High Temperature Gauge Theories Research Articles

The dimensionally reduced description of the high energy scattering and the effective action for the reggeized gluons

We discuss the high energy scattering of hadrons with the multi-Regge kinematics. The effective 2D model for the interaction between the produced hard gluons appears as a result of the dimensional reduction, which is similar to the dimensional reduction 3+1 D rightarrow 3 D of the high temperature gauge theory. It is demonstrated that being supplemented by the exchange by virtual 3+1 D gluons this 2D model gives rise to the hermitian version of the effective action of Lipatov for the interaction between the ordinary and the reggeized gluons.

Systematics of high temperature perturbation theory: The two-loop electron self-energy in QED

In order to investigate the systematics of the loop expansion in high temperature gauge theories beyond the leading order hard thermal loop (HTL) approximation, we calculate the two-loop electron proper self-energy in high temperature QED. The two-loop bubble diagram contains a linear infrared divergence. Even if regulated with a non-zero photon mass M of order of the Debye mass, this infrared sensitivity implies that the two-loop self-energy contributes terms to the fermion dispersion relation that are comparable to or even larger than the next-to-leading-order (NLO) contributions at one-loop. Additional evidence for the necessity of a systematic restructuring of the loop expansion comes from the explicit gauge parameter dependence of the fermion damping rate at both one and two-loops. The leading terms in the high temperature expansion of the two-loop self-energy for all topologies arise from an explicit hard-soft factorization pattern, in which one of the loop integrals is hard, nested inside a second loop integral which is soft. There are no hard-hard contributions to the two-loop Sigma at leading order at high T. Provided the same factorization pattern holds for arbitrary ell loops, the NLO high temperature contributions to the electron self-energy come from ell-1 hard loops factorized with one soft loop integral. This hard-soft pattern is both a necessary condition for the resummation over ell to coincide with the one-loop self-energy calculated with HTL dressed propagators and vertices, and to yield the complete NLO correction to the self-energy at scales ~eT, which is both infrared finite and gauge invariant. We employ spectral representations and the Gaudin method for evaluating finite temperature Matsubara sums, which facilitates the analysis of multi-loop diagrams at high T.

Transport coefficients in high temperature gauge theories, 2. Beyond leading log

Results are presented of a full leading-order evaluation of the shear viscosity, flavor diffusion constants, and electrical conductivity in high temperature QCD and QED. The presence of Coulomb logarithms associated with gauge interactions imply that the leading-order results for transport coefficients may themselves be expanded in an infinite series in powers of 1/log(1/g); the utility of this expansion is also examined. A next-to-leading-log approximation is found to approximate the full leading-order result quite well as long as the Debye mass is less than the temperature.

Effective kinetic theory for high temperature gauge theories

Quasiparticle dynamics in relativistic plasmas associated with hot, weakly-coupled gauge theories (such as QCD at asymptotically high temperature T) can be described by an effective kinetic theory, valid on sufficiently large time and distance scales. The appropriate Boltzmann equations depend on effective scattering rates for various types of collisions that can occur in the plasma. The resulting effective kinetic theory may be used to evaluate observables which are dominantly sensitive to the dynamics of typical ultrarelativistic excitations. This includes transport coefficients (viscosities and diffusion constants) and energy loss rates. In this paper, we show how to formulate effective Boltzmann equations which will be adequate to compute such observables to leading order in the running coupling g(T) of high-temperature gauge theories [and all orders in 1/log g(T)−1]. As previously proposed in the literature, a leading-order treatment requires including both 2↔2 particle scattering processes as well as effective ``1↔2'' collinear splitting processes in the Boltzmann equations. The latter account for nearly collinear bremsstrahlung and pair production/annihilation processes which take place in the presence of fluctuations in the background gauge field. Our effective kinetic theory is applicable not only to near-equilibrium systems (relevant for the calculation of transport coefficients), but also to highly non-equilibrium situations, provided some simple conditions on distribution functions are satisfied.

Nonperturbative dynamics of hot non-Abelian gauge fields: Beyond the leading log approximation

Many aspects of high-temperature gauge theories, such as the electroweak baryon number violation rate, color conductivity, and the hard gluon damping rate, have previously been understood only at leading logarithmic order (that is, neglecting effects suppressed only by an inverse logarithm of the gauge coupling). We discuss how to systematically go beyond leading logarithmic order in the analysis of physical quantities. Specifically, we extend to next-to-leading-log order (NLLO) the simple leading-log effective theory due to B\"odeker that describes non-perturbative color physics in hot non-Abelian plasmas. A suitable scaling analysis is used to show that no new operators enter the effective theory at next-to-leading-log order. However, a NLLO calculation of the color conductivity is required, and we report the resulting value. Our NLLO result for the color conductivity can be trivially combined with previous numerical work by Moore to yield a NLLO result for the hot electroweak baryon number violation rate.

Transport coefficients in high temperature gauge theories (I): leading-log results

Leading-log results are derived for the shear viscosity, electrical conductivity, and flavor diffusion constants in both Abelian and non-Abelian high temperature gauge theories with various matter field content.

Spinodal decomposition in high temperature gauge theories

After a rapid increase in temperature across the deconfinement temperature T d , pure gauge theories exhibit unstable long wavelength fluctuations in the approach to equilibrium. This phenomenon is analogous to spinodal decomposition observed in condensed matter physics, and also seen in models of disordered chiral condensate formation. At high temperature, the unstable modes occur only in the range 0≤ k ≤ k c , where k c is on the order of the Debye screening mass m D . Equilibration always occurs via spinodal decomposition for SU(2) at temperatures T> T d and for SU(3) for T≫ T d . For SU(3) at temperatures T≳ T d , nucleation may replace spinodal decomposition as the dominant equilibration mechanism. Monte Carlo simulations of SU(2) lattice gauge theory exhibit the predicted phenomena. The observed value of k c is in reasonable agreement with a value predicted from previous lattice measurements of m D .

Electromagnetic properties of a neutrino stream

In a medium that contains a neutrino background in addition to the matter particles, the neutrinos contribute to the photon self-energy as a result of the effective electromagnetic vertex that they acquire in the presence of matter. We calculate the contribution to the photon self-energy in a dense plasma, due to the presence of a gas of charged particles, or neutrinos, that moves as a whole relative to the plasma. General formulas for the transverse and longitudinal components of the photon polarization tensor are obtained in terms of the momentum distribution functions of the particles in the medium, and explicit results are given for various limiting cases of practical interest. The formulas are used to study the electromagnetic properties of a plasma that contains a beam of neutrinos. The transverse and longitudinal photon dispersion relations are studied in some detail. Our results do not support the idea that neutrino streaming instabilities can develop in such a system. We also indicate how the phenomenon of optical activity of the neutrino gas is modified due to the velocity of the neutrino background relative to the plasma. The general approach and results can be adapted to similar problems involving relativistic plasmas and high-temperature gauge theories in other environments.

Tricritical point of finite-temperature phase transitions in largeN(Higgs) gauge theories

Gauge theories broken by a single Higgs field are known to have first-order phase transitions in temperature if $\ensuremath{\lambda}{/g}^{2}\ensuremath{\ll}1$, where $g$ is the gauge coupling and $\ensuremath{\lambda}$ the Higgs self-coupling. If the theory is extended from one to $N$ Higgs doublets, with U$(N)$ flavor symmetry, the transition is known to be second order for $\ensuremath{\lambda}{/g}^{2}\ensuremath{\gtrsim}1$ in the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ limit. We show that one can, in principle, compute the tricritical value of $\ensuremath{\lambda}{/g}^{2}$, separating first- from second-order transitions, to any order in $1/N$. In particular, scalar fluctuations at the transition damp away the usual problems with the infrared behavior of high-temperature non-Abelian gauge theories. We explicitly compute the tricritical value of $\ensuremath{\lambda}{/g}^{2}$ for U(1) and SU(2) gauge theory to next-to-leading order in $1/N$.

A non-perturbative analysis of the finite- T phase transition in SU (2) × U (1) electroweak theory

The continuum 3D SU(2) × U(1)+Higgs theory is an effective theory for a large class of 4D high-temperature gauge theories, including the minimal standard model and some of its supersymmetric extensions. We study the effects of the U(1) subgroup using lattice Monte Carlo techniques. When g′ 2/ g 2 is increased from the zero corresponding to pure SU(2)+Higgs theory, the phase transition gets stronger. However, the increase in the strength is close to what is expected perturbatively, and the qualitative features of the phase diagram remain the same as for g′ 2 = 0. In particular, the first-order transition still disappears for m H > m H, c . We measure the photon mass and mixing angle, and find that the mass vanishes in both phases within the statistical errors.

Long range physics in a hot non-Abelian plasma

We derive a set of equations describing the real time dynamics of modes with spatial momentum of order g 2 T in a high temperature gauge theory, where g is the coupling constant and T is the temperature. This dynamics is stochastic in nature. Important implications for baryon number violation at high temperature and for the physics at the electroweak phase transition, are discussed.

Domain walls and perturbation theory in high-temperature gauge theory: SU(2) in 2+1 dimensions

We study the detailed properties of ${Z}_{2}$ domain walls in the deconfined high-temperature phase of the $d=2+1$ SU(2) gauge theory. These walls are studied both by computer simulations of the lattice theory and by one-loop perturbative calculations. The latter are carried out both in the continuum and on the lattice. We find that leading order perturbation theory reproduces the detailed properties of these domain walls remarkably accurately even at temperatures where the effective dimensionless expansion parameter ${g}^{2}/T$ is close to unity. The quantities studied include the surface tension, the action density profiles, roughening, and the electric screening mass. It is only for the last quantity that we find an exception to the precocious success of perturbation theory. All this shows that, despite the presence of infrared divergences at higher orders, high-$T$ perturbation theory can be an accurate calculational tool.

Approximate spectral functions in thermal field theory.

Causality requires, that the (anti-) commutator of two interacting field operators vanishes for space-like coordinate differences. This implies, that the Fourier transform of the spectral function of this quantum field should vanish in the space-like domain. We find, that this requirement imposes some constraints on the use of resummed propagators in high temperature gauge theory.

The electroweak phase transition: a non-perturbative analysis

We study on the lattice the 3d SU(2)+Higgs model, which is an effective theory of a large class of 4d high-temperature gauge theories. Using the exact constant physics curve, continuum ( V → ∞, a → 0) results for the properties of the phase transition (critical temperature, latent heat, interface tension) are given. The 3-loop linear correction to the effective potential of the scalar field is determined. The masses of scalar and vector excitations are determined and found to be larger in the symmetric than in the broken phase. The vector mass is considerably larger than the scalar one, which suggests a further simplification to a scalar effective theory at large m H . The use of consistent 1-loop relations between 3d parameters and 4d physics permits one to convert the 3d simulation results to quantitatively accurate numbers for different physical theories, such as the Standard Model — excluding possible non-perturbative effects of the U(l) subgroup — for Higgs masses up to about 70 GeV The applications of our results to cosmology are discussed.

Fermion and antifermion effective masses in high temperature gauge theories in a CP-asymmetric background.

We calculate the splitting between fermion and antifermion effective masses in high temperature gauge theories in the presence of a nonvanishing chemical potential due to the $\mathrm{CP}$-asymmetric fermionic background. In particular we consider the case of left-handed leptons in the SU(2)\ensuremath{\bigotimes}U(1) theory when the temperature is above 250 GeV and the gauge symmetry is restored.

Spontaneous symmetry breaking versus spontaneous parity violation

We discuss the possibility of spontaneous parity violation in three-dimensional minkowskian and euclidean gauge theories with scalar fields. In perturbation theory, it is found that parity can be broken spontaneously only in the phase with restored gauge invariance, but is unbroken if the scalars have vacuum expectation values. We note that the spontaneous parity violation in the euclidean case may be related to the breaking of translational invariance. Implications of these results for high temperature gauge theories and cosmology are considered.