Supersymmetric Electroweak Corrections to Sbottom Decay into Lighter Stop and Charged Higgs Boson

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 width of sbottom decay into lighter stop plus charged Higgs boson are calculated in the Minimal Supersymmetric Standard Model. These corrections depend on the masses of charged Higgs boson and lighter stop, and the parameters $\tan\beta$ and $\mu$. For favorable parameter values, the corrections decrease or increase the decay widths significantly. Especially for high values of $\tan\beta$(=30) the corrections exceed at least 10% for both $\tilde b_1$ and $\tilde b_2$ decay. But for low values of $\tan\beta$(=4,10) the corrections are small and the magnitudes are less than 10%. The numerical calculations also show that using the running bottom quark mass which includes the QCD effects and resums all high order $\tan\beta$-enhanced effects can improve much the convergence of the perturbation expansion.