Supersymmetric Electroweak Corrections to Heavier Top Squark Decay into Lighter Top Squark and Neutral Higgs Boson

We calculate the Yukawa corrections of order ${\cal O}(\alpha_{ew}m_{t(b)}^2/m_W^2)$, ${\cal O}(\alpha_{ew}m_{t(b)}^3/m_W^3)$ and ${\cal O}(\alpha_{ew}m_{t(b)}^4/m_W^4)$ to the widths of the decays $\tilde t_2\to \tilde t_1 + (h^0,H^0,A^0)$ in the Minimal Supersymmetric Standard Model, and perform a detailed numerical analysis. We also compare the results with the ones presented in an earlier literature, where the ${\cal O}(\alpha_{s})$ SUSY-QCD corrections to the same three decay processes have been calculated. Our numerical results show that for the decays $\tilde t_2\to \tilde t_1 + h^{0}$, $\tilde t_2\to \tilde t_1 + H^{0}$, the Yukawa corrections are significant in most of the parameter range, which can reach a few ten percent, and for the decay $\tilde t_2\to\tilde t_1 + A^{0}$, the Yukawa corrections are relatively smaller, which are only a few percent. The numerical calculations also show that using the running quark masses and the running trilinear coupling $A_t$, which include the QCD, SUSY-QCD, SUSY-Electroweak effects and resume all high order ($\tan\beta$)-enhanced effects, can vastly improve the convergence of the perturbation expansion. We also discuss the effects of the running of the higgsino mass parameter $\mu$ on the corrections, and find that they are significant, too, especially for large $\tan\beta$.