On the Effective Mass of the Electron Neutrino in Beta Decay ∗

In the presence of mixing between massive neutrino states, the distortion of the electron spectrum in beta decay is, in general, a function of several masses and mixing angles. For 3ν-schemes which describe the solar and atmospheric neutrino data, this distortion can be described by a single effective mass, under certain conditions. In the literature, two different definitions for the effective mass have been suggested. We show that for quasi-degenerate mass schemes (with an overall mass scale m and splitting ∆m 2) the two definitions coincide up to (∆m 2) 2 /m 4 corrections. We consider the impact of different effective masses on the integral energy spectrum. We show that the spectrum with a single mass can be used also to fit the data in the case of 4ν-schemes motivated, in particular, by the LSND results. In this case the accuracy of the mass determination turns out to be better than (10 − 15)%.