# Impacts of radiative corrections on measurements of lepton flavour universality in $B \to D \ell \nu_{\ell}$ decays

## TL;DR

This paper examines how radiative corrections, including soft-photon effects and Coulomb interactions, influence measurements of lepton flavour universality in B to D decays, highlighting potential biases in current analyses.

## Contribution

It compares recent calculations of radiative corrections with PHOTOS simulations and discusses the impact of high-energy photon emissions on measurements.

## Key findings

- Bias in R(D) measurements can reach 7% due to photon emission misestimations.
- Long-distance Coulomb interactions not included in PHOTOS can affect results.
- Accurate QED correction evaluation is essential for future high-precision measurements.

## Abstract

Radiative corrections to $B \to D \ell \nu_{\ell}$ decays may have an impact on predictions and measurements of the lepton flavour universality observables $\mathcal{R}(D^+)$ and $\mathcal{R}(D^0)$. In this paper, a comparison between recent calculations of the effect of soft-photon corrections on $\mathcal{R}(D^+)$ and $\mathcal{R}(D^0)$, and corrections generated by the widely used package PHOTOS is given. The impact of long-distance Coulomb interactions, which are not simulated in PHOTOS, is discussed. Furthermore, the effect of high-energy photon emission is studied through pseudo-experiments in an LHCb-like environment. It is found that over- or underestimating these emissions can cause a bias on $\mathcal{R}(D)$ as high as 7%. However, this bias depends on individual analyses, and future high precision measurements require an accurate evaluation of these QED corrections.