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

Abstract

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 Bödeker 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 G. Moore to yield a NLLO result for the hot electroweak baryon number violation rate.

The quark–gluon plasma: collective dynamics and hard thermal loops

“…The complete result for σ to NLLA has been obtained in Refs. [254] (see also [255]). Quite remarkably, by using this result within the simplified effective theory (7.61), one obtains an estimate for the hot sphaleron rate which is rather close (within 20%) to the HTL result in Refs.…”

“…Recently, it has been argued [253,254] that the local form (7.61) of the ultrasoft theory remains valid also to "next-to-leading logarithmic accuracy" (NLLA), i.e., at the next order in an expansion in powers of the inverse logarithm ln −1 ≡ 1/ ln(1/g). The only modification refers to the value of the parameter σ, which now must be computed to NLLA.…”

“…The only modification refers to the value of the parameter σ, which now must be computed to NLLA. This in turns involves the matching between two calculations: the expansion of the solution to the Boltzmann equation to NLLA [72,254], and a perturbative calculation within the "high energy" sector of the ultrasoft theory [254] (by which we mean loop diagrams with internal momenta of order g 2 T ln(1/g) which must be computed with USA-resummed propagators and vertices). The complete result for σ to NLLA has been obtained in Refs.…”

Perturbative and non-perturbative aspects non-Abelian Boltzmann–Langevin equation

“…To determine the next-to-leading log color conductivity γ we follow Arnold and Yaffe [21] and match the results for a rectangular Wilson loop W(t, R), with spatial extent R and temporal extent t, in the theory (6.4) and in the underlying "microscopic" theory, which in our case is Eq. (1.1).…”

“…(1.6) is still valid at next-to-leading logarithmic order (NLLO), if one uses the next-to-leading logarithmic order (NLLO) color conductivity γ, which was calculated in Ref. [21]. It was argued that the additional terms in the path integral action mentioned above do not contribute at next-to-leading logarithmic order.…”