Hard Thermal Loop Effective Theory Research Articles

Soft Interactions in Cold Quark Matter.

Accurate knowledge of the thermodynamic properties of zero-temperature, high-density quark matter plays an integral role in attempts to constrain the behavior of the dense QCD matter found inside neutron-star cores, irrespective of the phase realized inside the stars. In this Letter, we consider the weak-coupling expansion of the dense QCD equation of state and compute the next-to-next-to-next-to-leading-order contribution arising from the non-Abelian interactions among long-wavelength, dynamically screened gluonic fields. Accounting for these interactions requires an all-loop resummation, which can be performed using hard-thermal-loop (HTL) kinematic approximations. Concretely, we perform a full two-loop computation using the HTL effective theory, valid for the long-wavelength, or soft, modes. We find that the soft sector is well behaved within cold quark matter, contrary to the case encountered at high temperatures, and find that the new contribution decreases the renormalization-scale dependence of the equation of state at high density.

Hard loop effective theory of the (anisotropic) quark gluon plasma

The generalization of the hard thermal loop effective theory to anisotropic plasmas is described with a detailed discussion of anisotropic dispersion laws and plasma instabilities. The numerical results obtained in real-time lattice simulations of the hard loop effective theory are reviewed, both for the stationary anisotropic case and for a quark-gluon plasma undergoing boost-invariant expansion.

Fermion mass at next-to-leading order in the hard thermal loop effective theory

The calculation of the real part of a quasiparticle dispersion relation at next-to-leading order in the hard thermal loop effective theory is a very difficult problem. Even though the hard thermal loop effective theory is almost 20 years old, there is only one next-to-leading order calculation of the real part of a quasiparticle dispersion relation in the literature [H. Schulz, Nucl. Phys. B413, 353 (1994)]. In this paper, we calculate the fermion mass in QED and QCD at next-to-leading order. For QED the result is $M=eT/\sqrt{8}(1\ensuremath{-}(1.427\ifmmode\pm\else\textpm\fi{}0.02)e/4\ensuremath{\pi})$ and for QCD with ${N}_{f}=2$ and ${N}_{c}=3$ we obtain $M=gT/\sqrt{6}(1+(1.867\ifmmode\pm\else\textpm\fi{}0.02)g/4\ensuremath{\pi})$.

Energetic dileptons from the quark-gluon plasma

In this paper we study the production of energetic dileptons. We calculate the rate for $2\ensuremath{\rightarrow}2$ processes. The log term is obtained analytically and the constant term is calculated numerically. When the photon mass is of the order of the thermal quark mass, the result is insensitive to the photon mass and the soft logarithmic divergence is regulated by the thermal quark mass, exactly as in the case of real photons. We also consider the production of thermal Drell-Yan dileptons (thermal quark and antiquark pairs annihilating into virtual photons) and calculate the rate systematically in the context of the hard thermal loop effective theory. We obtain analytic and numerical results. We compare our results with those of previous calculations.

Heavy Quark Diffusion in Perturbative QCD at Next-to-Leading Order

We compute the momentum diffusion coefficient of a heavy quark in a hot QCD plasma, to next-to-leading order in the weak-coupling expansion. Corrections arise at [see formula]; physically they represent interference between overlapping scatterings, as well as soft, electric scale (p approximately gT) gauge field physics, which we treat using the hard thermal loop effective theory. In 3-color, 3-flavor QCD, the momentum diffusion constant of a fundamental representation heavy quark at next-to-leading order is kappa = 16pi/3alpha(s)(2)T(3)(ln1/g(s)+0.07428+1.9026 g(s)). The convergence of the perturbative expansion is poor.

Nonlinear dynamics of soft fermion excitations in hot QCD plasma I: Soft-quark–soft-gluon scattering

Within the framework of the hard thermal loop effective theory we derive a system of Boltzmann-like kinetic equations taking into account the simplest processes of nonlinear interaction of soft fermionic and bosonic QCD plasma excitations: elastic scattering of soft-(anti)quark excitations off soft-gluon and soft-quark excitations, pair production of soft quark–antiquark excitations, annihilation into two soft-gluon excitations. The matrix elements of these processes to leading order in the coupling constant g are obtained. The iterative method of calculation of the matrix elements for the higher processes of soft-mode interactions is proposed. The most general expression for the emitted radiant power induced by the effective currents and effective sources in a quark–gluon plasma (QGP) taking into account an existence of fermion sector of plasma excitations is defined. The explicit form of the linearized Boltzmann equation accounting for scattering of color(less) plasminos off color(less) plasmons is written out.

Kinetic-theory approach to gluon self-energy beyond hard thermal loops

We compare the effective dynamics of soft fields, based on temperature field theory, with the mean field dynamics from non-Abelian kinetic theory. We derive the polarization tensor with the leading logarithmic factor log(gT/μ) from the effective Boltzmann–Langevin equation given by Litim and Manuel. The tensor is identical with effective one-loop contributions within the hard thermal loop effective theory.

Enhanced thermal production of hard dileptons by 3→2 processes

In the framework of the Hard Thermal Loop effective theory, we calculate the two-loop contributions to hard lepton pair production in a quark-gluon plasma. We show that the result is free of any infrared and collinear singularity. We also recover the known fact that perturbation theory leads to integrable singularities at the location of the threshold for $q\bar{q}\to\gamma^*$. It appears that the process calculated here significantly enhances the rate of low mass hard dileptons.

Diagrammatic approach to soft non-Abelian dynamics at high temperature

The dynamics of soft (| p |∼ g 2 T) non-Abelian gauge fields at finite temperature is non-perturbative. The effective theory for the soft scale is determined by diagrams with external momenta p 0≲ g 2 T, | p |∼ g 2 T and loop momenta larger than g 2 T. We consider the polarization tensor beyond the hard thermal loop approximation, which accounts for loop momenta of order T. There are higher loop diagrams, involving also the scale gT, which are as important as the hard thermal loops. These higher loop contributions are characteristic for non-Abelian gauge theories and their calculation is simplified by using the hard thermal loop effective theory. Remarkably, the effective one-loop polarization tensor is found to be gauge fixing independent and transverse at leading order in the gauge coupling g. The transversality indicates that this approach leads to a gauge invariant effective theory.

From hard thermal loops to Langevin dynamics

In hot non-Abelian gauge theories, processes characterized by the momentum scale g 2 T (such as electroweak baryon number violation in the very early universe) are non-perturbative. An effective theory for the soft (| p| ∼ g 2T) field modes is obtained by integrating out momenta larger than than g 2 T. Starting from the hard thermal loop effective theory, which is the result of integrating out the scale T, it is shown how to integrate out the scale gT in an expansion in the gauge coupling g. At leading order in g, one obtains Vlasov-Boltzmann equations for the soft field modes, which contain a Gaussian noise and a collision term. The 2-point function of the noise and the collision term are explicitly calculated in a leading logarithmic approximation. In this approximation the Boltzmann equation is solved. The resulting effective theory for the soft field modes is described by a Langevin equation. It determines the parametric form of the hot baryon number violation rate as Γ = κg 10 log(1/ g) gT 4, and it allows for a calculation for κ on the lattice.