New physics effects with right-handed neutrinos in semileptonic decay $$B_c^+ \rightarrow B_s \mu ^+ \nu _{\mu }$$

Abstract We extend the Standard Model with the general effective Hamiltonian for the quark level transition $$c \rightarrow s \ell \nu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>c</mml:mi> <mml:mo>→</mml:mo> <mml:mi>s</mml:mi> <mml:mi>ℓ</mml:mi> <mml:mi>ν</mml:mi> </mml:mrow> </mml:math> with a complete set of four fermion operators including right-handed neutrinos. The current experimental measurements in charm decays are compatible with the Standard Model predictions and are used to constrain the new physics. With the available experimental data, we fit a $$\chi ^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>χ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> function to get the best-fit values of the NP WCs. We investigate the impact of allowed new physics in the observables such as differential branching fraction, forward–backward asymmetry, lepton polarization asymmetry, and convexity parameter in the semileptonic decay $$B_c^+ \rightarrow B_s \mu ^+ \nu _{\mu }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>B</mml:mi> <mml:mi>c</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> <mml:mo>→</mml:mo> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:msup> <mml:mi>μ</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msub> <mml:mi>ν</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> </mml:mrow> </mml:math> . The different types of new physics scenarios significantly affect these considered observables. Future experimental information on these observables can help disentangle the structure of new physics.