In the model based on gauge group symmetry \(SU(3)_C\times SU(2)_L\times SU(3)_R\times U(1)_X\) (3-2-3-1 model), we study the phenomenology of the standard model–like Higgs boson \(H_1\) , which was not considered in previous works (Dong et al., Phys. Rev. D 95, 075034, 2017, and Huong et al., Phys. Rev. D 98, 055033, 2018). Specifically, we study couplings of \(H_1\) with pairs of charged fermions, gauge, charged scalar bosons, and trilinear Higgs boson self-coupling by employing the \(\kappa \) -framework. Based on these parameters, we explore the parameters \(\kappa _{\gamma }\) and \(\kappa _{Z\gamma }\) representing the \(H_1\rightarrow \gamma \gamma \) and \(H_1\rightarrow Z\gamma \) decays and find that the model can fulfill both 2 \(\sigma \) ATLAS and CMS constraints. Besides, new physics effects to lepton flavor-violating (LFV) decays \(H_1\rightarrow e_a^{\pm }e_b^{\mp }\) ( \(a\ne b\) ) are also discussed. The result indicates that the lower bound of the new physics scale, \(\Lambda \ge 10\) TeV, derived from LFV decay limits, is stronger than other constraints \(\Lambda \ge 6.6\) TeV (for charge parameter \(q=0\) ) and \(\Lambda \ge 4.6\) TeV (for charge parameter \(q=-1\) ) for electroweak precision tests and FCNCs obtained in Dong et al. (Phys. Rev. D 95, 075034, 2017) and Huong et al. (Phys. Rev. D 98, 055033, 2018).
