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Supersymmetric Electroweak Baryogenesis

Nuria Rius, Veronica Sanz

TL;DR

This paper develops a first-principles calculation of the baryon asymmetry generated during the electroweak phase transition in the MSSM by employing a Higgs-insertion expansion to compute CP-violating Higgsino currents in a planar bubble wall. At leading order, the CP asymmetry vanishes when tanβ is constant across the wall and is sensitive to the wall profile and damping, with resonant enhancement near mass degeneracy |μ| ≈ m. At next-to-leading order, the Δβ suppression disappears, producing a nonzero CP asymmetry even for constant tanβ, which translates into a baryon-to-entropy ratio n_B/s when fed into diffusion equations with weak sphalerons; the results are compatible with the observed BAU for plausible CP phases, albeit with order-one uncertainties from wall dynamics and transport coefficients. Overall, the work provides a coherent, broadly applicable framework for MSSM electroweak baryogenesis and clarifies the role of Δβ suppression in determining the viability of such scenarios.

Abstract

We calculate the baryon asymmetry generated at the electroweak phase transition in the minimal supersymmetric standard model, using a new method to compute the CP-violating asymmetry in the Higgsino flux reflected into the unbroken phase. The method is based on a Higgs insertion expansion. We find that the CP asymmetry at leading order is proportional to the change in $\tan β$ in the bubble wall, which is at most of order $10^{-2}$, while at next-to-leading order this suppression factor disappears. This result may enhance the final baryon asymmetry generated during the electroweak phase transition for small $Δβ(< 10^{-3}$).

Supersymmetric Electroweak Baryogenesis

TL;DR

This paper develops a first-principles calculation of the baryon asymmetry generated during the electroweak phase transition in the MSSM by employing a Higgs-insertion expansion to compute CP-violating Higgsino currents in a planar bubble wall. At leading order, the CP asymmetry vanishes when tanβ is constant across the wall and is sensitive to the wall profile and damping, with resonant enhancement near mass degeneracy |μ| ≈ m. At next-to-leading order, the Δβ suppression disappears, producing a nonzero CP asymmetry even for constant tanβ, which translates into a baryon-to-entropy ratio n_B/s when fed into diffusion equations with weak sphalerons; the results are compatible with the observed BAU for plausible CP phases, albeit with order-one uncertainties from wall dynamics and transport coefficients. Overall, the work provides a coherent, broadly applicable framework for MSSM electroweak baryogenesis and clarifies the role of Δβ suppression in determining the viability of such scenarios.

Abstract

We calculate the baryon asymmetry generated at the electroweak phase transition in the minimal supersymmetric standard model, using a new method to compute the CP-violating asymmetry in the Higgsino flux reflected into the unbroken phase. The method is based on a Higgs insertion expansion. We find that the CP asymmetry at leading order is proportional to the change in in the bubble wall, which is at most of order , while at next-to-leading order this suppression factor disappears. This result may enhance the final baryon asymmetry generated during the electroweak phase transition for small ).

Paper Structure

This paper contains 6 sections, 42 equations, 3 figures.

Table of Contents

  1. Introduction
  2. CP asymmetry for Higgsinos
  3. Leading order
  4. Next-to-leading order
  5. Baryon asymmetry
  6. Conclusions

Figures (3)

  • Figure 1: $F^{(1)}_t(p_m)$ as a function of $p_m$ for Higgsino mass $|\mu|=1.$ and Wino mass $m = 0.5$ (solid), $m = 1.5$ (dashed-dotted), $m = 2.$ (dashed) and $m = 3.$ (dotted). All in units of the temperature.
  • Figure 2: $F^{(2)}_t(p_m)$ as a function of $p_m$ for $\tan \beta = 2$, $|\mu|=1.$ and $m = 0.5$ (solid), $m = 1.5$ (dashed-dotted), $m = 2.$ (dashed) and $m = 3.$ (dotted). All masses in units of the temperature.
  • Figure 3: Contour plot of $|\sin \phi \,|$ in the plane $(|\mu|,m)$ for fixed $n_B/s \simeq 4 \times 10^{-11}$, according to our leading order result for the CP asymmetry in the Higgsino current. The masses are in units of the temperature.