Sphalerons in the MSSM

Abstract

We construct the sphaleron solution, at zero and finite temperature, in the Minimal Supersymmetric Standard Model as a function of the supersymmetric parameters, including the leading one-loop corrections to the effective potential in the presence of the sphaleron. At zero temperature we have included the one-loop radiative corrections, dominated by the top/stop sector. The sphaleron energy $E_{\rm MSSM}$ mainly depends on an effective Higgs mass ${\displaystyle m_h^{\rm eff}=\lim_{m_A\gg m_W} m_h}$, where $m_h$ is the lightest CP-even Higgs mass and $m_A$ the pseudoscalar mass. We have compared it with the Standard Model result, with $m_h^{\rm SM}=m_h^{\rm eff}$, and found small differences (1-2\%) in all cases. At finite temperature we have included the one-loop effective potential improved by daisy diagram resummation. The sphaleron energy at the critical temperature can be encoded in the temperature dependence of the vacuum expectation value of the Higgs field with an error $\simlt 10$\%. The light stop scenario has been re-examined and the existence of a window where baryon asymmetry is not erased after the phase transition, confirmed. Although large (low) values of $m_h$ ($m_A$) are disfavoured by the strength of the phase transition, that window (along with LEP results) allows for $m_h\simlt 80$ GeV, $m_A\simgt 110$ GeV and $A_t\simlt 0.4\; m_Q$.