Resummation scheme for 3d Yang-Mills and the two-loop magnetic mass for hot gauge theories

Perturbation theory for non-Abelian gauge theories at finite temperature is plagued by infrared divergences caused by magnetic soft modes $\sim g^2T$, which correspond to the fields of a 3d Yang-Mills theory. We revisit a gauge invariant resummation scheme to solve this problem by self-consistent mass generation using an auxiliary scalar field, improving over previous attempts in two respects. First, we generalise earlier SU(2) treatments to SU(N). Second, we obtain a gauge independent two-loop gap equation, correcting an error in the literature. The resulting two-loop approximation to the magnetic mass represents a $\sim 15$ correction to the leading one-loop value, indicating a reasonable convergence of the resummation.Comment: 16 pages, 3 figure

Do metric fluctuations affect the Higgs dynamics during inflation?

We show that the dynamics of the Higgs field during inflation is not affected by metric fluctuations if the Higgs is an energetically subdominant light spectator. For Standard Model parameters we find that couplings between Higgs and metric fluctuations are suppressed by Script O(10−7). They are negligible compared to both pure Higgs terms in the effective potential and the unavoidable non-minimal Higgs coupling to background scalar curvature. The question of the electroweak vacuum instability during high energy scale inflation can therefore be studied consistently using the Jordan frame action in a Friedmann-Lemaître-Robertson-Walker metric, where the Higgs-curvature coupling enters as an effective mass contribution. Similar results apply for other light spectator scalar fields during inflation

Next-to-leading order thermal spectral functions in the perturbative domain

Laine M, Vuorinen A, Zhu Y. Next-to-leading order thermal spectral functions in the perturbative domain. JHEP. 2011;2011(9): 84.Motivated by applications in thermal QCD and cosmology, we elaborate on ageneral method for computing next-to-leading order spectral functions forcomposite operators at vanishing spatial momentum, accounting for real, virtualas well as thermal corrections. As an example, we compute these functions(together with the corresponding imaginary-time correlators which can becompared with lattice simulations) for scalar and pseudoscalar densities inpure Yang-Mills theory. Our results may turn out to be helpful innon-perturbative estimates of the corresponding transport coefficients, whichare the bulk viscosity in the scalar channel and the rate of anomalouschirality violation in the pseudoscalar channel. We also mention links tocosmology, although the most useful results in that context may come from afuture generalization of our methods to other correlators