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, $i$.$e$., 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 $B\to K^{(\ast )}$ decays, the corrections improve the agreement for the differential distributions, while the behavior is more complicated for ${\Lambda }_b\to {\Lambda }^{(\ast )}$ decays. Rather intriguingly, the corrections serve to regenerate the tension for the lepton flavor universality observables $R_K$ and $R_{K^{\ast }}$.

Comments: 27 pages, 9 figures