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Laurence G. Yaffe

Publications and source records attributed to Laurence G. Yaffe.

68 records · Page 4Linked to original sources
arXiv1999

High temperature color conductivity at next-to-leading log order

The non-Abelian analog of electrical conductivity at high temperature has previously been known only at leading logarithmic order: that is, neglecting effects suppressed only by an inverse logarithm of the gauge coupling. We calculate the first sub-leading correction. This has immediate application to improving, to next-to-leading log order, both effective theories of non-perturbative color dynamics, and calculations of the hot electroweak baryon number violation rate.

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arXiv1999

From Instantons to Sphalerons: Time-Dependent Periodic Solutions of SU(2)-Higgs Theory

We solve numerically for periodic, spherically symmetric, classical solutions of SU(2)-Higgs theory in four-dimensional Euclidean space. In the limit of short periods the solutions approach tiny instanton-anti-instanton superpositions while, for longer periods, the solutions merge with the static sphaleron. A previously predicted bifurcation point, where two branches of periodic solutions meet, appears for Higgs boson masses larger than $3.091 M_W$.

hep-ph↗
arXiv1999

Longitudinal subtleties in diffusive Langevin equations for non-Abelian plasmas

Boedeker has recently argued that non-perturbative processes in very high temperature non-Abelian plasmas (such as electroweak baryon number violation in the very hot early Universe) can be quantitatively described, to leading logarithmic accuracy, by a simple diffusive effective theory. Boedeker's effective theory is intended to describe the long-distance transverse electric and magnetic fields which are responsible for non-perturbative dynamics. His effective theory, however, also contains long-wavelength longitudinal electric fields. We discuss several subtleties in the treatment of longitudinal dynamics which were not closely examined in Boedeker's original treatment. Somewhat to our surprise, we find that within its domain of validity Boedeker's effective theory does correctly describe both longitudinal and transverse fluctuations. We also show that, as far as the transverse dynamics of interest is concerned, Boedeker's effective theory could be replaced by a transverse-only theory that removes the longitudinal dynamics altogether. In the process, we discuss several interesting aspects of stochastic field theories.

hep-ph↗
arXiv1998

Periodic Euclidean Solutions of SU(2)-Higgs Theory

We examine periodic, spherically symmetric, classical solutions of SU(2)-Higgs theory in four-dimensional Euclidean space. Classical perturbation theory is used to construct periodic time-dependent solutions in the neighborhood of the static sphaleron. The behavior of the action, as a function of period, changes character depending on the value of the Higgs mass. The required pattern of bifurcations of solutions as a function of Higgs mass is examined, and implications for the temperature dependence of the baryon number violation rate in the Standard Model are discussed.

hep-ph↗
arXiv1998

Hot B violation, color conductivity, and log(1/alpha) effects

Bodeker has recently argued that non-perturbative processes in very high temperature non-Abelian plasmas (such as electroweak baryon number violation in the very hot early Universe) are logarithmically enhanced over previous estimates and take place at a rate per unit volume of order $α^5 T^4 \ln(1/α)$ for small coupling. We give a simple physical interpretation of Bodeker's qualitative and quantitative results in terms of Lenz's Law -- the fact that conducting media resist changes in the magnetic field -- and earlier authors' calculations of the color conductivity of such plasmas. In the process, we resolve some confusions in the literature about the value of the color conductivity and present an independent calculation. We also discuss the issue of whether the classical effective theory proposed by Bodeker has a good continuum limit.

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arXiv1997

Effective theories for real-time correlations in hot plasmas

We discuss the sequence of effective theories needed to understand the qualitative, and quantitative, behavior of real-time correlators < A(t) A(0) > in ultra-relativistic plasmas. We analyze in detail the case where A is a gauge-invariant conserved current. This case is of interest because it includes a correlation recently measured in lattice simulations of classical, hot, SU(2)-Higgs gauge theory. We find that simple perturbation theory, free kinetic theory, linearized kinetic theory, and hydrodynamics are all needed to understand the correlation for different ranges of time. We emphasize how correlations generically have power-law decays at very large times due to non-linear couplings to long-lived hydrodynamic modes.

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arXiv1996

Weakly first-order phase transitions: the epsilon expansion vs. numerical simulations

Some phase transitions of cosmological interest may be weakly first-order and cannot be analyzed by a simple perturbative expansion around mean field theory. We propose a simple two-scalar model--the cubic anisotropy model--as a foil for theoretical techniques to study such transitions, and we review its similarities and dissimilarities to the electroweak phase transition in the early universe. We present numerical Monte Carlo results for various discontinuities across very weakly first-order transitions in this model and, as an example, compare them to epsilon-expansion results. For this purpose, we have computed through next-to-next-to-leading order in epsilon.

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arXiv1996

$\eps$ expansion analysis of very weak first-order transitions in the cubic anisotropy model: Part I

The cubic anisotropy model provides a simple example of a system with an arbitrarily weak first-order phase transition. We present an analysis of this model using $\eps$-expansion techniques with results up to next-to-next-to-leading order in $\eps$. Specifically, we compute the relative discontinuity of various physical quantities across the transition in the limit that the transition becomes arbitrarily weakly first-order. This provides a useful test-bed for the application of the $\eps$ expansion in weakly first-order transitions.

hep-ph↗
arXiv1996

The hot baryon violation rate is $O(α_W^5 T^4)$

The rate per unit volume for anomalous electroweak baryon number violation at high temperatures, in the symmetric phase, has been estimated in the literature to be $O(α_W^4 T^4)$ based on simple scaling arguments. We argue that damping effects in the plasma suppress the rate by an extra power of $α_W$ to give $O(α_W^5 T^4)$. We show how to understand this effect in a variety of ways ranging from an effective description of the long-distance modes responsible for baryon number violation, to a microscopic picture of the short-distance modes responsible for damping. In particular, we resolve an old controversy as to whether damping effects are relevant. Finally, we argue that similar damping effects should occur in numerical simulations of the rate in classical thermal field theory on a spatial lattice, and we point out a potential problem with simulations in the literature that have not found such an effect.

hep-ph↗
arXiv1995

From Quantum Field Theory to Hydrodynamics: Transport Coefficients and Effective Kinetic Theory

The evaluation of hydrodynamic transport coefficients in relativistic field theory, and the emergence of an effective kinetic theory description, is examined. Even in a weakly-coupled scalar field theory, interesting subtleties arise at high temperatures where thermal renormalization effects are important. In this domain, a kinetic theory description in terms of the fundamental particles ceases to be valid, but one may derive an effective kinetic theory describing excitations with temperature dependent properties. While the shear viscosity depends on the elastic scattering of typical excitations whose kinetic energies are comparable to the temperature, the bulk viscosity is sensitive to particle non-conserving processes at small energies. As a result, the shear and the bulk viscosities have very different dependence on the interaction strength and temperature, with the bulk viscosity providing an especially sensitive test of the validity of an effective kinetic theory description.

hep-ph↗
arXiv1995

The non-Abelian Debye screening length beyond leading order

In quantum electrodynamics, static electric fields are screened at non-zero temperatures by charges in the plasma. The inverse screening length, or Debye mass, may be analyzed in perturbation theory and is of order $eT$ at relativistic temperatures. An analogous situation occurs when non-Abelian gauge theories are studied perturbatively, but the perturbative analysis breaks down when corrections of order $e^2 T$ are considered. At this order, the Debye mass depends on the non-perturbative physics of confinement, and a perturbative ``definition'' of the Debye mass as the pole of a gluon propagator does not even make sense. In this work, we show how the Debye mass can be defined non-perturbatively in a manifestly gauge invariant manner (in vector-like gauge theories with zero chemical potential). In addition, we show how the $O(e^2 T)$ correction could be determined by a fairly simple, three-dimensional, numerical lattice calculation of the perimeter-law behavior of large, adjoint-charge Wilson loops.

hep-ph↗
arXiv1993

The $ε$-expansion and the electroweak phase transition

Standard perturbative (or mean field theory) techniques are not adequate for studying the finite-temperature electroweak phase transition in some cases of interest to scenarios for electroweak baryogenesis. We instead study the properties of this transition using the renormalization group and the $ε$-expansion. This expansion, based on dimensional continuation from 3 to $4{-}ε$ spatial dimensions, provides a systematic approximation for computing the effects of (near)-critical fluctuations. The $ε$-expansion is known to predict a first-order transition in Higgs theories, even for heavy Higgs boson masses. The validity of this conclusion in the standard model is examined in detail. A variety of physical quantities are computed at leading and next-to-leading order in $ε$. For moderately light Higgs masses (below 100~GeV), the $ε$-expansion suggests that the transition is more strongly first order than is predicted by the conventional analysis based on the one-loop (ring-improved) effective potential. Nevertheless, the rate of baryon non-conservation after the transition is found to be {\em larger\/} than that given by the one-loop effective potential calculation. Detailed next-to-leading order calculations of some sample quantities suggests that the $\eps$-expansion is reasonably well behaved for Higgs masses below 100--200 GeV. We also compare the $\eps$-expansion with large-$N$ results (where $N$ is the number of scalar fields) and find that the $\eps$-expansion is less well behaved in this limit.

hep-ph↗
arXiv1992

Large-order perturbation theory for the electromagnetic current-current correlation function

The constraints imposed by asymptotic freedom and analyticity on the large-order behavior of perturbation theory for the electromagnetic current-current correlation function are examined. By suitably applying the renormalization group, the coefficients of the asymptotic expansion in the deep Euclidean region may be expressed explicitly in terms of the perturbative coefficients of the Minkowski space discontinuity (the $R$-ratio in $e^+ e^-$ scattering). This relation yields a ``generic'' prediction for the large-order behavior of the Euclidean perturbation series and suggests the presence of non-perturbative $1/q^2$ correction in the Euclidian correlation function. No such ``generic'' prediction can be made for the physically measurable $R$-ratio. A novel functional method is developed to obtain these results.

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