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Peter Arnold

Publications and source records attributed to Peter Arnold.

At least 91 records · Page 5Linked to original sources
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.

hep-ph↗
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.

hep-ph↗
arXiv1997

Monte Carlo study of very weak first-order transitions in the three-dimensional Ashkin-Teller model

We propose numerical simulations of the Ashkin-Teller model as a foil for theoretical techniques for studying very weakly first-order phase transitions in three dimensions. The Ashkin-Teller model is a simple two-spin model whose parameters can be adjusted so that it has an arbitrarily weakly first-order phase transition. In this limit, there are quantities characterizing the first-order transition which are universal: we measure the relative discontinuity of the specific heat, the correlation length, and the susceptibility across the transition by Monte Carlo simulation.

hep-lat↗
arXiv1997

B Violation in the Hot Standard Model

I explain, as simply and pedagogically as I can, recent arguments that the high-temperature baryon number violation rate depends on the electroweak coupling as $Γ= # α_\w^5 T^4$ (up to higher order corrections). This is in contrast to the form $Γ= # α_\w^4 T^4$ that has historically been assumed in discussions of electroweak baryogenesis. I will give a general analysis of the time scale for non-perturbative gauge field fluctuations in hot non-Abelian plasmas.

hep-ph↗
arXiv1997

Hot B violation, the lattice, and hard thermal loops

It has recently been argued that the rate per unit volume of baryon number violation (topological transitions) in the hot, symmetric phase of electroweak theory is of the form $ηα_w^5 T^4$ in the weak-coupling limit, where $η$ is a non-perturbative numerical coefficient. Over the past several years, there have been attempts to extract the rate of baryon number violation from real-time simulations of classical thermal field theory on a spatial lattice. Unfortunately, the coefficient $η$ will not be the same for classical lattice theories and the real quantum theory. However, by analyzing the appropriate effective theory on the lattice using the method of hard thermal loops, I show that the only obstruction to precisely relating the rates in the real and lattice theories is the fact that the long-distance physics on the lattice is not rotationally invariant. (This is unlike Euclidean-time measurements, where rotational invariance is always recovered in the continuum limit.) I then propose how this violation of rotational invariance can be eliminated - and the real B violation rate measured - by choosing an appropriate lattice Hamiltonian. I also propose a rough measure of the systematic error to be expected from using simpler, unimproved Hamiltonians. As a byproduct of my investigation, the plasma frequency and Debye mass are computed for classical thermal field theory on the lattice.

hep-ph↗
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.

hep-ph↗
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 tricritical point of finite-temperature phase transitions in large N(Higgs) gauge theories

Gauge theories broken by a single Higgs field are known to have first-order phase transitions in temperature if $λ/g^2 \ll 1$, where $g$ is the gauge coupling and $λ$ 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 $λ/g^2 \gtrsim 1$ in the $N\to\infty$ limit. We show that one can in principal compute the tricritical value of $λ/g^2$, 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 $λ/g^2$ for U(1) and SU(2) gauge theory to next-to-leading order in $1/N$.

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

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↗
arXiv1994

The Three-Loop Free Energy for High-Temperature QED and QCD with Fermions

We compute the free energy density for gauge theories, with fermions, at high temperature and zero chemical potential. Specifically, we analytically compute the free energy through $O(g^4)$, which requires the evaluation of three-loop diagrams. This computation extends our previous result for pure gauge QCD.

hep-ph↗
arXiv1994

The Three-Loop Free Energy for Pure Gauge QCD

We compute the free energy density for pure non-Abelian gauge theory at high temperature and zero chemical potential. The three-loop result to $O(g^4)$ is [a lovely formula. Get the paper and print it out.] We examine the sensitivity of this result to the choice of renormalization scale. We also give a result for the free energy of scalar $ϕ^4$ theory, correcting a result previously given in the literature.

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↗
arXiv1993

One-loop fluctuation-dissipation formula for bubble-wall velocity

The limiting bubble wall velocity during a first-order electroweak phase transition is of interest in scenarios for electroweak baryogenesis. Khlebnikov has recently proposed an interesting method for computing this velocity based on the fluctuation-dissipation theorem. I demonstrate that at one-loop order this method is identical to simple, earlier techniques for computing the wall velocity based on computing the friction from particles reflecting off or transmitting through the wall in the ideal gas limit.

hep-ph↗
arXiv1992

A Review of the Instability of Hot Electroweak Theory and its Bounds on $m_h$ and $m_t$

[Talk presented at the International Seminar Quarks `92, Zvenigorod, Russia, May 11-17, 1992.] The electroweak vacuum need not be absolutely stable. For certain top and Higgs masses in the Minimal Standard Model, it is instead metastable with a lifetime exceeding the present age of the Universe. The decay of our vacuum may be nucleated at low temperature by quantum tunneling or at high temperature in the early Universe by thermal excitation. I briefly review the constraints on top and Higgs masses from requiring that the electroweak vacuum be sufficiently stable to have survived to the present day.

hep-ph↗