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

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 (RHNs). If $H_3$ is light, say below the GeV scale, it will lead to rich signals, e.g. the LFV muon and tauon decays $\ell_\beta \to \ell_\alpha + X$ ($X$ being either visible or invisible final states) and the anomalous supernova signatures. Combined with the diphoton coupling of $H_3$, and recasting the existing constraints onto the light $H_3$ scenario, 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, if the Yukwa couplings for RHN masses are of order one and the RHN mixing is maximal, and further up to $6\times10^{11}$ GeV by supernova observations, reaching the non-resonant leptogenesis scale in the LRSM.