Explaining the $\mathcal{R}(D)$ and $\mathcal{R}(D^{\ast })$ Anomalies in the $B-L$ Supersymmetric Standard Model with Inverse Seesaw

We investigate the $\mathcal{R}(D)$ and $\mathcal{R}(D^{\ast })$ anomalies in the context of the $B-L$ extension of the Minimal Supersymmetric Standard Model with Inverse Seesaw. We demonstrate that the lepton penguin $W^{\pm }l{\bar{\nu }}_l$ ($l=e,\mu ,\tau$) mediated by CP-even/odd right-handed sneutrinos, charginos and neutralinos can account for these anomalies simultaneously.