Abstract
With the help of current neutrino oscillation data, we illustrate the three-dimensional (3D) profiles of all the six distinct effective Majorana neutrino masses |〈m〉αβ| (for α,β=e,μ,τ) with respect to the unknown neutrino mass scale and effective Majorana CP phases. Some salient features of |〈m〉αβ| and their phenomenological implications are discussed in both the normal and inverted neutrino mass ordering cases.
Highlights
In the standard three-flavor scheme the phenomenology of neutrino oscillations can be fully described in terms of the neutrino mass-squared differences ∆m2ij ≡ m2i − m2j, the lepton flavor mixing angles θij and the Dirac CP-violating phase δ [1]
We are left with three unknown parameters which are completely insensitive to normal neutrino oscillation experiments: the absolute neutrino mass scale and two Majorana CP-violating phases
The Majorana CP phases are only sensitive to those lepton-number-violating processes which have never been measured [10]. Before such challenging measurements are successfully implemented in the foreseeable future, one has to use the available neutrino oscillation data to constrain the moduli of six distinct effective Majorana neutrino masses m αβ ≡ miUαiUβi i=1 in the basis of diagonal charged-lepton flavors, where Uαi are the elements of the Pontecorvo-Maki-Nakawaga-Sakata (PMNS) lepton flavor mixing matrix [6,11,12]
Summary
Given the available neutrino oscillation data, one has so far paid a lot of attention to the two-dimensional (2D) mapping of | m αβ| as functions of the smallest neutrino mass m1 (normal mass ordering, NMO) or m3 (inverted mass ordering, IMO) [13], especially to the allowed region of | m ee| which is closely associated with the observability of the 0ν2β decays In such a 2D mapping one usually requires the unknown CP-violating phases of U to vary from 0 to 2π, and it is almost impossible to see the explicit dependence of | m αβ| on those phase parameters. The ultimate goal of such efforts is to pin down all the CP-violating phases of U and have a full understanding of the flavor structure of massive neutrinos This goal seems to be too remote from our today’s experimental techniques, the 3D mapping of | m αβ| may at least help shed light on the underlying flavor symmetry behind the observed neutrino mass spectrum and flavor mixing pattern. Δ is of the Majorana nature, it determines the strength of CP violation in normal neutrino oscillations and often referred to as the “Dirac” CP phase
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