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

We conduct a model-independent analysis of the distinct signatures of various generic new physics possibilities in the decay $B \to K \, \nu \, \overline{\nu}$ 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 $B \to K$ 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 $B^+ \to K^+ \, \nu \, \overline{\nu}$ branching ratio by the Belle-II collaboration. In future, if the missing mass-square distribution for $B^+ \to K^+ \, \nu \, \overline{\nu}$ 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.