Abstract: We consider a supersymmetric type-I seesaw framework with non-universal scalar masses at the GUT scale to explain the long-standing discrepancy of the anomalous magnetic moment of the muon. We find that it is difficult to accommodate the muon g-2 while keeping charged-lepton flavor violating processes under control for the conventional SO(10)-based relation between the up sector and neutrino sector. However, such tension can be relaxed by adding a Georgi-Jarlskog factor for the Yukawa matrices, which requires a non-trivial GUT-based model. In this model, we find that both observables are compatible for small mixings, CKM-like, in the neutrino Dirac Yukawa matrix.

Abstract: We formulate an alternative approach based on unitarity triangles to describe neutrino oscillations in presence of non-standard interactions (NSI). Using perturbation theory, we derive the expression for the oscillation probability in case of NSI and cast it in terms of the three independent parameters of the leptonic unitarity triangle (LUT). The form invariance of the probability expression (even in presence of new physics scenario as long as the mixing matrix is unitary) facilitates a neat geometric view of neutrino oscillations in terms of LUT. We examine the regime of validity of perturbative expansions in the NSI case and make comparisons with approximate expressions existing in literature. We uncover some interesting dependencies on NSI terms while studying the evolution of LUT parameters and the Jarlskog invariant. Interestingly, the geometric approach based on LUT allows us to express the oscillation probabilities for a given pair of neutrino flavours in terms of only three (and not four) degrees of freedom which are related to the geometric properties (sides and angles) of the triangle. Moreover, the LUT parameters are invariant under rephasing transformations and independent of the parameterization adopted.

Abstract: We have studied the consequences of breaking the CPT symmetry in the neutrino sector, using the expected high-energy neutrino flux from distant cosmological sources such as active galaxies. For this purpose we have assumed three different hypotheses for the neutrino production model, characterised by the flavour fluxes at production phi(0)(e) : phi(0)(mu) : phi(0)(tau) = 1 : 2 : 0, 0 : 1 : 0, and 1 : 0 : 0, and studied the theoretical and experimental expectations for the muon-neutrino flux at Earth, phi(mu), and for the flavour ratios at Earth, R = phi(mu)/phi(e) and S = phi(tau)/phi(mu). CPT violation (CPTV) has been implemented by adding an energy-independent term to the standard neutrino oscillation Hamiltonian. This introduces three new mixing angles, two new eigenvalues and three new phases, all of which have currently unknown values. We have varied the new mixing angles and eigenvalues within certain bounds, together with the parameters associated to pure standard oscillations. Our results indicate that, for the models 1 : 2 : 0 and 0 : 1 : 0, it might be possible to find large deviations of phi(mu), R, and S between the cases without and with CPTV, provided the CPTV eigenvalues lie within 10(-29) – 10(-27) GeV, or above. Moreover, if CPTV exists, there are certain values of R and S that can be accounted for by up to three production models. If no CPTV were observed, we could set limits on the CPTV eigenvalues of the same order. Detection prospects calculated using IceCube suggest that for the models 1 : 2 : 0 and 0 : 1 : 0, the modifications due to CPTV are larger and more clearly separable from the standard-oscillations predictions. We conclude that IceCube is potentially able to detect CPTV but that, depending on the values of the CPTV parameters, there could be a mis-determination of the neutrino production model.