Theoretical corrections of $$R_D$$ R D and $$R_{D^*}$$ R D ∗

Abstract

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