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It is well-known that within the standard three flavor neutrino oscillation formalism, the Majorana phases appearing in the neutrino mixing matrix cannot have any effect on neutrino oscillation probabilities thereby evading testability at neutrino oscillation experiments. We consider an effective non-Hermitian Hamiltonian describing three flavor neutrino oscillations with the possibility of neutrino decay and demonstrate that the two Majorana phases can entangle with the off-diagonal decay terms and appear at the level of oscillation probabilities. Using the Cayley-Hamilton theorem, we derive approximate analytical expressions for three flavor neutrino oscillation probabilities in the presence of neutrino decay, taking into account matter effects. In the context of a long baseline neutrino experiment, we then analyse the impact of Majorana phases on the oscillation probabilities for different channels as well as on observables related to CP violation effects in neutrino oscillations. Finally, we discuss the effect of Majorana phases on the parameter degeneracies in the neutrino oscillation framework., Comment: 27 pages, 8 figures. Comments Welcome

Motivated by the recent Belle II result indicating a $2.7\,\sigma$ excess of $B^+\to K^+ + E_{\text{miss}}$ events compared to the Standard Model (SM) prediction for $B^+ \to K^+ \nu\bar{\nu}$, we explore an explanation to this anomaly based on a KSVZ-type QCD axion model featuring a Peccei-Quinn (PQ) symmetry breaking at high-scale, that can provide a solution to the strong CP problem with dark matter relic abundance. The model contains a PQ-charged scalar} leptoquark which can interact with the SM quarks only via mass-mixing of the latter with vector-like quarks. The mixing between SM and vector-like quarks is determined by the PQ mass scales and can explain the excess $B^+\to K^+ + E_{\text{miss}}$ events while respecting other flavour constraints. The same PQ-charged scalar leptoquarks and vector-like quarks also mediate the two-loop radiative neutrino masses., Comment: 25 pages, 6 figures

We introduce a framework for hybrid neutrino mass generation, wherein scotogenic dark sector particles, including dark matter, are charged non-trivially under the $A_4$ flavor symmetry. The spontaneous breaking of the $A_4$ group to residual $\mathcal{Z}_2$ subgroup results in the ``cutting" of the radiative loop. As a consequence the neutrinos acquire mass through the hybrid ``scoto-seesaw" mass mechanism, combining aspects of both the tree-level seesaw and one-loop scotogenic mechanisms, with the residual $\mathcal{Z}_2$ subgroup ensuring the stability of the dark matter. The flavor symmetry also leads to several predictions including the normal ordering of neutrino masses and ``generalized $\mu-\tau$ reflection symmetry" in leptonic mixing. Additionally, it gives testable predictions for neutrinoless double beta decay and a lower limit on the lightest neutrino mass. Finally, $A_4 \to \mathcal{Z}_2$ breaking also leaves its imprint on the dark sector and ties it with the neutrino masses and mixing. The model allows only scalar dark matter, whose mass has a theoretical upper limit of $\lesssim$ 600 GeV, with viable parameter space satisfying all dark matter constraints, available only up to about 80 GeV. Conversely, fermionic dark matter is excluded due to constraints from the neutrino sector. Various aspects of this highly predictive framework can be tested in both current and upcoming neutrino and dark matter experiments., Comment: 38 pages, 3 tables, 18 figures