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Do Stops Slow Down Electroweak Bubble Walls?

P. John, M. G. Schmidt

TL;DR

The authors develop a framework to compute the velocity of electroweak bubble walls during a first-order phase transition in the MSSM by generalizing SM wall dynamics to include multiple Higgs fields and MSSM particle species in the plasma. They derive the bubble-wall equation of motion with friction from out-of-equilibrium distributions via linearized fluid equations, and compute the corresponding viscosity parameters $oldsymbol{ ext{η}}_1$ and $oldsymbol{ ext{η}}_2$ from detailed scattering rates for stops, tops, and W bosons. Using a kink Higgs profile and a virial balance, they obtain an analytic expression for the wall velocity $v_w$ and show that, in a parameter region compatible with baryogenesis, stops slow the wall to $v_w oughly (5-10) imes 10^{-2}$, significantly below the SM value. They discuss assumptions and potential corrections from additional SUSY states and thermal effects, noting that the results support electroweak baryogenesis in the MSSM under these friction considerations.

Abstract

We compute the wall velocity in the MSSM. We therefore generalize the SM equations of motion for bubble walls moving through a hot plasma at the electroweak phase transition and calculate the friction terms which describe the viscosity of the plasma. We give the general expressions and apply them to a simple model where stops, tops and W bosons contribute to the friction. In a wide range of parameters including those which fulfil the requirements of baryogenesis we find a wall velocity of order v = 0.05-0.1 much below the SM value.

Do Stops Slow Down Electroweak Bubble Walls?

TL;DR

The authors develop a framework to compute the velocity of electroweak bubble walls during a first-order phase transition in the MSSM by generalizing SM wall dynamics to include multiple Higgs fields and MSSM particle species in the plasma. They derive the bubble-wall equation of motion with friction from out-of-equilibrium distributions via linearized fluid equations, and compute the corresponding viscosity parameters and from detailed scattering rates for stops, tops, and W bosons. Using a kink Higgs profile and a virial balance, they obtain an analytic expression for the wall velocity and show that, in a parameter region compatible with baryogenesis, stops slow the wall to , significantly below the SM value. They discuss assumptions and potential corrections from additional SUSY states and thermal effects, noting that the results support electroweak baryogenesis in the MSSM under these friction considerations.

Abstract

We compute the wall velocity in the MSSM. We therefore generalize the SM equations of motion for bubble walls moving through a hot plasma at the electroweak phase transition and calculate the friction terms which describe the viscosity of the plasma. We give the general expressions and apply them to a simple model where stops, tops and W bosons contribute to the friction. In a wide range of parameters including those which fulfil the requirements of baryogenesis we find a wall velocity of order v = 0.05-0.1 much below the SM value.

Paper Structure

This paper contains 10 sections, 48 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Bubble Wall Equation of Motion
  3. Fluid Equations
  4. Higgs Equation of Motion and Friction
  5. Wall Velocity in the MSSM
  6. Viscosity and Wall Velocity
  7. Conclusion and Discussion
  8. Strong interactions
  9. Annihilation
  10. Scattering

Figures (2)

  • Figure 1: Wall velocity in dependence on the parameter $\tan\!\beta(T\!=\!0)$ for $m_Q=2$TeV, $A_t=\mu=0$, and $m_A=400$GeV for $m_U^2=-60^2, 0, 60^2$GeV${}^2$. Lower bunch of graphs for $\delta'=0$, upper for $\delta'\neq 0$.
  • Figure 2: Wall velocity for increasing stop mass parameter $m_U$. At very large $m_U$ (physically disfavoured) the stops decouple from the plasma leading to a large velocity while the first approximation $\delta'=0$ contrarily leads to decreasing $v_W$. The diagram is calculated for $\tan\!\beta=3$, $A_t=\mu=0$, and $m_A=400$GeV.