Loop-Level Lepton Flavor Violation and Diphoton Signals in the Minimal Left-Right Symmetric Model

TL;DR

The paper analyzes 1-loop radiative couplings of a light $H_3$ in the minimal LRSM, focusing on lepton flavor-violating (LFV) and lepton flavor-conserving (LFC) couplings to charged leptons and the $H_3\gamma\gamma$ diphoton channel, generated by heavy LRSM states such as the RHNs $N_i$, the $W_R$, and charged scalars. It derives the dependence of these couplings on the right-handed scale $v_R$ and shows that current laboratory and astrophysical data impose strong bounds, with gamma-ray observations of SN1987A providing the leading constraint $v_R \gtrsim 2\times 10^{9}$ GeV; future high-precision muon experiments and supernova observations could extend sensitivity to $v_R \sim 5\times 10^{9}$ GeV and $6\times 10^{11}$ GeV, respectively. The work also highlights rich phenomenology for a light $H_3$, including LFV decays $\ell_\beta \to \ell_\alpha + X$ and diphoton decays, and emphasizes the complementarity of laboratory and astrophysical probes in testing LRSM parameter space. Overall, it demonstrates that radiative $H_3$ couplings provide a powerful, multi-pronged test of the LRSM and the scale of $SU(2)_R$ breaking.

Abstract

The left-right symmetric model (LRSM) could not only restore parity of the weak interaction, but also provide natural explanations of the tiny active neutrino masses via the seesaw mechanisms. The $SU(2)_R$-breaking scalar $H_3$ can induce lepton flavor violating (LFV) effects in the minimal version of LRSM at the 1-loop order, originating from the mixing of heavy right-handed neutrinos. If $H_3$ is light, say below the GeV scale, it will lead to rich signals, e.g. the LFV muon and tauon decays $\ell_β\to \ell_α+ X$ ($X$ being either visible or invisible final states) and the anomalous supernova signatures. Combined with the diphoton coupling of $H_3$, the right-handed scale $v_R$ is excluded up to $2\times10^9$ GeV. In the future, the $v_R$ scale can be probed up to $5\times10^9$ GeV in high-precision muon experiments, and further up to $6\times10^{11}$ GeV by supernova observations.

Figures (3)

• Figure 1: The 1-loop Feynman diagrams for the LFV couplings of $H_3$ in the minimal LRSM.
• Figure 2: Constraints on $m_{H_3}$ and $v_R$ from the LFV, LFC and diphoton couplings of $H_3$ in the minimal LRSM, labeled as solid, dot-dashed and dashed lines, respectively. The shaded regions are for current limits, and the lines are for future prospects. The long dashed back line indicates the current LHC limits from direct searches of heavy $W_R$ boson ATLAS:2023cjoCMS:2021dzb. See text and Tables \ref{['tab:LFV']} and \ref{['tab:gauge']} for details.
• Figure S1: Left panel: The BRs of $H_3$ decaying into $e^+e^-$, $e^\pm\mu^\mp$, $\mu^+\mu^-$ and $\gamma\gamma$ as functions of its mass $m_{H_3}$. Right panel: The proper lifetime of $H_3$ as function of its mass $m_{H_3}$. We have set $v_R = 10$ TeV. Other parameter setups can be found in the main text.