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

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.