Magnetic moment of neutrinos in a left-right symmetric model and Interplay of type-I and type-II seesaw

In left-right symmetric models, the Majorana coupling matrix, $f$, and hence the right-handed neutrino (RHN) mass matrix, admits eight solutions assuming the form of Dirac coupling matrix is known. Additionally, the coupling matrix depends on the parity-breaking scale, $v_R$, as a new physics scale. RHNs being Majorana in nature can possess a transition magnetic moment (TMM). Neutrino magnetic moments are inherently related to neutrino masses, as neutrino masses imply neutrino magnetic moments. We study, along with small neutrino TMM, the heavy RHN transition magnetic moment contributions to muon $g-2$, $(g-2)_\mu$ anomaly for all eight solutions of $f$. We find, of the eight solutions, only two solutions of $f$ matrix contribute to the $(g-2)_\mu$ in the experimental predicted range. The range of $v_R$ in these cases is found to be $3.4 \times 10^3 - 1.5 \times 10^4$ GeV. For a complementary check, we also study TMM induced neutrinoless double beta decay ($0\nu\beta\beta$), for the same set of choice of parameters. While certain parameter choices allow RHNs to explain the $(g-2)_\mu$ anomaly, the same configurations lead to an extremely long half-life for $0\nu\beta\beta$ decay, well beyond experimental reach. Even under extreme magnetic field enhancements, the half-life decreases only marginally, reinforcing the dominance of weak interaction vertices over TMM contributions in $0\nu\beta\beta$ decay.