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Register a new userBuilding the full PMNS Matrix from six independent Majorana-type phases
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In the framework of three light Majorana neutrinos, we show how to reconstruct, through the use of 3 x 3 unitarity, the full PMNS matrix from six independent Majorana-type phases. In particular, we express the strength of Dirac-type CP violation in terms of these Majorana-type phases by writing the area of the unitarity triangles in terms of these phases. We also study how these six Majorana phases appear in CP-odd weak basis invariants as well as in leptonic asymmetries relevant for flavoured leptogenesis.
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We propose a new scenario for baryogenesis through leptogenesis, where the CP phase relevant for leptogenesis is connected directly to the PMNS phase(s) in the light neutrino mixing matrix. The scenario is realized in case only one CP phase appears in the full theory, originating from the complex vacuum expextation value of a standard model singlet field. In order to realize this scheme, the electroweak symmetry is required to be broken during the leptogenesis era and a new loop diagram with an intermediate $W$ boson exchange including the low energy neutrino mixing matrix should play the dominant contribution to the CP violation for leptogenesis. In this letter, we discuss the new basic mechanism, which we call type-II leptogenesis, and give an estimate for maximally reachable baryon asymmetry depending on the PMNS phases.
As a result of a non-trivial mixing matrix, neutrinos cannot be simultaneously in a flavor and mass eigenstate. We formulate and discuss information entropic relations that quantify the associated quantum uncertainty. We also formulate a protocol to determine the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix from quantum manipulations and measurements on an entangled lepton-neutrino pair. The entangled state features neutrino oscillations in a conditional probability involving measurements on the lepton and the neutrino. They can be switched off by choosing a specific observable on the lepton side which is determined by the PMNS matrix. The parameters of the latter, including the CP-violating phase $delta$, can be obtained by guessing them and improving the guess by minimizing the remaining oscillations.
By postulating the relation theta_{23} simeq 45^circ + etatheta_{13}, we seek preferable correction terms to tri-bi-maximal mixing and discuss their origins. Global analyses of the neutrino oscillation parameters favor eta=pm 1/sqrt{2}; this corresponds to the relation found by Edy, Frampton, and Matsuzaki some years ago in the context of a T^prime flavor symmetry. In contrast, the results of the u_mu disappearance mode reported by the T2K and Super-Kamiokande collaborations seem to prefer eta=0, which gives an almost maximal theta_{23}. We derive a general condition for ensuring theta_{23} simeq 45^circ + etatheta_{13} and find that the condition is complicated by the neutrino masses and CP violating phases. We investigate the condition under simplified environments and arrive at several correction terms to the mass matrices. It is found that the obtained correction terms can arise from flavor symmetries or one-loop radiative corrections.
The Tri-Bi-Maximal pattern has been long investigated as the symmetric scenario that lies behind the neutrino mixing matrix. It predicts a null reactor angle and hence forbids $CP$ violation in the lepton sector, which is in contrast to the current experimental determinations. We explore different deviations from this pattern to restore the compatibility with the latest fits of neutrino mixing parameters. We consider two unitary matrices to correct the symmetric pattern, each of them is written in terms of one single angle and one complex phase, which will be constrained by the experimental mixings and from symmetry restrictions in the mass matrix. We note that these correction parameters would allow us to obtain simultaneous information about the Dirac and Majorana $CP$ phases in some specific scenarios. We show that the predicted values lead to sharped regions for the neutrinoless double beta decay amplitude, in the selected cases, that could be tested with forthcoming results.
Geometric (Aharonov--Anandan) phases in neutrino oscillations have been claimed [Phys. Lett. B 780 (2018) 216] to be sensitive to the Majorana phases in neutrino mixing. More recently, however, it has been pointed out [Phys. Lett. B 818 (2021) 136376] that the proposed phases are not gauge invariant. Using both kinematic and geometric approaches, we show that all gauge-invariant Aharonov--Anandan phases (including the off-diagonal geometric phases associated with flavor transitions) are independent of the Majorana phases. This finding, which generalizes the well-known fact that conventional oscillation experiments cannot discern the Dirac or Majorana nature of the neutrino, implies that a hypothetical interference experiment cannot distinguish between the two either.
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