Neutrino Masses and Mixing: Where We Stand and Where We Are Going

Our present understanding of neutrino masses and mixing comes from the interpretation of data on solar and atmospheric neutrinos as well as the results from the LSND experiment in terms of neutrino oscillations [1]. If neutrinos have masses, flavour is mixed in the CC interactions of the leptons, and a leptonic mixing matrix will appear analogous to the CKM [2] matrix for the quarks. The possibility of arbitrary mixing between two massive neutrino states was first introduced in Ref. [3]. The discussion of leptonic mixing in generic models is complicated by two factors. First the number massive neutrinos (n) is unknown, since there are no constraints on the number of right-handed, SM-singlet, neutrinos (m = n−3). Second, since neutrinos carry neither color nor electromagnetic charge, they could be Majorana fermions. In general the mixing matrix in the CC current is a 3×n matrix which contains n(n−1) 2 mixing angles and (n−1)(n−2) 2 phases if neutrinos are Dirac particles and n− 1 additional phases if neutrinos are Majorana particles. The presence of the leptonic mixing, allows for flavour oscillations of the neutrinos [4]. A neutrino of energy E produced in a CC interaction with a charged lepton lα can be detected via a CC interaction with a charged lepton lβ with a probability