Symmetries of Hot SM, Magnetic Flux & Baryogenesis from Helicity Decay

TL;DR

The paper analyzes the electroweak crossover in the Standard Model through a dimensionally reduced 3d EFT, framing the dynamics in terms of generalized symmetries and a gauge-invariant magnetic mixing between hypercharge and the SU(2) sector.A key result is the gauge-invariant, temperature-dependent effective mixing angle $\theta_{\rm eff}(T)$, which differs from previous, gauge-dependent definitions and affects the conversion of hypermagnetic helicity into baryon number during the crossover.The authors identify three main effects on baryogenesis: (i) an ${\cal O}(1)$ shift from the proper mixing angle, (ii) approximate conservation of the unconfined magnetic flux, and (iii) a novel non-perturbative process in the presence of magnetic flux that can alter the Chern–Simons dynamics, potentially suppressing net baryogenesis.These insights imply sizable uncertainties in earlier helicity-based baryogenesis estimates and motivate further non-perturbative and magnetogenesis studies within hot SM cosmology.

Abstract

We revisit the electroweak crossover of the Standard Model (SM) in the early Universe, focusing on the interplay between generalized global symmetries, magnetic flux dynamics, and baryogenesis. Employing the dimensionally reduced 3d effective field theory of the SM at high temperature, we identify the symmetry structure -- including higher-form and magnetic symmetries -- and analyze their spontaneous breaking patterns across the crossover. We further define a gauge-invariant mixing angle that interpolates between $\mathrm{U}(1)_Y$ and $\mathrm{U}(1)_\mathrm{em}$ magnetic fields. Based on this framework, we examine baryogenesis via decaying magnetic helicity and identify three key effects: the baryon asymmetry is modified by an $\mathcal{O}(1)$ factor due to (1) the gauge-invariant definition of the mixing angle and (2) the approximate conservation of the unconfined magnetic flux; (3) a novel non-perturbative process in the presence of magnetic flux, which has been overlooked in previous analyses. Our findings suggest that the previous estimation of baryon asymmetry from the magnetic helicity decay may have sizable uncertainties, and we caution against relying on it, calling for further investigation.

Figures (35)

• Figure 1: Electric (left) and magnetic (right) charge lattices of $G=\mathrm{SU}(2)_{\mathrm L}\times {\mathrm U}(1)_Y$ theory. The green lines correspond to the electric and magnetic charges of $\mathfrak{u}(1)_\mathrm{em}$.
• Figure 2: Electric (left) and magnetic (right) charge lattices of $\tilde{G}=(\mathrm{SU}(2)_{\mathrm L}\times \mathrm{U}(1)_Y)/\mathbb{Z}_2$ theory. The green lines correspond to the electric and magnetic charges of $\mathfrak{u}(1)_\mathrm{em}$.
• Figure 3: Possible phase diagrams consistent with the mixed anomaly. Left: Electroweak crossover. This scenario is supported by Monte Carlo simulation. Right: An intermediate phase with mass gap.
• Figure 4: The Nambu monopole in the SM. The monopole has $(0, \sqrt{2})$ magnetic charge, which is the minimal unit in the magnetic charge lattice (right panel of Fig. \ref{['fig:charge_lattices_withoutZ2']}). The monopole has both electromagnetic and confinement charges from \ref{['eq:electric_charge']} and \ref{['eq:confinement_charge']}. Consequently, the monopole is confined and is connected by the flux tube.
• Figure 5: The behavior of the magnetic field from high to low temperature. Left: At the high temperature before the electroweak crossover, the large scale $\mathrm{U}(1)_Y$ magnetic field is not screened thanks to the Bianchi identity. Right: At low temperature after the electroweak crossover, the constant $\mathrm{U}(1)_Y$ magnetic field is no longer stable profile as it carries the confined charge \ref{['eq:confinement_charge']}. To remove the flux tube, the Nambu monopole-antimonopole pairs are created. In this way, the $\mathrm{U}(1)_Y$ magnetic field becomes the $\mathrm{U}(1)_\mathrm{em}$ magnetic field.