An Alternative: Two-Mixing Texture for Three Neutrinos or Three-Mixing Texture for Four Neutrinos

The alternative formulated in the title has a chance to be settled, when the existence of the LSND effect is experimentally excluded or confirmed. The first option, much discussed in literature, works in the case of three active neutrinos νe, νμ, ντ, when among their massive states ν1, ν2, ν3 there is no direct mixing between ν1 and ν3, and the mass hierarchy m12≤m22≤m32 holds. This option is consistent with the observed deficits of solar νe's and atmospheric νμ's, if Δm212↔Δmsol2 and Δm322↔Δmatm2. On the other hand, the second option is an extension of the idea of the former to the case of four neutrinos νs, νe, νμ, ντ (including one sterile neutrino νs), when among their massive states ν0, ν1, ν2, ν3 there are no direct mixings between ν0 and ν2, ν0 and ν3, ν1 and ν3, and the mass hierarchy m02≤m12<<m22≤m32 is now valid. Such an option, belonging to a class of textures widely discussed in literature, may be consistent with the observed deficits of solar νe's and atmospheric νμ 's as well as with the LSND appearance of νe's in the beam of accelerator νμ's, if now Δm102↔Δmsol2, Δm322↔Δmatm2 and Δm212↔ΔmLSND2 (however, in the case of solar νe's the role of ν's in the disappearance of νe's is recently questioned). In both options, only the close neighbours in the hierarchies of massive neutrinos ν1, ν2, ν3 and ν0, ν1, ν2, ν-3, respectively, mix directly. This characteristic feature of the two-mixing texture for three neutrinos or the three-mixing texture for four neutrinos may be somehow physically significant. (author)