New physics in inclusive $B\to X_c\ell \bar{\nu }$ decay in light of $R(D^{(\ast )})$ measurements

Abstract

In this work we study the effects of new-physics (NP) operators with different Lorentz structures on the inclusive $B\to X_c\tau \bar{\nu }$ decay and make predictions for the ratio of total decay rates $R(X_c)=\frac{\Gamma (B\to X_c\tau {\bar{\nu }}_{\tau })}{\Gamma (B\to X_c\ell {\bar{\nu }}_{\ell })}$ with $\ell =e,\mu$, the differential decay rates, $\frac{d\Gamma }{d{q}^2}$ and $\frac{d\Gamma }{d{E}_{\tau }}$, forward-backward asymmetry $A_{FB}$ and the ratio of the differential decay rates $B(q^2)=\frac{d\Gamma (B\to X_c\tau {\bar{\nu }}_{\tau })/d{q}^2}{d\Gamma (B\to X_c\ell {\bar{\nu }}_{\ell })/d{q}^2}$. In addition, we introduce some leptoquark models as explicit models of the NP operators and study their effects on the inclusive decay. We consider $\mathcal{O}({\alpha }_s)$ radiative and $1/m_b$ nonperturbative corrections to the Standard Model (SM) decay rate and ignore their small effects in the NP contributions.

Comments: 29 pages, 59 figures