Discovering heavy neutrino oscillations in rare $B^\pm_c$ meson decays at HL-LHCb

In this work, we study the lepton flavor and lepton number violating <math display="inline"><msub><mi>B</mi><mi>c</mi></msub></math> meson decays via two intermediate on-shell Majorana neutrinos <math display="inline"><msub><mi>N</mi><mi>j</mi></msub></math> into two charged leptons and a charged pion <math display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>±</mo></msubsup><mo stretchy="false">→</mo><msup><mi>μ</mi><mo>±</mo></msup><msub><mi>N</mi><mi>j</mi></msub><mo stretchy="false">→</mo><msup><mi>μ</mi><mo>±</mo></msup><msup><mi>τ</mi><mo>±</mo></msup><msup><mi>π</mi><mo>∓</mo></msup></math>. We evaluated the possibility to measure the modulation of the decay width along the detector length produced as a consequence of the lepton flavor violating process, in a scenario where the heavy neutrinos masses range between <math display="inline"><mrow><mn>2.0</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>≤</mo><msub><mi>M</mi><mi>N</mi></msub><mo>≤</mo><mn>6.0</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>. We study some realistic conditions, which could lead to the observation of this phenomenon at future <math display="inline"><mi>B</mi></math> factories, such as the HL-LHCb.