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The Sphaleron Rate in the Minimal Standard Model

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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 $\log(\Gamma/T^4) = (0.83\pm 0.01)T/{\rm GeV} - (147.7\pm 1.9)$. The freeze-out temperature in the early Universe, where the Hubble rate wins over the baryon number violation rate, is $T_* = (131.7\pm 2.3)$\,GeV. These values, beyond being intrinsic properties of the Standard Model, are relevant for e.g. low-scale leptogenesis scenarios.

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hep-ph 14

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2026 9 2025 5

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representative citing papers

Leptogenesis and Low Reheating Temperatures

hep-ph · 2026-07-09 · conditional · novelty 7.0

Standard non-thermal leptogenesis works at arbitrarily low reheating temperatures above the BBN bound when the inflaton potential has a quartic minimum (k≥4), because the inflaton's evolving mass kinematically shuts off RHN production early.

Gauged Flavour for Asymmetric Dark Matter

hep-ph · 2026-05-19 · unverdicted · novelty 6.0 · 2 refs

A gauged SO(3) flavour symmetry broken at multiple scales generates SM fermion masses, redistributes a lepton asymmetry into baryon and dark matter asymmetries via sphalerons, and yields dark matter as bound states of a confining SU(3), with mirror fermions required for anomaly cancellation.

Electroweak Baryogenesis from Collapsing Domain Walls

hep-ph · 2026-04-30 · unverdicted · novelty 6.0

Collapsing axion-like domain walls generate the baryon asymmetry by acting as an effective chemical potential through coupling to the electroweak topological term, with the asymmetry produced via sphaleron processes.

Nucleosynthesis and CMB bounds on photophilic ALPs: a fresh look

hep-ph · 2025-10-31 · unverdicted · novelty 5.0

Updated model-independent BBN and CMB bounds on photophilic ALPs that incorporate rare decays to light hadrons, show extended constraints for multiple reheating temperatures, and flag parameter space that may alleviate tensions in N_eff and deuterium abundance.

Revisiting constraints on magnetogenesis from baryon asymmetry

hep-ph · 2025-09-28 · unverdicted · novelty 5.0

Maximally helical primordial U(1)_Y magnetic fields can generate both intergalactic magnetic fields and baryon asymmetry; non-helical fields may work if Higgs dynamics compensate helicity loss to ≲10^{-9-10} precision during electroweak crossover.

Type II Seesaw Leptogenesis in a Majoron background

hep-ph · 2025-06-29 · unverdicted · novelty 5.0

Spontaneous wash-in leptogenesis in Type II Seesaw with Majoron pNGB background enables baryon asymmetry generation alongside dark matter cogenesis for specific v_T, v_sigma and m_j ranges.

$SO(10)$-inspired leptogenesis

hep-ph · 2026-04-21 · unverdicted · novelty 3.0

SO(10)-inspired leptogenesis implies N2-leptogenesis, ruling out inverted neutrino ordering under strict conditions and enabling initial-condition-independent asymmetry in subsets of solutions.

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