Abstract: We study the constraints imposed by neutrino oscillation experiments on the minimal extension of the Standard Model that can explain neutrino masses, which requires the addition of just two singlet Weyl fermions. The most general renormalizable couplings of this model imply generically four massive neutrino mass eigenstates while one remains massless: it is therefore a minimal 3+2 model. The possibility to account for the confirmed solar, atmospheric and long-baseline oscillations, together with the LSND/MiniBooNE and reactor anomalies is addressed. We find that the minimal model can fit oscillation data including the anomalies better than the standard 3 nu model and similarly to the 3 + 2 phenomenological models, even though the number of free parameters is much smaller than in the latter. Accounting for the anomalies in the minimal model favours a normal hierarchy of the light states and requires a large reactor angle, in agreement with recent measurements. Our analysis of the model employs a new parametrization of seesaw models that extends the Casas-Ibarra one to regimes where higher order corrections in the light-heavy mixings are significant.

Abstract: A class of discrete flavor-symmetry-based models predicts constrained neutrino mass matrix schemes that lead to specific neutrino mass sum rules. One of these implies a lower bound on the effective neutrinoless double beta mass parameter, even for normal hierarchy neutrinos. Here we propose a new model based on the S-4 flavor symmetry that leads to the new neutrino mass sum rule and discuss how to generate a nonzero value for the reactor angle theta(13) indicated by recent experiments, and the resulting correlation with the solar angle theta(12).

Abstract: Two metallacyclic complexes of general formula Na-8[(M2L3)-L-II]center dot xH(2)O [M = Ni (4) and Co (5) with x = 15 (4) and 17 (5)] have been self-assembled in aqueous solution from N,N'-1,3-phenylenebis(oxamic acid) (H4L) and M2+ ions in a ligand/metal molar ratio of 3 : 2 in the presence of NaOH acting as base. X-Ray structural analyses of 4 and 5 show triple-stranded, dinuclear anions of the meso-helicate-type (so-called mesocates) with C-3h molecular symmetry. The two octahedral metal-tris(oxamate) moieties of opposite chiralities (Delta, Lambda form) are connected by three m-phenylene spacers at intermetallic distances of 6.822(2) (4) and 6.868(2) angstrom (5) to give a metallacryptand core. In the crystal lattice, the binding of these heterochiral dinickel(II) and dicobalt(II) triple mesocates to sodium(I) ions leads to oxamato-bridged heterobimetallic three-dimensional open-frameworks with a hexagonal diamond architecture having small pores of 17.566(4) (4) and 17.640(2) angstrom (5) in diameter where the crystallization water molecules and the sodium(I) countercations are hosted. Variable temperature (2.0-300 K) magnetic susceptibility measurements reveal relatively anisotropic S = 2 Ni-2(II) (4) and S = 3 Co-2(II) (5) ground states resulting from the moderate to weak intramolecular ferromagnetic coupling between the two high-spin Ni-II (S-Ni = 1) or Co-II (S-Co = 3/2) ions across the m-phenylenediamidate bridges [J = +3.6 (4) and +1.1 cm(-1) (5); H = -JS(1)center dot S-2]. A simple molecular orbital analysis of the electron exchange interaction identifies the p-type pathways of the meta-substituted phenylene spacers involving the d(z2) and d(x2-y2) pairs of magnetic orbitals of the two trigonally distorted octahedral high-spin M-II ions (M = Ni and Co) as responsible for the overall ferromagnetic coupling observed in 4 and 5 in agreement with a spin polarization mechanism. The decrease of the overall ferromagnetic coupling from 4 to 5 is in turn explained by the additional antiferromagnetic exchange contribution involving the d(xy) pair of magnetic orbitals of the two trigonally distorted octahedral high-spin Co-II ions across the sigma-type pathway of the meta-substituted phenylene spacers.