Searching for signatures of new physics in $$\varvec{B \rightarrow K \, \nu \, \overline{\nu }}$$ to distinguish between Dirac and Majorana neutrinos

Abstract We conduct a model-independent analysis of the distinct signatures of various generic new physics possibilities in the decay $$B \rightarrow K \, \nu \, \overline{\nu }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo>→</mml:mo> <mml:mi>K</mml:mi> <mml:mspace/> <mml:mi>ν</mml:mi> <mml:mspace/> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> </mml:math> by analyzing the branching ratio as well as the missing mass-square distribution. Considering the final neutrinos to be of the same flavor with non-zero mass, we discuss the new physics contributions for both Dirac and Majorana neutrino possibilities. In our study, we utilize the analytical relations among form factors in semi-leptonic $$B \rightarrow K$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo>→</mml:mo> <mml:mi>K</mml:mi> </mml:mrow> </mml:math> transitions, which are consistent with current lattice QCD predictions to a very high numerical accuracy. We provide constraints on different new physics parameters, taking into account the recent measurement of $$B^+ \rightarrow K^+ \, \nu \, \overline{\nu }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>B</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mspace/> <mml:mi>ν</mml:mi> <mml:mspace/> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> </mml:math> branching ratio by the Belle-II collaboration. In future, if the missing mass-square distribution for $$B^+ \rightarrow K^+ \, \nu \, \overline{\nu }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>B</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mspace/> <mml:mi>ν</mml:mi> <mml:mspace/> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> </mml:math> decay gets reported by Belle-II with analysis of more events than their present data set, one can not only investigate possible new physics effects in these decays, but also probe the Dirac/Majorana nature of the neutrinos using quantum statistics, since a difference between the two cases is known to exist in the presence of non-standard neutrino interactions.