The QED nonfactorizable correction to the semileptonic charmed three-body $B$ decays

Abstract

In this paper, the nonfactorizable photonic corrections to the effective four-fermion vertex for the $\overline{B}$ $\to$ $D^{(\ast )}$ $+$ ${\ell }^{-}$ $+$ $\bar{\hat{I}}{½}_{\ell }$ decays are considered at the quark level within SM, where $\ell$ $=$ $e$, $\hat{I}¼$ and $\ddot{I}„$. It is found that the QED corrections are closely related with the mass of the charged lepton. The QED contributions will enhance branching ratios, which results in the slight reduction of ratios $R(D^{(\ast )})$ and the relationship $R(D^{(\ast )}{)}_e$ $<$ $R(D^{(\ast )}{)}_{\hat{I}}¼$.

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