# 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

## TL;DR

This paper calculates strong interaction effects between B and D mesons in B decays, revealing significant corrections that impact the R_D ratio, crucial for testing the Standard Model with high precision.

## Contribution

It introduces a model accounting for meson exchange effects in B decays, providing corrections to decay amplitudes and ratios not previously considered.

## Key findings

- Corrections to decay amplitudes are 15-25%.
- R_D ratio corrections are around 10%.
- Implications for high-precision tests of the Standard Model.

## Abstract

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 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 \bar{\nu}_\tau \tau $ and $\bar{B} \to D \bar{\nu}_e \ell$ 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.