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Meson exchange between initial and final state and the $R_D$ ratio in the $\bar{B} \to D \barν \ell (\barν_ττ)$ reactions

We perform a calculation of the strong interaction effects between the $B$ and $D$ mesons in the $\bar{B} \to D \barν \ell$ reaction, as a crossing process of reactions with $BD$ in the final state, where the strong interaction between the mesons leads to a bound $BD$ state. We find corrections to the tree level amplitude of the order of $15-25\%$. We further see the effect of the corrections studied in the $R_D$ ratio for the rates of $\bar{B} \to D \barν_ττ$ and $\bar{B} \to D \barν_e \ell$ decays and find corrections of the order of $10\%$. Given the claims of $1.5\%$ precision in this ratio from fits to data within the standard model, any theoretical model aiming at describing this ratio within the same precision must take into account the corrections described in the present work.