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arXiv · 2010.10853

On the Impact of Soft Photons on $B\rightarrow K \ell^+ \ell^-$

Dayanand Mishra·Namit Mahajan
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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, $R^{\mu e}_K$ are also discussed.

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Dayanand Mishra, Namit Mahajan. 2020-10-21. On the Impact of Soft Photons on $B\rightarrow K \ell^+ \ell^-$. https://doi.org/10.1103/physrevd.103.056022

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