密度对手征与退禁闭热交叉的影响，发现两者温度均随自旋势递减，并给出物理夸克质量下的抛物线曲率。
Thermal field theory and the QCD Equation of State
本文通过热有效场论研究有限温度和密度下QCD的方程状态及相图。
We calculate the thermodynamic functions of a quark-gluon plasma for general N_c and N_f to three-loop order using hard-thermal-loop perturbation theory. At this order, all the ultraviolet divergences can be absorbed into renormalizations of the vacuum, the HTL mass parameters, and the strong coupling constant.We show that at three loops, the results for the pressure and trace anomaly are in very good agreement with recent lattice data down to temperatures T~2T_c.
We study the gravity dual of a thermal gauge theory whose behavior parallels that of thermal QCD in the far IR. The UV of our theory has infinite degrees of freedom. We holographically renormalize the supergravity action to compute the stress tensor of the dual gauge theory with fundamental flavors incorporating the logarithmic running of the gauge coupling. From the stress tensor we obtain the shear viscosity and the entropy of the medium at a temperature T, and investigate the violation of the bound for the viscosity to the entropy ratio. This is a shortened and simplified companion paper to…
I discuss how the initial conditions for QGP-production in ultrarelativistic heavy ion collisions at the LHC and RHIC can be computed from perturbative QCD.
Thermodynamic properties of the QCD nonperturbative vacuum with two light quarks are studied. It is shown that at low temperatures T<M_πrelativistic massive pions can be treated within the dilute gas approximation. Analytic temperature dependence of the quark condensate is found in perfect agreement with the numerical calculations obtained at the three-loop level of the chiral perturbation theory with non-zero quark mass. The gluon condensate slightly varies with the increase of the temperature. It is shown that the temperature derivatives of the anomalous and normal (quark massive term) contr…
Thermal quarks and Polyakov loops in two-color dense QCD
本文研究密集双色QCD中热激发的特性，通过聚变环和双夸克间隙分析，揭示了热物质中强子主导的特性。
A new perspective on thermal transition in QCD
本文提出基于部分退禁闭图像的新方法分析QCD热相变，通过WHOT-QCD格点构型发现Polyakov线在低温下遵循Haar随机分布，并识别出介于完全禁闭与完全退禁闭之间的中间相，瞬子凝聚证据进一步支持该三相结构。
The thermal response of the hot QCD matter has been studied in the presence of a time-varying magnetic field. The impact of magnetic field, its time dependence, and the collision aspects of the medium on thermal transport have been studied within the relativistic kinetic theory. The decay time of the magnetic field in the medium seems to have a strong dependence on thermal conductivity. The applicability of the Wiedemann-Franz law for the QCD medium has been investigated in the presence of time-varying external electromagnetic fields. The phenomenological significance of thermal transport in h…
The hypothesis is investigated, that the thermal structure of QCD phases at and near zero chemical potentials is determined by long range coherence, inducing the gauge boson pair condensate, and its thermal extension, representing a fundamental order parameter.The condensate does not produce any latent heat as it vanishes at the critical temperature inducing a second order phase transition with respect to energy density neglecting eventual numerically small critical exponents. Localization and delocalization of color fields are thus separated by a unique critical temperature.
We argue that the chiral phase transition and the deconfinement phase transition in finite temperature QCD are just different limits of a single crossover phase transition driven by the lightest scalar field which is a mixture of the glueball and the sigma meson. The key mechanism, the level repulsion between the sigma and the glueball, gives not only a unified description of the finite temperature phase transitions, but also a consistent characterization of the entire QCD phase diagram in the temperature-quark mass plane.
We calculate the bulk viscosity, drag force and jet quenching parameter in Improved Holographic QCD. We find that the bulk viscosity rises near the phase transition but does not exceed the shear viscosity. The drag force shows the effects of asymptotic freedom both as a function of velocity and temperature. It indicates diffusion times of heavy quarks in rough agreement with data. The jet quenching parameter values computed via the light-like Wilson loop are in the lower range suggested by data.
We propose a new method to investigate the thermal properties of QCD with a small quark chemical potential $μ$. Derivatives of the phase transition point with respect to $μ$ are computed at $μ=0$ for 2 flavors of p-4 improved staggered fermions with $ma=0.1,0.2$ on a $16^3\times4$ lattice. The resulting Taylor expansion is well behaved for the small values of $μ_{\rm q}/T_c\sim0.1$ relevant for RHIC phenomenology, and predicts a critical curve $T_c(μ)$ in reasonable agreement with estimates obtained using exact reweighting. In addition, we contrast the case of isoscalar and isovector chemical …
The conventional results for hard thermal loops, which are the building blocks of resummed perturbation theory in thermal field theories, have collinear singularities when external momenta are light-like. It is shown that by taking into account asymptotic thermal masses these singularities are removed. The thus improved hard thermal loops can be summarized by compact gauge-invariant effective actions, generalizing the ones found by Taylor and Wong, and by Braaten and Pisarski.
Thermalization of a heavy quark near rest is controlled by the correlator of two electric fields along a temporal Wilson line. We address this correlator within real-time, classical lattice Yang-Mills theory, and elaborate on the analogies that exist with the dynamics of hot QCD. In the weak-coupling limit, it can be shown analytically that the dynamics on the two sides are closely related to each other. For intermediate couplings, we carry out non-perturbative simulations within the classical theory, showing that the leading term in the weak-coupling expansion significantly underestimates the…
We study an 't Hooft anomaly of massless QCD at finite temperature. With the imaginary baryon chemical potential at the Roberge-Weiss point, there is a $\mathbb{Z}_2$ symmetry which can be used to define confinement. We show the existence of a mixed anomaly between the $\mathbb{Z}_2$ symmetry and the chiral symmetry, which gives a strong relation between confinement and chiral symmetry breaking. The anomaly is a parity anomaly in the QCD Lagrangian reduced to three dimensions. It is reproduced in the chiral Lagrangian by a topological term related to Skyrmion charge, matching the anomaly befor…
NLO and LPM-resummed computations of thermal dilepton production from a hot QCD plasma are reviewed. An interpolation applicable for all positive photon invariant masses is presented, and possibilities for comparisons with lattice and experimental data are pointed out.
We discuss divergences of loop functions in thermal QCD and compute perturbatively the Polyakov loop, the Polyakov loop correlator and the cyclic Wilson loop. We show how these functions get mixed under renormalization.
Naively resummed perturbative approximations to the thermodynamic functions of QCD do not converge at phenomenologically relevant temperatures. Here we review recent results of a three-loop hard-thermal-loop perturbation theory calculation of the thermodynamic functions of a quark-gluon plasma for general N_c and N_f. We show comparisons of our recent results with lattice data from both the hotQCD and Wuppertal-Budapest groups. We demonstrate that the three-loop hard-thermal-loop perturbation result for QCD thermodynamics agrees with lattice data down to temperatures T ~ 2 T_c.
Classical transport theory is employed to analyze the hot quark-gluon plasma at the leading order in the coupling constant. A condition on the (covariantly conserved) color current is obtained. {}From this condition, the generating functional of hard thermal loops with an arbitrary number of soft external bosonic legs can be derived. Our approach, besides being more direct than alternative ones, shows that hard thermal loops are essentially classical.
In this talk, I review new developments of QCD calculations of photon and dilepton production rates in a Quark-Gluon plasma. All the rates are now known up to $O(α_s)$ both for photons and dileptons, thanks to the resummation of multiple scatterings. For dileptons, a direct numerical calculation on the lattice attempted recently will also be discussed.
We perform a joint jet tomographic analysis of the data on the nuclear modification factor $R_{AA}$ from PHENIX at RHIC and ALICE at LHC. The computations are performed accounting for radiative and collisional parton energy loss with running coupling constant. Our results show that the observed slow variation of $R_{AA}$ from RHIC to LHC indicates that the QCD coupling constant is suppressed in the quark-gluon plasma produced at LHC.
Thermal phase transitions in rotating QCD with dynamical quarks
本文首次用格点方法研究含N_f=2动力学clover改进Wilson夸克的旋转QCD，发现胶子与费米子旋转对临界温度作用相反，但总体上赝临界温度随角速度增大而升高。
We investigate the thermal QCD phase transition and its scaling properties on the lattice. The simulations are performed with $N_f=2+1+1$ Wilson twisted mass fermions at pion masses from physical up to heavy quark regime. We introduce a novel chiral order parameter, which is free from linear mass contributions and turns out to be very useful for the study of scaling behaviour. Our results are compatible with $O(4)$ universal scaling for the physical pion mass and the temperature range $[120:300]$ MeV. Violations to scaling at larger masses and other possible scenarios, including mean field beh…
We estimate the thermal width of a heavy quark anti-quark pair inside a strongly coupled plasma using a holographic AdS/QCD model. The imaginary part of the quark potential that produces the thermal width appears in the gravity dual from quantum fluctuations of the string world sheet in the vicinity of the horizon. The results, obtained using a soft wall background that involves an infrared mass scale, are consistent with previous analisys where the mass scale was introduced by averaging over quark anti-quark states.
We present a self-consistent determination of the screening mass for chromomagnetic fields in QCD within the framework of dimensional reduction. The three-dimensional Chern-Simons density is used as a mass term for a self-consistent perturbative calculation that yields a value of m ~ 1.604 g^2 N/2pi for the magnetic screening mass.
We discuss the entropy carried by a quark-antiquark pair, in particular across the deconfinement transition. We therefore rely on a self-consistent solution to Einstein-Maxwell-dilaton gravity, capable of mimicking essential features of QCD. In particular we introduce a novel model that still captures well the QCD confinement and deconfinement phases, while allowing the introduction of a temperature in a phase which resembles the confined phase, this thanks to it being dual to a small black hole. We pay due attention to some subtleties of such model. We confirm the lattice picture of a strong …
We have computed the charge and heat transport coefficients of hot QCD matter by solving the relativistic Boltzmann transport equation using the BGK model approximation with a modified collision integral in the weak magnetic field regime. This modified collision integral enhances both charge and heat transport phenomena which can be understood by the large values of the above-mentioned coefficients in comparison to the relaxation collision integral. We have also presented a comparative study of coefficients like the electrical conductivity ($σ_{el}$), Hall conductivity ($σ_{H}$), thermal condu…
We present the first study of the thermal effects on the quark-gluon mixed condensate g<\bar{q} σG q>, which is another chiral order parameter, in SU(3)c lattice QCD with the Kogut-Susskind fermion at the quenched level. Using the lattices at β=6.0, 6.1, 6.2 in high statistics, we calculate the mixed condensate as well as the quark condensate in the chiral limit for the temperature 0MeV <= T <= 500MeV. Except for the sharp decrease of both the condensates around T_c \simeq 280MeV, the thermal effects are found to be weak below T_c. We also find that the ratio m_0^2 = g<\bar{q} σG q>/ <\bar{q}q…
In the present work, the temperature dependence of the scalar mesons parameters is investigated in the framework of thermal QCD sum rules. We calculate sigma-pole and the non-resonant two-pion continuum contributions to the spectral density. Taking into account additional operators appearing at finite temperature, the thermal QCD sum rules are derived. The temperature dependence of the shifts in the mass and leptonic decay constant of scalar sigma(600) meson is calculated.
In this proceedings, I consider two-loop contributions to real photon production in thermal QCD. If the photon is strictly massless, strong collinear divergences appear in this calculation. These singularities are regularized by the quark thermal mass of order $gT$, which generates powers of $1/g$, so that the corresponding terms are strongly enhanced with respect to naive expectations of their order of magnitude.
Thermal axion production in QCD from the lattice
本文提出用欧几里得晶格QCD直接计算光锥上拓扑荷密度谱函数的加权积分，从而无需解析延拓即可获得早期宇宙热轴子产生率，并在纯胶子QCD中验证了可行性。
These lectures give an introduction to thermal perturbation theory, hard thermal loops, and their use in a nonperturbative, approximately self-consistent resummation of the thermodynamical potentials of quantum chromodynamics.
Perturbative calculations of corrections to the behavior of an ideal gas of quarks and gluons, the limit that is formally realized at infinite temperature, are obstructed by severe infrared divergences. The limits to computability that the infrared problem poses can be overcome in the framework of dimensionally reduced effective theories. Here, we give details on the evaluation of the highest perturbative coefficient needed for this setup, in the continuum.
Based on the IR-improved bulk holographic AdS/QCD model which provides a consistent prediction for the mass spectra of resonance scalar, pseudoscalar, vector and axial vector mesons, we investigate its finite temperature behavior. By analyzing the spectral function of mesons and fitting it with a Breit-Wigner form, we perform an analysis for the critical temperature of mesons. The back-reaction effects of bulk vacuum are considered, the thermal mass spectral function of resonance mesons is calculated based on the back-reaction improved action. A reasonable melting temperature is found to be $T…
We report on a continuum extrapolation of the vector current correlation function for light valence quarks in the deconfined phase of quenched QCD. This is achieved by performing a systematic analysis of the influence of cut-off effects on light quark meson correlators at $T\simeq 1.45 T_c$ using clover improved Wilson fermions. We discuss resulting constraints on the electrical conductivity and the thermal dilepton rate in a quark gluon plasma. In addition new results at 1.2 and 3.0 $T_c$ will be presented.
A holographic model of probe vector mesons (quarkonia) is presented, where the dynamical gravity-dilaton background is adjusted to the thermodynamics of 2 +1 flavor QCD with physical quark masses. The vector meson action is modified to account for various quark masses. We focus on the $Φ$, $J/ψ$ and $Υ$ meson melting in agreement with hadron phenomenology in heavy-ion collisions at LHC, that is the formation of hadrons at the observed freeze-out temperature of 155 MeV.
Enthalpy-Based Thermal Response and Its Exact Relation to the Speed of Sound in Finite-Temperature QCD
本研究针对QCD相变的非微扰特性，构建焓的热力学标度框架，定义反常热维度h(T)，经格点QCD数据验证，揭示其对有限夸克质量标度破缺的敏感性，建立量子标度反常与信息几何曲率的新关联。
A comprehensive determination of the quark mass dependence in the dispersion relations of thermal excitations of gluons and quarks in non-Abelian gauge theory (QCD) is presented for the one-loop approximation in Feynman gauge. Larger values of the coupling are admitted, and the gauge dependence is discussed. In a Dyson-Schwinger type approach, the effect of higher orders is estimated for asymptotic thermal masses.
Recent progress of lattice investigations in thermal physics is summarized in this contribution. Hadronic spectral functions can be reconstructed from correlation functions in Euclidean time based on the Maximum Entropy Method without a priori assumptions on the spectral shape. The thermal modifications of hadron properties are investigated in the scalar, pseudo-scalar, vector and axial-vector channels near and above the deconfinement transition temperature for charmonium systems as well as for light quarks. Moreover, the reconstructed vector meson spectral function allows to extract the therm…
Classical transport theory for colored particles is reviewed and used to derive the hard thermal loops of QCD. A perturbative study of the non-Abelian transport equations that preserves their gauge symmetry is used to compute the induced color current in a hot quark-gluon plasma. From this approach the effective action of hard thermal loops can be derived. This derivation is more direct than alternative ones based on perturbative quantum field theory, and shows that hard thermal effects in hot QCD are essentially classical.
We consider thermal QCD in the large N_C limit, mainly in 1+1 dimensions. The gauge coupling is only taken into account to minimal order, by projection onto colour singlets. An expression for the free energy, exact as N_C goes to infinity, is then obtained. A third order phase transition will occur. The critical temperature depends on the ratio N_C/L, where L is the (infinite) spatial length. In the high temperature limit, the free energy will approach the same value as in the free theory, whereas we have a mesonic like phase at low temperature. Expressions for the quark condensate, <\barΨΨ>, …
Classical transport theory for colored particles is investigated and employed to derive the hard thermal loops of QCD. A formal construction of phase-space for color degrees of freedom is presented. The gauge invariance of the non-Abelian Vlasov equations is verified and used as a guiding principle in our approximation scheme.We then derive the generating functional of hard thermal loops from a constraint satisfied at leading-order by the color current. This derivation is more direct than alternative ones based on perturbative quantum field theory, and shows that hard thermal effects in hot QC…
Charmonium properties at high temperatures from lattice QCD
利用格点QCD研究高温下介子性质，通过计算扩展介子算符的相关函数，发现所有低于开底夸克阈值的charmonium态在该温度范围内存在，但随温度升高热宽度显著增加，且热宽度大小遵循charmonium大小的层次结构。
We use the method of thermal QCD sum rules to investigate the effects of temperature on the neutron electric dipole moment d_n induced by the vacuum \barθ-angle. Then, we analyze and discuss the thermal behaviour of the ratio {d_n \over \barθ} in connection with the restoration of the strong CP symmetry breaking.
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