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In this work, we study the lepton flavor and lepton number violating $B_{c}$meson decays via two intermediate on-shell Majorana neutrinos $N_j$ into twocharged leptons and a charged pion $B_{c}^{\pm} \to \mu^{\pm} \ N_j \to\mu^{\pm} \tau^{\pm} \pi^{\mp}$. We evaluated the possibility to measure themodulation of the decay width along the detector length produced as aconsequence of the lepton flavor violating process, in a scenario where theheavy neutrinos masses range between $2.0$ GeV $\leq M_N \leq 6.0$ GeV. Westudy some realistic conditions which could lead to the observation of thisphenomenon at futures $B$ factories such HL-LHCb.

Discovering heavy neutrino oscillations in rare Bc meson decays at HL-LHCb