Magnetic Fields at First Order Phase Transition: A Threat to Electroweak Baryogenesis

TL;DR

The paper investigates how magnetic fields produced during a first-order electroweak phase transition can destabilize the baryon asymmetry generated by electroweak baryogenesis by coupling to the sphaleron magnetic dipole and lowering the sphaleron energy inside broken-phase bubbles. Focusing on the MSSM in the light-stop scenario, it uses a finite-temperature potential and bounce calculations to determine the nucleation temperature $T_n$ and then analyzes how a background field $B=b\,T^2$ shifts the sphaleron energy via $E_{\rm sph}(T,B)=E_{\rm sph}(T)-\mu(T)B$. Numerical scans show that even modest magnetic fields can tighten or close the MSSM EWBG window by requiring smaller Higgs masses or lighter stops than current bounds permit, highlighting sensitivity to the magnetic-field magnitude. The work calls for precise modeling of magnetic fields during the electroweak transition and cautions that magnetic-field effects may threaten a broad class of first-order EWPT-based baryogenesis scenarios, with implications for LHC Higgs/stop searches.

Abstract

The generation of the observed baryon asymmetry may have taken place during the electroweak phase transition, thus involving physics testable at LHC, a scenario dubbed electroweak baryogenesis. In this paper we point out that the magnetic field which is produced in the bubbles of a first order phase transition endangers the baryon asymmetry produced in the bubble walls. The reason being that the produced magnetic field couples to the sphaleron magnetic moment and lowers the sphaleron energy; this strengthens the sphaleron transitions inside the bubbles and triggers a more effective wash out of the baryon asymmetry. We apply this scenario to the Minimal Supersymmetric extension of the Standard Model (MSSM) where, in the absence of a magnetic field, successful electroweak baryogenesis requires the lightest CP-even Higgs and the right-handed stop masses to be lighter than about 127 GeV and 120 GeV, respectively. We show that even for moderate values of the magnetic field, the Higgs mass required to preserve the baryon asymmetry is below the present experimental bound. As a consequence electroweak baryogenesis within the MSSM should be confronted on the one hand to future measurements at the LHC on the Higgs and the right-handed stop masses, and on the other hand to more precise calculations of the magnetic field produced at the electroweak phase transition.

Figures (4)

• Figure 1: The temperature dependence of the sphaleron energy (with and without magnetic field) and the magnetic dipole moment. Top left panel: sphaleron energy without magnetic field; Top right panel: sphaleron magnetic dipole moment; Bottom panel: sphaleron energy for $B=0.1\,T^2$. We have fixed $m_H=120.2 {\rm \,GeV}$ and $\widetilde{m}=10^3 {\rm \,TeV}$. We show both the results of numerical calculations using the Higgs potentials at nonzero temperatures (blue solid line) and the result of a simple scaling relation (red dashed line).
• Figure 2: The maximal sphaleron energy $E(T_n, B)/T_n$ achieved for a Higgs mass $m_H$ evaluated with $\widetilde{m}=50$ TeV (left panel) and $\widetilde{m}=10^3 {\rm \,TeV}$ (right panel). The horizontal dashed line corresponds to the requirement $E(T_n)/T_n\gtrsim 35$. The bands correspond to the uncertainty on the location of $T_n$ in the interval $[T_c-3.5 {\rm \,GeV}, T_c-2 {\rm \,GeV}]$. The upper lines correspond to $T_n=T_c-3.5 {\rm \,GeV}$. Different bands correspond to different values of $b=B/T_n^2= 0.0, 0.1, 0.2$.
• Figure 3: The sphaleron energy $E(T_n, B)/T_n$ as a function of the maximal right-handed stop mass $m_{\widetilde{t}_R}$ allowed for $\widetilde{m}=10^3 {\rm \,TeV}$ and $m_H=114.4 {\rm \,GeV}$ (left panel) or $m_H=118 {\rm \,GeV}$ (right panel). The horizontal dashed line corresponds to the requirement $E(T_n)/T_n\gtrsim 35$. The bands correspond to the uncertainty on the location of $T_n$ in the interval $[T_c-3.5 {\rm \,GeV}, T_c-2 {\rm \,GeV}]$. The upper lines correspond to $T_n=T_c-3.5 {\rm \,GeV}$. Different bands correspond to different values of $b=B/T_n^2= 0.0, 0.1, 0.2$.
• Figure 4: The values of the magnetic field for which the maximal $m_H$ is at the experimental bound. The band corresponds to the uncertainty on the location of $T_n$ in the interval $[T_c-3.5 {\rm \,GeV}, T_c-2 {\rm \,GeV}]$. The upper line corresponds to $T_n=T_c-3.5 {\rm \,GeV}$.