Soft photon corrections in $B \to K^{(\ast)} \ell^+ \ell^-$ and $\Lambda_b \to \Lambda^{(\ast)} \ell^+ \ell^-$ decays

Abstract

We calculate QED corrections to the semileptonic decays $H_1 \to H_2\ell^+\ell^-$ where $\ell=e, \mu$ and $H_{1,2}$ are hadrons. The soft and/or collinear divergences are regulated in a gauge-invariant manner and demonstrably cancel, leaving behind a finite residue that depends on the (infrared) momentum cutoff below which a photon is considered to be indistinguishable. On resuming, the said sensitivity reduces drastically, $\mathcal{i}$.$\mathcal{e}$., for the NLL result as compared to the NLO one. The overall correction is negative and its magnitude is larger for a lighter lepton. For $B \to K^{(*)}$ decays, the corrections improve the agreement for the differential distributions, while the behavior is more complicated for $\Lambda_b \to \Lambda^{(*)}$ decays. Rather intriguingly, the corrections serve to regenerate the tension for the lepton flavor universality observables $R_K$ and $R_{K^*}$.