# Precise prediction for the Higgs-Boson Masses in the $\mu\nu$SSM with three right-handed neutrino superfields

## TL;DR

This paper provides a detailed one-loop calculation of the Higgs boson masses in the $
u$SSM, demonstrating compatibility with experimental data and exploring unique phenomenological scenarios involving right-handed sneutrinos.

## Contribution

It performs the first complete one-loop renormalization of the neutral scalar sector in the $
u$SSM with three right-handed neutrinos, including higher-order MSSM corrections.

## Key findings

- Achieves a SM-like Higgs mass consistent with experimental bounds.
- Identifies scenarios with light right-handed sneutrinos that are experimentally accessible.
- Shows the model can explain the LEP and LHC excesses around 96 GeV.

## Abstract

The $\mu\nu$SSM is a simple supersymmetric extension of the Standard Model (SM) capable of describing neutrino physics in agreement with experiments. We perform the complete one-loop renormalization of the neutral scalar sector of the $\mu\nu$SSM with three generation of right-handed neutrinos in a mixed on-shell/$\overline{\mathrm{DR}}$ scheme. We calculate the full one-loop corrections to the neutral scalar masses of the $\mu\nu$SSM. The one-loop contributions are supplemented by available MSSM higher-order corrections. We obtain numerical results for a SM-like Higgs-boson mass consistent with experimental bounds, while simultaneously agreeing with neutrino oscillation data. We illustrate the distinct phenomenology of the $\mu\nu$SSM in scenarios in which one or more right-handed sneutrinos are lighter than the SM-like Higgs boson, which might be substantially mixed with them. These scenarios are experimentally accessible, on the one hand, through direct searches of the right-handed sneutrinos decaying into SM particles, and on the other hand, via the measurements of the SM-like Higgs-boson mass and its couplings. In this way the parameter space of the $\mu\nu$SSM can be probed without the need to propose model dependent searches at colliders. Finally, we demonstrate how the $\mu\nu$SSM can simultaneously accommodate two excesses measured at LEP and LHC at $\sim 96$ GeV at the $1\sigma$ level, while at the same time reproducing neutrino masses and mixings in agreement with neutrino oscillation measurements.