# The Higgs boson decays with the lepton flavor violation

## TL;DR

This paper investigates lepton flavor violating decays of a Higgs-like boson within the left-right symmetric model, calculating decay widths and comparing theoretical predictions with experimental bounds to explore neutrino sector implications.

## Contribution

It provides the first detailed calculation of these rare decay widths in the LRM, highlighting their dependence on neutrino mixing angles and experimental constraints.

## Key findings

- Decay widths are dominated by diagrams with neutrinos in the virtual state.
- Theoretical branching ratios are two orders of magnitude below experimental bounds.
- Constraints on mixing angles are derived from existing experimental data.

## Abstract

Within the left-right symmetric model (LRM) the decays $$S_1\to\mu^++\tau^-,\qquad S_1\to\mu^-+\tau^+$$ where $S_1$ is an analog of the standard model Higgs boson, are considered. The widths of this decays are found in the third order of the perturbation theory. Since the main contribution to the decay widths is caused by the diagram with the light and heavy neutrinos in the virtual state then investigation of this decays could shed light upon the neutrino sector structure. The obtained decay widths critically depend on the charged gauge bosons mixing angle $\xi$ and the heavy-light neutrinos mixing angle $\varphi$. The LRM predicts the values of these angles as functions of the vacuum expectation values $v_L$ and $v_R$. Using the results of the existing experiments, on looking for the additional charged gauge boson $W_2$ and on measuring the electroweak $\rho$ parameter, gives $$\sin\xi\leq5\times10^{-4},\qquad\sin\varphi\leq2.3\times10^{-2}. $$ However, even using the upper bounds on $\sin\xi$ and $\sin\varphi$ one does not manage to get the upper experimental bound on the branching ratio $\mbox{BR}(S_1\to\tau\mu)_{exp}$ being equal to $0.25\times10^{-2}$. The theoretical expression proves to be on two orders of magnitude less than $\mbox{BR}(S_1\to\tau\mu)_{exp}$.