Mixing Effects in the Finite-Temperature Effective Potential of the MSSM with a Light Stop

We incorporate the effects of mixing arising from the trilinear terms in the MSSM potential to the effective three dimensional theory for the MSSM at high temperature in the limit of large $m_{A}$. There are relevant one-loop effects that modify the 3D parameters of the effective theory. We calculate the two-loop effective potential of the 3D theory for the Higgs and the right handed stop to analyse the possible phase transitions and to determine the precise region in the $m_{h}$-$m_{\tilde{t}_{2}}$ plane for which the sphaleron constraint for preservation of the baryon asymmetry is satisfied. There is an upper bound on the value of the mixing parameter coming from stop searches. We also compare with previous results obtained using 4D calculations of the effective potential for the regime of large $m_{Q}$. A two-stage phase transition persists for a small range of values of $m_{\tilde{t}_{2}}$ for given values of the mixing parameter and $\tan\beta$. This can further constrain the allowed region of parameter space. Electroweak baryogenesis requires a value of $m_{\tilde{t}_{2}}\lsi 170$ and $m_{h} \lsi 105$ GeV for $m_{Q}=300$ GeV.