Production of charged $\rho$ meson in bottom hadron charmed decays and the effect of the finite width correction of the $\rho$ meson

TL;DR

This paper calculates the impact of the finite width correction of the $ ho$ meson on the branching ratios of bottom hadron decays into charmed hadrons and charged $ ho$ mesons, showing significant numerical effects.

Contribution

It introduces the finite width correction of the $ ho$ meson into the QCD factorization calculations of bottom hadron decay branching ratios, providing more accurate predictions.

Findings

Finite width correction reduces some branching ratios by 9-11%.

Finite width correction increases the branching ratio for $ extstyleoldsymbol{ ho^-}$ channel by about 10%.

Numerical results demonstrate the importance of considering the $ ho$ meson width in decay calculations.

Abstract

We calculate the branching ratio of a bottom hadron decaying into a charmed hadron and a charged $\rho$ meson within the QCD factorization approach. We consider the effect of the finite width correction of the $\rho$ meson. Our numerical calculation shows an obvious correction because of this effect. We find that the finite width effect of the $\rho$ meson reduces the branching ratios by about 9% to 11% for bottom meson decay channels: $B^+\to\bar{D^0}\rho^+$, $B^0\to D^-\rho^+$, and $B^0_s\to D^-_s\rho^+$, and increases the branching ratio by about 10% for $\Lambda_b^0\to\Lambda_c^+\rho^-$.