The $\rho$ parameter and $H^0\to \ell_i \ell_j$ in models with TeV sterile neutrinos

TL;DR

This paper investigates Higgs decays to different lepton flavors in models with TeV-scale sterile neutrinos, revealing that such processes are highly suppressed and unlikely to be observed with current collider capabilities.

Contribution

It provides a comprehensive analysis of Higgs flavor-violating decays in generic neutrino models, highlighting the effects of decoupling and cancellations on expected rates.

Findings

Decay rates are about 100 times smaller than previous estimates.

Perturbative Yukawa couplings consistent with the $ ho$ parameter yield branching ratios below 10^{-8}.

Such decays are not observable at current collider experiments.

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 $y_iy_j=2 \,s_{\nu_i} s_{\nu_j}\, m_N^2/v^2$, where $s_{\nu_{i,j}}$ 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 $\rho$ parameter imply ${\cal B}(H^0\to \bar{\ell}_i\ell_j)<10^{-8}$ for any lepton flavors, a rate that is not accessible at current colliders.