Abstract
We derive a new set of sum rules between the neutrino mass and mixing parameters in vacuum and their effective counterparts in matter. The moduli of nine genuine lepton mixing matrix elements can then be calculated in terms of the matter-corrected ones, and the latter can directly be determined from a variety of long-baseline neutrino oscillations. We show that it is possible to reconstruct the leptonic unitarity triangles and CP violation in a similar parametrization-independent way.
Highlights
Thanks to the Super-Kamiokande [1] and SNO [2] experiments, both solar and atmospheric neutrino oscillations are convincingly established
The terrestrial matter effects in all long-baseline neutrino experiments must be taken into account, since they can unavoidably modify the genuine behaviors of neutrino oscillations in vacuum
The exact formulas of mi and Vas functions of mi and V have been achieved by a number of authors [7,8,9,10], and the similar expressions of mi and V in terms of mi and Vhave been derived in Ref. [11]. The latter case is equivalently interesting in phenomenology, because our physical purpose is to determine the fundamental parameters of lepton flavor mixing from the effective ones, whose values can directly be measured from a variety of long-baseline neutrino oscillation experiments
Summary
Thanks to the Super-Kamiokande [1] and SNO [2] experiments, both solar and atmospheric neutrino oscillations are convincingly established. To formulate the probabilities of neutrino oscillations in matter in the same form as those in vacuum, one may define the effective neutrino masses mi and the effective lepton flavor mixing matrix Vin which the terrestrial matter effects are already included. The latter case is equivalently interesting in phenomenology, because our physical purpose is to determine the fundamental parameters of lepton flavor mixing from the effective ones, whose values can directly be measured from a variety of long-baseline neutrino oscillation experiments. This paper aims to reconstruct the genuine neutrino mixing matrix V and its unitarity triangles from possible long-baseline neutrino oscillations with terrestrial matter effects. The fundamental lepton flavor mixing matrix V and its unitarity triangles can be reconstructed from possible long-baseline neutrino oscillations straightforwardly and parametrization-independently.
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