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On the theory prediction of $R_K$ and radiative corrections

M. Bordone

in 9th International Workshop on the CKM Unitarity Triangle

Contribution: pdf


We review the theoretical prediction for the ratio $R_{K}$ which tests LFU in $B\to K\ell\ell$ with $\ell=e,\mu$. In particular we are interested in investigating the size of the uncertainty. To achieve this we perform a semi-analytical calculation of radiative corrections for the decay $B\to K\ell^{+}\ell^{-}$, and apply the results to $R_{K}$. We find out that the radiative corrections can be sizeable. However, applying the same cuts used in LHCb measurement, the overall effect of soft QED corrections diminishes. We perform also a comparison with PHOTOS, the Montecarlo (MC) tool used by LHCb to correct for QED correction. We find good agreement between our result and the MC with difference only at the at the per mill level. As an outlook we present also the effect of QED corrections on $R_{K^{*}}$, for which a measurement by LHCb is expected soon.