Abstract
Radiative corrections to {B} rightarrow {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.
Highlights
It is found that over- or underestimating these emissions can cause a bias on R(D) as high as 7%. This bias depends on individual analyses, and future high precision measurements require an accurate evaluation of these QED corrections
The Standard Model (SM) assumes lepton universality (LU) implying that once the mass difference is taken into account, all SM interactions treat the three charged leptons identically
The calculation by de Boer et al in Ref. [9] is the first that studies the impact of soft-photon corrections on R(D+) and R(D0). It is valid in the regime in which the maximum energy of the radiated photons is smaller than the lepton mass, which is the muon mass in this case
Summary
The Standard Model (SM) assumes lepton universality (LU) implying that once the mass difference is taken into account, all SM interactions treat the three charged leptons identically. LU can be tested by measuring the ratio of decay rates, ensuring that the Cabibbo–Kobayashi–Maskawa matrix elements, as well as most of the form factors, cancel in the ratio This results in more accurate theoretical predictions and in the cancellation of many experimental systematic uncertainties. The current tension between the SM and measurements could be weakened or strengthened if radiative corrections are not properly taken into account All experiments testing these types of LU are dependent on the simulation of QED radiative corrections in decays of particles and resonances. 2. The sensitivity of measurements of R(D+) and R(D0) to radiative corrections in the μ− and τ − decay modes is studied with pseudo-experiments in an LHCb-like environment, with different assumptions on the shape of the total energy of the radiated photons.
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