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Revisiting the $\Gamma(K \to e \nu)/\Gamma(K \to \mu \nu)$ ratio in supersymmetric unified models
R. M. Fonseca1, J. C. Romao1, A. M. Teixeira2

It has been pointed out that supersymmetric extensions of the Standard Model can induce significant changes to the theoretical prediction of the ratio $\Gamma(K \to e\nu)/\Gamma(K \to \mu\nu)= R_K$, through lepton flavor violating couplings. In this work we carry out a full computation of all one-loop corrections to the relevant $\nu \ell H^+$ vertex, and discuss the new contributions to $R_K$ arising in the context of different constrained (minimal supergravity inspired) models which succeed to account for neutrino data, further considering the possibility of accommodating a near future observation of a $\mu \to e \gamma$ transition. We also re-evaluate the prospects for $R_K$ in the framework of unconstrained supersymmetric models. In all cases, we address the question of whether it is possible to saturate the current experimental sensitivity on $R_K$ while in agreement with the recent limits on BR($B_{(s)} \to \mu \mu$). Our findings reveal that in view of the recent bounds, and even when enhanced by effective sources of flavour violation in the right-handed $\tilde e-\tilde \tau$ sector, constrained supersymmetric (seesaw) models typically provide excessively small contributions to $R_K$. While unconstrained models can indeed account for sizable contributions, the associated regions in parameter space are in general disfavoured due to the new $B_{s}\to \mu \mu$ bound.
1 :  Centro de Fisica Teorica de Particulas
2 :  LPC - Laboratoire de Physique Corpusculaire [Clermont-Ferrand]
Physique/Physique des Hautes Energies - Phénoménologie
Supersymmetry – neutrinos – meson decays – flavour violation
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