[en] We scrutinize corrections to tribimaximal (TBM), bimaximal (BM) and democratic (DC) mixing matrices for explaining recent global fit neutrino mixing data. These corrections are parameterized in terms of small orthogonal rotations (R) with corresponding modified PMNS matrices of the forms $(R_{ij}^l\cdot U,U\cdot R_{ij}^r,U\cdot R_{ij}^r\cdot R_{kl}^r,R_{ij}^l\cdot R_{kl}^l\cdot U)$ where $R_{ij}^{l,r}$ is rotation in ij sector and U is any one of these special matrices. We showed that for perturbative schemes dictated by single rotation, only $(R_{12}^l\cdot U_{BM},R_{13}^l\cdot U_{BM},U_{TBM}\cdot R_{13}^r)$ can fit the mixing data at 3σ level. However for $R_{ij}^l\cdot R_{kl}^l\cdot U$ type rotations, only $(R_{23}^l\cdot R_{13}^l\cdot U_{DC})$ is successful to fit all neutrino mixing angles within 1σ range. For $U\cdot R_{ij}^r\cdot R_{kl}^r$ perturbative scheme, only $(U_{BM}\cdot R_{12}^r\cdot R_{13}^r,U_{DC}\cdot R_{12}^r\cdot R_{23}^r,U_{TBM}\cdot R_{12}^r\cdot R_{13}^r)$ are consistent at 1σ level. The remaining double rotation cases are either excluded at 3σ level or successful in producing mixing angles only at $2\sigma -3\sigma$ level. We also updated our previous analysis on PMNS matrices of the form $(R_{ij}\cdot U\cdot R_{kl})$ with recent mixing data. We showed that the results modifies substantially with fitting accuracy level decreases for all of the permitted cases except $(R_{12}\cdot U_{BM}\cdot R_{13},R_{23}\cdot U_{TBM}\cdot R_{13}\text{and}{R}_{13}\cdot U_{TBM}\cdot R_{13})$ in this rotation scheme.

[en] A brief review of the status of neutrino oscillations is given. The phenomenology of neutrino mixing and the standard seesaw mechanism of neutrino mass generation is discussed. Different approaches to neutrino oscillations are considered and compared. The role of the Heisenberg space-momentum uncertainty relation and the Mandelstam-Tamm time-energy uncertainty relation in neutrino oscillations is discussed in some detail.

[en] In the light of non-zero and relatively large value of rector mixing angle (${\theta }_{13}$), we have performed a detailed analysis of texture one zero neutrino mass matrix $M_{\nu }$ in the scenario of vanishing determinant/trace conditions, assuming the Dirac nature of neutrinos. In both the scenarios, normal mass ordering is ruled out for all the six possibilities of $M_{\nu }$, however for inverted mass ordering, only two are found to be viable with the current neutrino oscillation data at 3σ confidence level. Numerical and some approximate analytical results are presented.

[en] We motivate the usage of finite groups as symmetries of the Lagrangian. After a presentation of basic group-theoretical concepts, we introduce the notion of characters and character tables in the context of irreducible representations and discuss their applications. We exemplify these theoretical concepts with the groups S₄ and A₄. Finally, we discuss the relation between tensor products of irreducible representations and Yukawa couplings and describe a model for tri-bimaximal lepton mixing based on A₄.

[en] We propose and analyse a new class of Littlest Seesaw models, with two right-handed neutrinos in their diagonal mass basis, based on preserving the first column of the Golden Ratio mixing matrix. We perform an exhaustive analysis of all possible remnant symmetries of the group $A_5$ which can be used to enforce various vacuum alignments for the flavon controlling solar mixing, for two simple cases of the atmospheric flavon vacuum alignment. The solar and atmospheric flavon vacuum alignments are enforced by different remnant symmetries. We examine the phenomenological viability of each of the possible Littlest Seesaw alignments in $A_5$, which preserve the first column of the Golden ratio mixing matrix, using figures and extensive tables of benchmark points and comparing our predictions to a recent global analysis of neutrino data. A benchmark model is constructed based on $A_5\times Z_6\times Z_5\times Z_5^{\prime }$.

[en] We analyse in details the phenomenological implications for lepton masses and mixing due to the breaking of the discrete symmetries $A_5$ and CP into the subgroups $Z_2\times$CP and $Z_5$ for the neutrino and charged-lepton sectors. The direct product of $Z_2$ and CP in the neutrino sector allows for a complete determination of masses, mixing and CP phases in terms of only four real parameters. Consequently, we derive accurate analytic expressions for the sum of the neutrino masses as well as the effective Majorana masses, $m_{\beta }$ and $m_{\beta \beta }$, under different hypotheses for the flavon vevs. Finally, we compare our predictions with the exact numerical results obtained from the diagonalisation of the neutrino mass matrix and discuss their accuracy.

[en] We propose a first model of quarks based on the discrete family symmetry Δ(6N"2) in which the Cabibbo angle is correctly determined by a residual Z_2×Z_2 subgroup, and the smaller quark mixing angles may be qualitatively understood from the model. The present model of quarks may be regarded as a first step towards formulating a complete model of quarks and leptons based on Δ(6N"2), in which the lepton mixing matrix is fully determined by a Klein subgroup. For example, the choice N=28 provides an accurate determination of both the reactor angle and the Cabibbo angle

[en] The Littlest Seesaw (LS) model involves two right-handed neutrinos and a very constrained Dirac neutrino mass matrix, involving one texture zero and two independent Dirac masses, leading to a highly predictive scheme in which all neutrino masses and the entire PMNS matrix is successfully predicted in terms of just two real parameters. We calculate the renormalisation group (RG) corrections to the LS predictions, with and without supersymmetry, including also the threshold effects induced by the decoupling of heavy Majorana neutrinos both analytically and numerically. We find that the predictions for neutrino mixing angles and mass ratios are rather stable under RG corrections. For example we find that the LS model with RG corrections predicts close to maximal atmospheric mixing, θ_2_3=45"∘±1"∘, in most considered cases, in tension with the latest NOvA results. The techniques used here apply to other seesaw models with a strong normal mass hierarchy.

[en] This paper discusses recent results and near-term prospects of the long-baseline neutrino experiments MINOS, MINOS+, T2K and NOvA. The non-zero value of the third neutrino mixing angle θ _1_3 allows experimental analysis in a manner which explicitly exhibits appearance and disappearance dependencies on additional parameters associated with mass-hierarchy, CP violation, and any non-maximal θ _2_3. These current and near-future experiments begin the era of precision accelerator long-baseline measurements and lay the framework within which future experimental results will be interpreted. (paper)

[en] We explicitly test, in a simplified 5-dimensional model with G ₂ gauge symmetry, the evolution of the gauge couplings. We assume that all the matter fields are propagating in the bulk, and consider orbifolds based on Abelian discrete groups which lead to 5-dimensional gauge theories compactified on an S ¹/ Z ₂. The gauge couplings evolution is derived at one-loop level and used to test the impact on lower energy observables, in particular the Weinberg angle. (paper)