We study a scotogenic extension of the minimal gauged $L_{\mu }-L_{\tau }$ model including three right-handed singlet fermions and a scalar doublet all odd under an in-built $Z_2$ symmetry to explain the anomalous magnetic moments of the muon, CDF-II $W$-mass anomaly, and the 95 GeV excess reported by the CMS collaboration. While the minimal model can successfully explain the muon ($g-2$) and CDF-II $W$-mass anomalies, the required diphoton signal strength for the 95 GeV scalar, together with that of the SM Higgs, cannot be obtained in the minimal model. The same can, however, be explained by incorporating one additional scalar doublet whose only role is to contribute radiatively to diphoton decay modes of the light, neutral scalars. Due to the scotogenic extension, the model remains consistent with the observed properties of light neutrinos and dark matter in the Universe.

• Received 15 November 2023
• Accepted 21 February 2024

DOI:https://doi.org/10.1103/PhysRevD.109.055021

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society