Role of heavy neutral lepton in lepton number violating $B$ meson decays

We study the phenomenology of heavy neutral leptons (HNLs) in $B$-meson decays as probes of physics beyond the Standard Model. Focusing on the leptonic channels $B\to \mu N$ and $B\to \tau N$, we constrain the allowed regions in the $M_N$–$\mathrm{\mid }{U}_{\mathrm{\ell }N}{\mathrm{\mid }}^2$ plane using current experimental data. Using these constraints, we investigate lepton-number violating ($\mathrm{\Delta }L=2$) processes mediated by on-shell HNLs, including $B_{(c)}^{-}\to {\pi }^{+}{\mu }^{-}{\mu }^{-}$ and $B_c^{-}\to J\mathrm{/}\psi {\pi }^{+}{\mu }^{-}{\mu }^{-}$. For benchmark values $\mathrm{\mid }{U}_{\mu N}{\mathrm{\mid }}^2={10}^{-6}$ and $M_N=2$– $3\mathrm{G}\mathrm{e}\mathrm{V}$, the predicted branching ratios lie in the range $\mathcal{O}({10}^{-13})$–$\mathcal{O}({10}^{-8})$. Among the channels, $B_c^{-}\to {\pi }^{+}{\mu }^{-}{\mu }^{-}$ shows the largest enhancement, while $B_c^{-}\to J\mathrm{/}\psi {\pi }^{+}{\mu }^{-}{\mu }^{-}$ is strongly suppressed. These results indicate a clear channel dependence, with $B_c$ modes providing enhanced sensitivity to HNL effects and offering promising avenues for future searches of lepton number violation.