The $\ddot{I}$ parameter and $H^0\to {\ell }_i{\ell }_j$ in models with TeV sterile neutrinos

Abstract

The presence of massive sterile neutrinos $N$ mixed with the active ones induces flavor violating processes in the charged lepton sector at the loop level. In particular, the amplitude of $H^0\to {\bar{\ell }}_i{\ell }_j$ is expected to be proportional to the product of heavy-light Yukawa couplings $y_i{y}_j=2s_{\hat{I}{½}_i}{s}_{\hat{I}{½}_j}{m}_N^2/v^2$, where $s_{\hat{I}{½}_{i,j}}$ express the heavy-light neutrino mixings. Here we revisit these Higgs decays in the most generic extension of the neutrino sector, focusing on large values of $y_i$. We show that decoupling effects and a cancellation between the two dominant contributions to these processes makes the amplitude about one hundred times smaller than anticipated. We find that perturbative values of $y_i$ giving an acceptable contribution to the $\ddot{I}$ parameter imply $\mathcal{B}(H^0\to {\bar{\ell }}_i{\ell }_j)<10^{-8}$ for any lepton flavors, a rate that is not accessible at current colliders.

Comments and references added, version accepted for publication in PRD