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${\cal O}(\alpha_{ew}m_{t(b)}^4/m_W^4)$tothewidthsofthedecays$\tilde t_2\to \tilde t_1 + (h^0,H^0,A^0)$ 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 $\tan \beta$.