Theoretical Corrections of $R_D$ and $R_{D^{\ast }}$

Abstract

$R_{D^{(\ast )}}$ is the ratio of branching ratio $\overline{B}\to D^{(\ast )}\tau {\overline{\nu }}_{\tau }$ to $\overline{B}\to D^{(\ast )}l{\overline{\nu }}_l(l=e,\mu )$. 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 $\overline{B}\to D^{(\ast )}l{\overline{\nu }}_l$ and calculate $R_{D^{(\ast )}}$. The numerical results of $R_{D^{(\ast )}}$ are further corrected under $U(1{)}_X$SSM, which are much better than the SM predictions. After correction, the theoretical value of $R_{D^{(\ast )}}$ can reach one ${\sigma }_{exp}$ range of the averaged experiment central value.

Comments: 25 pages, 16 figures