Hybrid Type-II and Type-III seesaw model for the muon $g-2$ anomaly

In this work we investigate the muon anomalous magnetic dipole moment $a_\mu$ in a model that extends the Standard Model with a scalar triplet and a lepton triplet. Different from previous studies, we find that there is still viable parameter space in this model to explain the discrepancy $\Delta a_\mu=a_{\mu}(\mathrm{Exp})-a_{\mu}(\mathrm{SM})$. While being consistent with the current data of neutrino mass, electroweak precision measurements and the perturbativity of couplings, our model can provide new physics contribution $a_\mu^\textrm{NP}$ to cover the central region of $\Delta a_\mu$ with new scalar and lepton mass as low as around TeV. This mass scale is allowed by the current collider searches for doubly charged scalars and the lepton triplet, and they can be tested at future high energy and/or high luminosity colliders.