Anomalous specific heat in high-density QED and QCD

Long-range quasi-static gauge-boson interactions lead to anomalous (non-Fermi-liquid) behavior of the specific heat in the low-temperature limit of an electron or quark gas with a leading $T\ln T^{-1}$ term. We obtain perturbative results beyond the leading log approximation and find that dynamical screening gives rise to a low-temperature series involving also anomalous fractional powers $T^{(3+2n)/3}$. We determine their coefficients in perturbation theory up to and including order $T^{7/3}$ and compare with exact numerical results obtained in the large-$N_f$ limit of QED and QCD.Comment: REVTEX4, 6 pages, 2 figures; v2: minor improvements, references added; v3: factor of 2 error in the T^(7/3) coefficient corrected and plots update

Perturbative QCD at non-zero chemical potential: Comparison with the large-Nf limit and apparent convergence

The perturbative three-loop result for the thermodynamic potential of QCD at finite temperature and chemical potential as obtained in the framework of dimensional reduction is compared with the exact result in the limit of large flavor number. The apparent convergence of the former as well as possibilities for optimization are investigated. Corresponding optimized results for full QCD are given for the case of two massless quark flavors.Comment: REVTEX4, 4 pages, 3 color figures. v2: fig. 3 now includes also lattice data for two-flavor QCD at nonzero chemical potentia

The pressure of deconfined QCD for all temperatures and quark chemical potentials

We present a new method for the evaluation of the perturbative expansion of the QCD pressure which is valid at all values of the temperature and quark chemical potentials in the deconfined phase and which we work out up to and including order g^4 accuracy. Our calculation is manifestly four-dimensional and purely diagrammatic -- and thus independent of any effective theory descriptions of high temperature or high density QCD. In various limits, we recover the known results of dimensional reduction and the HDL and HTL resummation schemes, as well as the equation of state of zero-temperature quark matter, thereby verifying their respective validity. To demonstrate the overlap of the various regimes, we furthermore show how the predictions of dimensional reduction and HDL resummed perturbation theory agree in the regime T~\sqrt{g}*mu. At parametrically smaller temperatures T~g*mu, we find that the dimensional reduction result agrees well with those of the nonstatic resummations down to the remarkably low value T~0.2 m_D, where m_D is the Debye mass at T=0. Beyond this, we see that only the latter methods connect smoothly to the T=0 result of Freedman and McLerran, to which the leading small-T corrections are given by the so-called non-Fermi-liquid terms, first obtained through HDL resummations. Finally, we outline the extension of our method to the next order, where it would include terms for the low-temperature entropy and specific heats that are unknown at present.Comment: 45 pages, 21 figures; v2: minor corrections and clarifications, references added; v3: Fig 16 added, version accepted for publication in PR

A nonequilibrium renormalization group approach to turbulent reheating

We use nonequilibrium renormalization group (RG) techniques to analyze the thermalization process in quantum field theory, and by extension reheating after inflation. Even if at a high scale $\Lambda$ the theory is described by a non-dissipative $\lambda\phi^{4}$ theory, the RG running induces nontrivial noise and dissipation. For long wavelength, slowly varying field configurations, the noise and dissipation are white and ohmic, respectively. The theory will then tend to thermalize to an effective temperature given by the fluctuation-dissipation theorem.Comment: 8 pages, 2 figures; to appear in J. Phys. A; more detailed account of the calculation of the noise and dissipation kernel

The magnetic mass of transverse gluon, the B-meson weak decay vertex and the triality symmetry of octonion

With an assumption that in the Yang-Mills Lagrangian, a left-handed fermion and a right-handed fermion both expressed as quaternion make an octonion which possesses the triality symmetry, I calculate the magnetic mass of the transverse self-dual gluon from three loop diagram, in which a heavy quark pair is created and two self-dual gluons are interchanged. The magnetic mass of the transverse gluon depends on the mass of the pair created quarks, and in the case of charmed quark pair creation, the magnetic mass $m_{mag}$ becomes approximately equal to $T_c$ at $T=T_c\sim 1.14\Lambda_{\bar{MS}}\sim 260$MeV. A possible time-like magnetic gluon mass from two self-dual gluon exchange is derived, and corrections in the B-meson weak decay vertices from the two self-dual gluon exchange are also evaluated.Comment: 22 pages, 9 figure

Three-loop HTLpt thermodynamics at finite temperature and chemical potential

In this proceedings we present a state-of-the-art method of calculating thermodynamic potential at finite temperature and finite chemical potential, using Hard Thermal Loop perturbation theory (HTLpt) up to next-to-next-leading-order (NNLO). The resulting thermodynamic potential enables us to evaluate different thermodynamic quantities including pressure and various quark number susceptibilities (QNS). Comparison between our analytic results for those thermodynamic quantities with the available lattice data shows a good agreement.Comment: 5 pages, 6 figures, conference proceedings of XXI DAE-BRNS HEP Symposium, IIT Guwahati, December 2014; to appear in 'Springer Proceedings in Physics Series

Advances in perturbative thermal field theory

The progress of the last decade in perturbative quantum field theory at high temperature and density made possible by the use of effective field theories and hard-thermal/dense-loop resummations in ultrarelativistic gauge theories is reviewed. The relevant methods are discussed in field theoretical models from simple scalar theories to non-Abelian gauge theories including gravity. In the simpler models, the aim is to give a pedagogical account of some of the relevant problems and their resolution, while in the more complicated but also more interesting models such as quantum chromodynamics, a summary of the results obtained so far are given together with references to a few most recent developments and open problems.Comment: 84 pages, 18 figues, review article submitted to Reports on Progress in Physics; v2, v3: minor additions and corrections, more reference

Perturbative and Nonperturbative Kolmogorov Turbulence in a Gluon Plasma

In numerical simulations of nonabelian plasma instabilities in the hard-loop approximation, a turbulent spectrum has been observed that is characterized by a phase-space density of particles $n(p)\sim p^{-\nu}$ with exponent $\nu\simeq 2$, which is larger than expected from relativistic $2\leftrightarrow 2$ scatterings. Using the approach of Zakharov, L'vov and Falkovich, we analyse possible Kolmogorov coefficients for relativistic $(m \ge 4)$-particle processes, which give at most $\nu=5/3$ perturbatively for an energy cascade. We discuss nonperturbative scenarios which lead to larger values. As an extreme limit we find the result $\nu=5$ generically in an inherently nonperturbative effective field theory situation, which coincides with results obtained by Berges et al.\ in large-$N$ scalar field theory. If we instead assume that scaling behavior is determined by Schwinger-Dyson resummations such that the different scaling of bare and dressed vertices matters, we find that intermediate values are possible. We present one simple scenario which would single out $\nu=2$.Comment: published versio

Thermodynamics of Large-N_f QCD at Finite Chemical Potential

We extend the previously obtained results for the thermodynamic potential of hot QCD in the limit of large number of fermions to non-vanishing chemical potential. We give exact results for the thermal pressure in the entire range of temperature and chemical potential for which the presence of a Landau pole is negligible numerically. In addition we compute linear and non-linear quark susceptibilities at zero chemical potential, and the entropy at small temperatures. We compare with the available perturbative results and determine their range of applicability. Our numerical accuracy is sufficiently high to check and verify existing results, including the recent perturbative results by Vuorinen on quark number susceptibilities and the older results by Freedman and McLerran on the pressure at zero temperature and high chemical potential. We also obtain a number of perturbative coefficients at sixth order in the coupling that have not yet been calculated analytically. In the case of both non-zero temperature and non-zero chemical potential, we investigate the range of validity of a scaling behaviour noticed recently in lattice calculations by Fodor, Katz, and Szabo at moderately large chemical potential and find that it breaks down rather abruptly at $\mu_q \gtrsim \pi T$, which points to a presumably generic obstruction for extrapolating data from small to large chemical potential. At sufficiently small temperatures $T \ll \mu_q$, we find dominating non-Fermi-liquid contributions to the interaction part of the entropy, which exhibits strong nonlinearity in the temperature and an excess over the free-theory value.Comment: 18 pages, 7 figures, JHEP style; v2: several updates, rewritten and extended sect. 3.4 covering now "Entropy at small temperatures and non-Fermi-liquid behaviour"; v3: additional remarks at the end of sect. 3.4; v4: minor corrections and additions (version to appear in JHEP

The pressure of hot QCD up to g^6 ln(1/g)

The free energy density, or pressure, of QCD has at high temperatures an expansion in the coupling constant g, known so far up to order g^5. We compute here the last contribution which can be determined perturbatively, g^6 ln(1/g), by summing together results for the 4-loop vacuum energy densities of two different three-dimensional effective field theories. We also demonstrate that the inclusion of the new perturbative g^6 ln(1/g) terms, once they are summed together with the so far unknown perturbative and non-perturbative g^6 terms, could potentially extend the applicability of the coupling constant series down to surprisingly low temperatures.Comment: 18 pages. Small clarifications added. To appear in Phys.Rev.