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We perform a calculation of the strong interaction effects between the $B$and $D$ mesons in the $\bar{B} \to D \bar{\nu} \ell$ reaction, as a crossingprocess of reactions with $BD$ in the final state, where the strong interactionbetween the mesons leads to a bound $BD$ state. We find corrections to the treelevel amplitude of the order of $15-25\%$. We further see the effect of thecorrections studied in the $R_D$ ratio for the rates of $\bar{B} \to D\bar{\nu}_\tau \tau $ and $\bar{B} \to D \bar{\nu}_e \ell$ decays and findcorrections of the order of $10\%$. Given the claims of $1.5\%$ precision inthis ratio from fits to data within the standard model, any theoretical modelaiming at describing this ratio within the same precision must take intoaccount the corrections described in the present work.

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