Radiative $\hat{I}¼$ and $\ddot{I}„$ leptonic decays at NLO

Abstract

We present the differential rates and branching ratios of the radiative decays $\ddot{I}„\to l\bar{\hat{I}}½\hat{I}½{\hat{I}}^3$, with $l=e$ or $\hat{I}¼$, and $\hat{I}¼\to e\bar{\hat{I}}½\hat{I}½{\hat{I}}^3$ in the Standard Model at next-to-leading order. Radiative corrections are computed taking into account the full depencence on the mass $m_l$ of the final charged leptons, which is necessary for the correct determination of the branching ratios. Only partial agreement is found with previous calculations performed in the $m_l\to 0$ limit. Our results agree with the measurements of the branching ratios $\mathcal{B}(\hat{I}¼\to e\bar{\hat{I}}½\hat{I}½{\hat{I}}^3)$ and $\mathcal{B}(\ddot{I}„\to \hat{I}¼\bar{\hat{I}}½\hat{I}½{\hat{I}}^3)$ for a minimum photon energy of 10 MeV in the $\hat{I}¼$ and $\ddot{I}„$ rest frames, respectively. Babar's recent precise measurement of the branching ratio $\mathcal{B}(\ddot{I}„\to e\bar{\hat{I}}½\hat{I}½{\hat{I}}^3)$, for the same photon energy threshold, differs from our prediction by 3.5 standard deviations.

13 pages, 1 figure, results included as ancillary files