The Sphaleron Rate in the Minimal Standard Model

Abstract

We use large-scale lattice simulations to compute the rate of baryon number violating processes (the sphaleron rate), the Higgs field expectation value, and the critical temperature in the Standard Model across the electroweak phase transition temperature. While there is no true phase transition between the high-temperature symmetric phase and the low-temperature broken phase, the cross-over is sharply defined at $T_c=(159\pm 1)$\,GeV. The sphaleron rate in the symmetric phase ($T>T_c$) is $\Gamma /T^4=(18\pm 3){\alpha }_W^5$, and in the broken phase in the physically interesting temperature range $130\mbox{\,GeV} < T < T_c$ it can be parametrized as $\log (\Gamma /T^4)=(0.83\pm 0.01)T/\mathrm{GeV}-(147.7\pm 1.9)$. The freeze-out temperature in the early Universe, where the Hubble rate wins over the baryon number violation rate, is $T_{\ast }=(131.7\pm 2.3)$\,GeV. These values, beyond being intrinsic properties of the Standard Model, are relevant for e.g. low-scale leptogenesis scenarios.

5 pages, 3 figures

References in corpus (3)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• The Sphaleron Rate through the Electroweak Cross-over

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