On the Impact of Soft Photons on $B\to K{\ell }^{+}{\ell }^{-}$

Abstract

We give detailed results of $\mathcal{O}(\alpha )$ QED corrections (both real emission and virtual corrections) to $B\to K{\ell }^{+}{\ell }^{-}$ modes. Requiring the real emission to be gauge invariant, the structure of the contact term(s) is fixed. The calculation is done with a fictitious photon mass as the IR regulator and results are shown to be independent of it, establishing cancellation of the soft divergences. Results are presented for a choice of photon energy, $k_{max}$, and photon angle ${\theta }_{cut}$. The QED effects are negative, thereby reducing the rate compared to that without QED effects. Electron channels are shown to receive large corrections ($\mathcal{O}(20\%)$). Impact on lepton flavour universality ratio, $R_K^{\mu e}$ are also discussed.

arXiv comment27 pages, 6 figues

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• Standard Model predictions for $B\to K{\ell }^{+}{\ell }^{-}$, $B\to K{\ell }_1^{-}{\ell }_2^{+}$ and $B\to K\nu \bar{\nu }$ using form factors from $N_f=2+1+1$ lattice QCD
• Light-cone distribution amplitudes of light mesons with QED effects
• Structure-dependent QED effects in exclusive $B$-meson decays
• $\frac{|V_{ub}|}{|V_{cb}|}$ and Quest for New Physics
• Addressing the $R_{\tau /\mu ,e}\left(D^{(\ast )}\right)$ puzzle through New Physics four-fermion operators and their impact on ${\Lambda }_b\to {\Lambda }_c\tau {\bar{\nu }}_{\tau }$ decay
• The Angular Observables of ${\Lambda }_b\to {\Lambda }_c(\to {\Lambda }^0{\pi }^{+}){\tau }^{-}(\to {\pi }^{-}{\nu }_{\tau }){\bar{\nu }}_{\tau }$ within the Paradigm of FCCC Anomalies