Probing muon anomaly and lepton flavor violation with scalar leptoquarks in the 331LHN model

We extend the $SU(3{)}_C\times SU(3{)}_L\times U(1{)}_X$ model with neutral leptons (331LHN) by introducing scalar leptoquarks. We determine the particle content of the leptoquark multiplets and their Yukawa interactions with fermions. We find that a singlet leptoquark can fully account for the $4.2\sigma$ discrepancy in the muon anomalous magnetic moment $\mathrm{\Delta }{a}_{\mu }^{2021}$. The corresponding leptoquark mass is constrained to be $m_S\gtrsim 1.8$~TeV, consistent with current LHC bounds. We further consider the updated $\mathrm{\Delta }{a}_{\mu }^{2025}$ based on recent lattice QCD results, which strengthen the lower bound to $m_S\gtrsim 6$~TeV. Combining $\mathrm{\Delta }{a}_{\mu }$ with low-energy leptonic observables, including charged lepton flavor violation and the $\mu$–$e$ conversion rate, we constrain the viable parameter space. The allowed leptoquark Yukawa couplings exhibit a normal hierarchical pattern under all constraints. We also investigate the collider phenomenology of the singlet leptoquark, showing that its QCD-driven pair production leads to suppressed signal rates at the LHC for multi-TeV masses, while future hadron colliders can significantly extend the discovery reach.