Texture Zeros and Majorana Phases of the Neutrino Mass Matrix

We present the generic formulas to calculate the ratios of neutrino masses and the Majorana phases of CP violation from the neutrino mass matrix with two independent vanishing entries in the flavor basis where the charged lepton mass matrix is diagonal. An order-of-magnitude illustration is given for seven experimentally acceptable textures of the neutrino mass matrix, and some analytical approximations are made for their phenomenological consequences at low energy scales. ∗Electronic address: [email protected] 1 1 The atmospheric and solar neutrino oscillations observed in the Super-Kamiokande experiment [1] have provided robust evidence that neutrinos are massive and lepton flavors are mixed. A full description of the mass spectrum and flavor mixing in the framework of three lepton families requires twelve real parameters: three charged lepton masses (me, mμ, mτ ), three neutrino masses (m1, m2, m3), three flavor mixing angles (θx, θy, θz), one Dirac-type CP-violating phase (δ) and two Majorana-type CP-violating phases (ρ and σ). So far only the masses of charged leptons have been accurately measured [2]. Although we have achieved some preliminary knowledge on two neutrino mass-squared differences and three flavor mixing angles from current neutrino oscillation experiments, much more effort is needed to determine these parameters precisely. The more challenging task is to pin down the absolute neutrino mass scale and the CP-violating phases. Towards reaching these goals, a number of new neutrino experiments have been proposed [3]. After sufficient information on neutrino masses and lepton flavor mixing parameters is experimentally accumulated, a determination of the textures of lepton mass matrices should become possible. On the other hand, the textures of charged lepton and neutrino mass matrices may finally be derived from a fundamental theory of lepton mass generation, which is unfortunately unknown for the time being. It is therefore important in phenomenology to investigate how the textures of lepton mass matrices can link up with the observables of lepton flavor mixing. Recently Frampton, Glashow and Marfatia [4] have examined the possibility that a restricted class of lepton mass matrices may suffice to describe current experimental data. They find seven acceptable textures of the neutrino mass matrix with two independent vanishing entries in the flavor basis where the charged lepton mass matrix is diagonal. In this paper we carry out a further study of two-zero textures of the neutrino mass matrix. Our work is different from Ref. [4] in several aspects: (a) we write out the generic constraint equations for the neutrino mass matrix with two independent vanishing entries, from which the analytically exact expressions of neutrino mass ratios can be derived; (b) the formulas to calculate the Majorana-type CP-violating phases are presented; (c) the relative magnitudes of neutrino masses, the Majorana phases, the ratio of two neutrino mass-squared differences, and the effective mass term of the neutrinoless double beta decay are estimated by taking typical inputs of the flavor mixing angles and the Dirac-type CP-violating phase; and (d) an order-of-magnitude illustration is given for seven two-zero textures of the neutrino mass matrix. 2 In the flavor basis where the charged lepton mass matrix is diagonal, the neutrino mass matrix can be written as M = V 