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Supersymmetric Electroweak Baryogenesis

James M. Cline, Michael Joyce, Kimmo Kainulainen

TL;DR

This work demonstrates that in the MSSM electroweak baryogenesis can be driven predominantly by CP-violating effects in the chargino sector. Using a gauge-invariant, semiclassical WKB framework, the authors derive dispersion relations and diffusion equations for MSSM quasiparticles, showing that a CP-violating mu-phase induces chiral asymmetries transported to left-handed quarks, which bias sphalerons to produce the baryon asymmetry. A key result is that a sufficient BAU can be generated even for arg(m2 mu) as small as ~10^-3, especially with a light right-handed stop, and in a broad region of parameter space. The analysis clarifies the source terms and transport dynamics, providing a consistent alternative to prior, gauge-variant treatments and connecting the BAU magnitude to wall dynamics and MSSM spectra.

Abstract

We re-examine the generation of the baryon asymmetry in the minimal supersymmetric standard model (MSSM) during the electroweak phase transition. We find that the dominant source for baryogenesis arises from the chargino sector. The CP-violation comes from the complex phase in the mu parameter, which provides CP-odd contributions to the particle dispersion relations. This leads to different accelerations for particles and antiparticles in the wall region which, combined with diffusion, leads to the separation of Higgsinos and their antiparticles in the front of the wall. These asymmetries get transported to produce perturbations in the left-handed chiral quarks, which then drive sphaleron interactions to create the baryon asymmetry. We present a complete derivation of the semiclassical WKB formalism, including the chargino dispersion relations and a self-consistent derivation of the diffusion equations starting from semiclassical Boltzmann equations for WKB-excitations. We stress the advantages of treating the transport equations in terms of the manifestly gauge invariant physical energy and kinetic momentum, rather than in the gauge variant canonical variables used in previous treatments. We show that a large enough baryon asymmetry can be created for the phase of the complex mu parameter as small as ~ 0.001, which is consistent with bounds from the neutron electric dipole moment.

Supersymmetric Electroweak Baryogenesis

TL;DR

This work demonstrates that in the MSSM electroweak baryogenesis can be driven predominantly by CP-violating effects in the chargino sector. Using a gauge-invariant, semiclassical WKB framework, the authors derive dispersion relations and diffusion equations for MSSM quasiparticles, showing that a CP-violating mu-phase induces chiral asymmetries transported to left-handed quarks, which bias sphalerons to produce the baryon asymmetry. A key result is that a sufficient BAU can be generated even for arg(m2 mu) as small as ~10^-3, especially with a light right-handed stop, and in a broad region of parameter space. The analysis clarifies the source terms and transport dynamics, providing a consistent alternative to prior, gauge-variant treatments and connecting the BAU magnitude to wall dynamics and MSSM spectra.

Abstract

We re-examine the generation of the baryon asymmetry in the minimal supersymmetric standard model (MSSM) during the electroweak phase transition. We find that the dominant source for baryogenesis arises from the chargino sector. The CP-violation comes from the complex phase in the mu parameter, which provides CP-odd contributions to the particle dispersion relations. This leads to different accelerations for particles and antiparticles in the wall region which, combined with diffusion, leads to the separation of Higgsinos and their antiparticles in the front of the wall. These asymmetries get transported to produce perturbations in the left-handed chiral quarks, which then drive sphaleron interactions to create the baryon asymmetry. We present a complete derivation of the semiclassical WKB formalism, including the chargino dispersion relations and a self-consistent derivation of the diffusion equations starting from semiclassical Boltzmann equations for WKB-excitations. We stress the advantages of treating the transport equations in terms of the manifestly gauge invariant physical energy and kinetic momentum, rather than in the gauge variant canonical variables used in previous treatments. We show that a large enough baryon asymmetry can be created for the phase of the complex mu parameter as small as ~ 0.001, which is consistent with bounds from the neutron electric dipole moment.

Paper Structure

This paper contains 15 sections, 159 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Introductory example: Fermion with complex mass
  3. Canonical equations of motion
  4. Currents
  5. Application of WKB to the MSSM
  6. Squarks
  7. Charginos
  8. Neutralinos
  9. Transport Equations
  10. Derivation of diffusion equations
  11. Transport in the MSSM
  12. Baryon asymmetry
  13. Sources
  14. Results
  15. Conclusions and outlook

Figures (3)

  • Figure 1: (a) The source for baryogenesis from the chiral classical force, eq. (\ref{['effsc']}), for the parameters $\mu = 100$ GeV and $m_2 = 150$ GeV and $\ell_w = 10/T$ (solid line) and $\ell_w = 14/T$ (dashed line). (b) The left-handed quark asymmetry $\xi_{q_L}$, eq. (\ref{['beeL']}), for the same parameters. The distance from the center of the wall $z$, is measured in units $1/T$.
  • Figure 2: $\eta_{10}$ as a function of wall velocity for $\mu = 100$ GeV and $\sin \delta_\mu=1$ for: (a) a varying gaugino mass parameter $m_2 =50$, $100$, $150$ and $200$ GeV and: (b) for a varying wall width, $\ell_w = 6/T$, $10/T$, $14/T$ and $18/T$.
  • Figure 3: Contours of constant CP-violating phase $\delta_\mu$, corresponding to baryon asymmetry $\eta_{ B} = 3 \times 10^{-10}$ for (a) $v_w = 0.1$ and (b) $v_w = 0.01$. Mass units are GeV.