Y. Schroder
In this talk we review the status concerning vacuum integrals needed in perturbative expansions of QCD at non-zero temperature. We will focus on the differences as compared to familiar zero-temperature techniques, and provide a list of known basic master integrals.
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It is argued why quasiparticle models can be useful to describe the thermodynamics of hot QCD excluding, however, the case of a large number of flavors, for which exact results have been calculated by Moore.
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 review recent progress made in determining the pressure of hot QCD up to the first non-perturbative term in its weak-coupling expansion.
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.
Various mechanisms of thermal photon production are reviewed and their implications for heavy ion collisions are briefly sketched.
The effective amplitudes for gluon momentum p<<gT in hot QCD exhibit damping as a result of collisions. The whole set of n-point amplitudes is shown to be generated from one functional K(x,y;A), in addition to the induced current j(x;A).
Hot scalar electrodynamics is adopted as a toy model for a hot gluon plasma to display some aspects of the compulsory resummation of hard thermal loops when next-to-leading order quantities at soft momentum scales are to be calculated. [Talk given by A.K.R. at a one-day meeting dedicated to the memory of Tanguy ALTHERR, held on November 4, 1994 at CERN, Geneva. To appear in a Gedenkschrift published by World Scientific.]
I present an effective classical theory which describes the non-perturbative real-time dynamics in hot gauge theories and has the potential for numerical implementation.
The goal of this paper is two-fold. The first aim is to present a detailed version of the computation of the two-loop renormalization of the magnetic coupling in hot QCD. The second is to compare with lattice simulations the string tension of a spatial Wilson loop using the result of our two-loop computation
By using conformable fractional of the Nikiforov-Uvarov (CF-NU) method, the radial Schrodinger equation is analytically solved. The energy eigenvalues and corresponding functions are obtained, in which the dependent temperature potential is employed. The effect of fraction-order parameter is studied on heavy-quarkonium masses such as charmonium and bottomonium in a hot QCD medium in the 3D and the higher dimensional space. A comparison is studied with recent works. We conclude that the fractional-order plays an important role in a hot QCD medium in the 3D and higher-dimensional space.
These lectures start with a brief overview of salient features of the critical region of hot QCD. The main emphasis is on the accurate description of static plasma observables by the well-known hierarchy of reduced actions combined with 3D simulations above T\sim 2T_c. A striking pattern emerges, put in perspective by completing the quasi-particle picture
Using an approach developed in the context of zero-temperature QCD to systematically sum higher order effects whose form is fixed by the renormalization group equation, we sum to all orders the leading log (LL) and next-to-leading log (NLL) contributions to the thermodynamic free energy in hot QCD. While the result varies considerably less with changes in the renormalization scale than does the purely perturbative result, a novel ambiguity arises which reflects the strong scheme dependence of thermal perturbation theory.
Using a program of perturbative resummation I compute the damping rates for fields at nonzero spatial momentum to leading order in weak coupling in hot $QCD$. Sum rules for spectral densities are used to simplify the calculations. For massless fields the damping rate has an apparent logarithmic divergence in the infrared limit, which is cut off by the screening of static magnetic fields (``magnetic mass''). This demonstrates how at high temperature even perturbative quantities are sensitive to nonperturbative phenomenon.
In a recent paper (arXive:hep-ph/0406125) entitled {\em Parity violation in hot QCD: why it can happen, and how to look for it}, D. Kharzeev argues for the possibility of P- and/or CP- violation effects in heavy-ion collisions, the effects that can manifest themselves via asymmetry in $π^{\pm}$ production with respect to the direction of the system angular momentum. Here we present an experimental observable that can be used to detect and measure the effects.
We extend our earlier work on static color singlet correlators in high T QCD (DeTar correlators) to baryonic and gluonic sources, and estimate the corresponding screening masses using the dimensionally reduced theory. We discuss spin and polarization dependence of meson and baryon masses in the $T \rightarrow \infty$ limit, and possible nonperturbative effects at non-asymptotic temperatures.
We determine the quark damping rates in the context of next-to-leading order hard-thermal-loop summed perturbation of high-temperature QCD where weak coupling is assumed. The quarks are ultrasoft. Three types of divergent behavior are encountered: infrared, light-cone and at specific points determined by the gluon energies. The infrared divergence persists and is logarithmic whereas the two others are circumvented.
Magnetic quasi-particles in hot QCD predict Casimir scaling for the tension $σ$ of spatial Wilson loops. Recently this scaling has been verified on the lattice to 1--2% precision. We review how spatial loops tell us about the nature of the plasma state. The strong first order nature for more than five colours and the fast drop of the topological susceptibilty at $T_c$ found in simulations of hot quenched QCD are consistent with a quasi-particle picture valid down to the critical temperature. The magnetic quasi-particles will Bose condense in the ground state below $T_c$, and may behave like a …
The gluon collisional width in hot QCD plasmas is discussed with emphasis on temperatures near $T_c$, where the coupling is large. Considering its effect on the entropy, which is known from lattice calculations, it is argued that the width, which in the perturbative limit is given by $γ\sim g^2 \ln(1/g) T$, should be sizeable at intermediate temperatures but has to be small close to $T_c$. Implications of these results for several phenomenologically relevant quantities, such as the energy loss of hard jets, are pointed out.
Certain spacelike mesonic correlation lengths serve as interesting theoretical probes for the reliability of perturbation theory in high-temperature QCD, are directly sensitive to chiral symmetry restoration and to the axial anomaly, and might also have indirect phenomenological signatures in idealised heavy ion collision experiments. I review here the weak-coupling predictions for some of these correlation lengths, to be compared with results from lattice Monte Carlo simulations.
In this article, we present analytical expansion results of two single mass scale four-loop vacuum integrals in d=3-2*ep dimensions. After finding hypergeometric representations with half-integer coefficients, we use algorithms which we implemented in FORM to expand these in terms of nested sums.
The dimensionally reduced action is believed to provide for a theoretically consistent and numerically precise effective description of the thermodynamics of the quark-gluon plasma, once the temperature is above a few hundred MeV. Although dramatically simpler than the original QCD it is, however, still a strongly interacting, confining theory. In this talk I speculate on whether there could exist a further simplified recipe within that theory, for physically relevant temperatures, which would already lead to a phenomenologically satisfactory description of the free energy and various correlat…
Within the framework of perturbative resummation scheme of Pisarski and Braaten, the decay- or damping-rate of a moving heavy quark (muon) to leading order in weak coupling in hot QCD (QED) is examined. Although, as is well known, the conventionally-defined damping rate diverges logarithmically at the infrared limit, shown is that no such divergence appears in the physically measurable decay rate. The cancellation occurs between the contribution from the \lq\lq real'' decay diagram and the contribution from the diagrams with \lq\lq thermal radiative correction''.
Within the framework of the effective theory for ultrasoft field modes a problem of interacting an energetic color particle with ultrasoft fluctuations in hot gluon plasma is considered. The procedure of calculation of certain effective current generating the process of interaction is proposed, and the problem of its gauge independence is discussed. The application of the theory developed to the problem of energy losses of the energetic color particle propagating through hot QCD-medium is given. It is shown that the perturbation approach for calculation of energy losses breaks down at the ultr…
The gluon and quark collisional widths in hot QCD plasmas are discussed with emphasis on temperatures near Tc, where the coupling is large. Considering the effect on the entropy, which is known from lattice calculations, it is argued that the width of the partons, which in the perturbative limit is given by gamma ~ g^2 ln(1/g) T, should be sizeable at intermediate temperatures but has to be small close to Tc. This behavior implies a substantial reduction of the radiative energy loss of jets near Tc.
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.
We compute the pressure and entropy of hot QCD in the limit of large number of fermions, N_f >> N_c ~ 1, to next to leading order in N_f. At this order the calculation can be done exactly, up to ambiguities due to the presence of a Landau pole in the theory; the ambiguities are O(T^8/Λ^4_{Landau}) and remain negligible long after the perturbative series (in g^2 N_f) has broken down. Our results can be used to test several proposed resummation schemes for the pressure of full QCD.
We discuss various aspects of parity, CP, and time reversal invariances in QCD. In particular, we focus attention on the previously proposed possibility that these experimentally established symmetries of strong interactions may be broken at finite temperature and/or density. This would have dramatic signatures in relativistic heavy ion collisions; we describe some of the most promising signals.
We give a short review on recent progress in the field of automated calculations in finite-temperature field theory, where integration-by-parts techniques have proven (almost) as useful as in the zero-temperature case. Furthermore, we provide one concrete example of an evaluation of a new three-loop master sum-integral that exhibits maximal divergence.
The principles of minimal sensitivity (PMS) criterion is applied to the perturbative free energy density, or pressure, of hot QCD, which include the $\sim g_s^6 \ln g_s$ and part of the $\sim g_s^6$ terms. Applications are made separately to the short- and long-distance parts of the pressure. Comparison with the lattice results, at low temperatures, shows that the resultant `` optimal'' approximants are substantially improved when compared to the $\bar{MS}$ results. In particular, for the realistic case of three quark flavors, the `` optimal'' approximants are comparable with the lattice resul…
We repeat and correct the recent calculation of the thermodynamic potential of hot QCD in the limit of large number N_f of fermions. The new result for the thermal pressure turns out to agree significantly better with results obtained from perturbation theory at small coupling. For large coupling, a nonmonotonic behaviour is reproduced, but the pressure of the strongly coupled theory does not exceed the free pressure as long as the Landau pole ambiguity remains negligible numerically.
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…
In this talk we review how a dilute gas of magnetic monopoles in the adjoint describes the spatial k-Wilson loops. We formulate an effective theory from $S_{MQCD}$ by integrating out dof's down to scales in between the magnetic screening mass and the string tension and relate the 3d pressure and the string tension. Lattice data are consistent with the gas being dilute for all temperatures.
In high temperature QCD, the perturbation theory is plagued with infrared divergences which reflect long-range non-perturbative phenomena. I argue that it is possible to study such phenomena within a classical thermal field theory which can be put on a three-dimensional lattice. The classical theory is an effective theory for the soft, non-perturbative modes, as obtained after integrating out the hard modes in perturbation theory. It is well suited for numerical studies of the non-perturbative real-time dynamics, which cannot be studied within the standard, imaginary-time formulations of latti…
We analyse the QCD chiral phase transition in the nonlinear and linear $σ$-model. The strategy is the same in both cases. We fix the parameters of the effective meson theory at temperature $T=0$ and extrapolate the models to temperatures in the vicinity of the phase transition. The linear $σ$-model in $SU(3)\times SU(3)$ gives a crossover around $T_c\approx190$ MeV. Around this temperature chiral $SU(2)\times SU(2)$ is almost restored. We also calculate meson masses as a function of temperature.
We consider QCD near but above critical temperature Tc. The pressure, susceptibilities and the renormalized Polyakov loop -- which is an order parameter for the deconfining phase transition -- dramatically change up to temperatures a few times Tc. We refer to this region as a "semi"-QGP, where partial confinement plays important role. We show that the shear viscosity ,eta, is suppressed by two powers of the Polyakov loop. This suggests that eta/T^3 decreases markedly as QCD cools down to temperatures near Tc. We also show a ratio of the viscosity to the entropy becomes small near Tc.
We calculate $γ_l(0)$, the damping rate for longitudinal on-shell gluons with zero momentum in hot QCD using the hard-thermal-loop (htl) scheme. We find it to be divergent in the infrared, which means that in this scheme $γ_l(0)$ is different from $γ_t(0)$, the corresponding damping rate for transverse gluons which is known to be finite. This result suggests that the htl scheme is infrared sensitive and thus may need to be improved upon in this sector. We discuss this issue after we present our calculation.
We study the extension of a phenomenologically successful quasiparticle model that describes lattice results of the equation of state of the deconfined phase of QCD for Tc <= T < 4 Tc, to finite quark chemical potential mu. The phase boundary line Tc(mu), the pressure difference (p(T,mu)-p(T,mu=0))/T^4 and the quark number density nq(T,mu)/T^3 are calculated and compared to recent lattice results. Good agreement is found up to quark chemical potentials of order mu = Tc.
Debye screening mass in hot QCD at three loops: Canonical form of the integrand
本研究针对热QCD三圈水平下的德拜屏蔽质量，利用热被积函数典范形式的新进展，重新整理相关计算项，强调积分变量平移的作用，以简化未来高阶计算。
The pressure of hot QCD has recently been determined to the last perturbatively computable order g^6 ln(g) by Kajantie et al. using three-dimensional effective theories. A similar method is applied here to the pressure in the presence of small but non-vanishing quark chemical potentials, and the result is used to derive the quark number susceptibilities in the limit mu = 0. The diagonal quark number susceptibility of QCD with n_f flavours of massless quarks is evaluated to order g^6ln(g) and compared with recent lattice simulations. It is observed that the results qualitatively resemble the la…
In this talk, I present the status of attempts to analyze the behavior of the so-called spatial 't Hooft loop, which can be taken as an order parameter for the deconfinement phase transition in pure SU(N) gauge theory. While lattice data show a strikingly universal scaling of extracted k-string tensions for various values of k and N, the analytic approach to these observables might need some refinement.
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…
We determine the first independent part of the g^6 coefficient in the weak coupling expansion of the QCD pressure at high temperatures, the one proportional to the maximal power of the number of quark flavors N_f. In addition to introducing and developing computational methods that can be used in evaluating other parts of the expansion, our calculation provides a result that becomes dominant in the limit of large N_f and a fixed effective coupling g_{eff}^2 = g^2 N_f/2.
We study shear viscosity in weakly coupled hot pure gauge field QCD theory basing on transport theory and the Kubo formula using the closed time path formalism (CTP) of real time finite temperature field theory. We show that the viscosity can be obtained as the integral of a retarded three-point function. Non-perturbative corrections to the bare one loop result can be obtained by solving a Schwinger-Dyson type integral equation for this vertex. This integral equation represents the resummation of an infinite series of ladder diagrams which all contribute to the leading-log order result. We sho…
I discuss some non-perturbative aspects of hot gauge theories as related to the unscreened static magnetic interactions. I first review some of the infrared divergences which cause the breakdown of the perturbation theory. Then I show that kinetic theory, as derived from quantum field theory, is a powerful tool to construct effective theories for the soft modes, which then can be treated non-perturbatively. The effective theory at the scale $gT$ follows from a collisionless kinetic equation, of the Vlasov type. The effective theory at the scale $g^2T$ is generated by a Boltzmann equation which…
We give a brief review of modern theoretical understanding of the physics of QCD at finite temperature and density. We concentrate in particular on the properties of hadron gas at relatively small temperatures and discuss in details the physics of the phase transition. We argue that the phase transition in temperature is probably absent, but it can appear with a vengeance when finite density effects are taken into account. We notice also that the temperatures one can expect to reach at the heavy ion collider at RHIC are not yet high enough for the perturbation theory in the QCD coupling consta…
The probability distribution D(epsilon) in the energy loss incurred by incoming and outgoing hard quarks in a QCD medium is computed numerically from the BDMPS gluon spectrum. It is shown to follow an empirical log-normal behavior which allows us to give the quenching weight a simple analytic parameterization. The dependence of our results under the infrared and ultraviolet sensitivity of the gluon spectrum is investigated as well. Finally, as an illustration, we discuss and compare estimates for the quenching of hadron spectra in nuclear matter and in a quark-gluon plasma to HERA and RHIC pre…
withdrawn due to detection of numerical errors
I give a physical explanation of what shear viscosity is, and what physics determines its value. Then I explain why determining the shear viscosity of the Quark-Gluon Plasma is interesting. I outline the leading-order calculation of the QGP shear viscosity (and baryon number diffusion constant), explaining why the quite complicated physics of parton splitting and Landau-Pomeranchuk-Migdal interference effects are required for its calculation. Then I briefly explore the range of applicability, emphasizing the importance of plasma instabilities.
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…
With deep learning techniques, the degree of modification of energetic jets that traversed hot QCD medium can be identified on a jet-by-jet basis. Due to the strong correlations between the degree of jet modification and its traversed length in the medium, we demonstrate the power of our novel method to locate the creation point of a dijet pair in the nuclear overlap region. In particular, jet properties, such as jet width and orientation can serve as additional handles to locate the creation points to a higher level of precision, which constitutes a significant development towards the long-st…
Very stringent experimental bounds exist on the amount of P and CP violation in strong interactions. Nevertheless, the presence of non-Abelian topological solutions and the axial anomaly make the issue of CP invariance in QCD non-trivial ("the strong CP problem"). Even in the absence of a global P and CP violation the fluctuations of topological charge in the QCD vacuum are expected to play an important role in the breaking of chiral symmetry, and in the mass spectrum and other properties of hadrons. Here I argue that topological fluctuations in hot QCD matter can become directly observable in…
A recently proposed generating functional allows the construction of the full set of n-point Green functions in QCD at high temperature and at distances larger than 1/gT. One may then learn how the system maintains its thermal equilibrium in the quantum field theory approach, i.e. which process compensates for the important dissipation due to collisions. This system may be characterized by quantities which have a classical limit. One finds that the fluctuations of the coloured field are not gaussian ones. A comparison is made with the semi-classical approach where a random noise is the source …
The entanglement extended Polyakov--Nambu--Jona-Lasinio model at zero chemical potential in the presence of an external magnetic field is studied. The effect of the entanglement parametrization is analyzed, in particular, on the pseudocritical transition temperatures and on the thermodynamical properties of the model. The model predicts that the coincidence or not of both chiral and deconfinement transition temperatures, in the presence of an external magnetic field, depends on the entanglement parametrization chosen.
In this paper we provide an exact formula for the area law of the 't Hooft loop for any SU(N) gauge group to cubic order in hot gauge theory. The correction is very small for all temperatures above $T_c$, in stark contrast to the cubic correction to the pressure. The gradient approximation in a previous paper, only valid for large N, is in excellent agreement with the present, exact evalution. Comparison to lattice data is good. Casimir scaling is violated by a small amount not yet resolved by the precision of lattice data.
We calculate the damping rate for transverse gluons with {\nineti finite} soft momentum to leading order in perturbative hot QCD. The internal momenta of the one-loop contributing diagrams are soft. This means we have to use effective vertices and propagators which incorporate the so-called hard thermal loops. We expand the damping rate in powers of the incoming momentum and argue that the series ought to converge within a finite radius of convergence. We contrast such a behavior with the one obtained from a previous calculation that produced a logarithmic behavior, a calculation based on lett…
We calculate the damping rate $γ_l$ for longitudinal gluons with zero momentum in finite high temperature QCD and show that some of its contributing terms are infrared divergent. This is in contrast with the expectation that this damping rate is to be equal to the corresponding one $γ_t$ for transverse gluons which is known to be finite. Our calculation was motivated by the fact that similar divergent terms occur when we calculated in a previous work $γ_t$ to order $ p^2$, p being the momentum of the gluon. After we present our results, we briefly discuss them.
The pinch technique (PT) is applied to obtain the gauge-independent resummed gluon self-energy in a hot Yang-Mills gas. Calculation is performed at one- loop level in linear gauges which preserve rotational invariance and the res ummed propagators and vertices are used. The effective gluon self-energy, w hich is obtained as the sum of the resummed gluon self-energy and the resumm ed pinch contributions, is not only gauge-independent but also satisfies the transversality relation. Using this gauge-independent effective gluon self- energy, we calculate the damping rate for transverse gluons in t…
We study the critical boundary on the quark-mass plane associated with the chiral phase transition in QCD at finite temperature. We point out that the critical boundaries obtained from the Lattice QCD simulation and the chiral effective model are significantly different; in the (Polyakov-loop coupled) Nambu--Jona-Lasinio (NJL) model we find that the critical mass is about one order of magnitude smaller than the value reported in the Lattice QCD case. It is known in the Lattice QCD study that the critical mass goes smaller in the continuum limit along the temporal direction. To investigate the …
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.
We discuss the recently devised one-loop gap equation for the magnetic mass of hot QCD. An alternative, and one would hope equivalent, gap equation is presented, which however shows no mass generation at the one-loop level.
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