Theoretical Corrections of $R_D$ and $R_{D^*}$

Abstract

$R_{D^{(*)}}$ is the ratio of branching ratio $\overline{B} \rightarrow D^{(*)}\tau\overline{\nu}_{\tau}$ to $\overline{B} \rightarrow D^{(*)}l\overline{\nu}_{l}~(l=e,~\mu)$. There is a gap of 2$\sigma_{exp}$ or more between its experimental value and the prediction under the standard model(SM). People extend the MSSM with the local gauge group $U(1)_X$ to obtain the $U(1)_X$SSM. Compared with MSSM, $U(1)_X$SSM has more superfields and effects. In $U(1)_X$SSM, we research the semileptonic decays $\overline{B} \rightarrow D^{(*)}l\overline{\nu}_{l}$ and calculate $R_{D^{(*)}}$. The numerical results of $R_{D^{(*)}}$ are further corrected under $U(1)_X$SSM, which are much better than the SM predictions. After correction, the theoretical value of $R_{D^{(*)}}$ can reach one $\sigma_{exp}$ range of the averaged experiment central value.