Abstract: One long-standing tension in the determination of neutrino parameters is the mismatched value of the solar mass square difference, Delta m(21)(2), measured by different experiments: the reactor antineutrino experiment KamLAND finds a best fit larger than the one obtained with solar neutrino data. Even if the current tension is mild (similar to 1.5 sigma.), it is timely to explore if independent measurements could help in either closing or reassessing this issue. In this regard, we explore how a future supernova burst in our galaxy could be used to determine Delta m(21)(2) at the future Hyper-Kamiokande detector, and how this could contribute to the current situation. We study Earth matter effects for different models of supernova neutrino spectra and supernova orientations. We find that, if supernova neutrino data prefers the KamLAND best fit for Delta m(21)(2), an uncertainty similar to the current KamLAND one could be achieved. On the contrary, if it prefers the solar neutrino data best fit, the current tension with KamLAND results could grow to a significance larger than 5 sigma. Furthermore, supernova neutrinos could significantly contribute to reducing the uncertainty on sin (2)theta(12).

Abstract: In modular invariant models of flavor, observables must be modular invariant. The observables discussed so far in the literature are functions of the modulus tau and its conjugate, (tau) over bar. We point out that certain combinations of observables depend only on tau , i.e. are meromorphic, and in some cases even holomorphic functions of tau. These functions, which we dub “invariants” in this Letter, are highly constrained, renormalization group invariant, and allow us to derive many of the models' features without the need for extensive parameter scans. We illustrate the robustness of these invariants in two existing models in the literature based on modular symmetries, Gamma(3) and Gamma(5). We find that, in some cases, the invariants give rise to robust relations among physical observables that are independent of tau. Furthermore, there are instances where additional symmetries exist among the invariants. These symmetries are relevant phenomenologically and may provide a dynamical way to realize symmetries of mass matrices.

Abstract: The decay of excited states of the nucleus Sn-135, with three neutrons outside the doubly-magic Sn-132 core, was studied in an experiment performed at the Radioactive Isotope Beam Factory at RIKEN. Several gamma rays emitted from excited Sn-135 ions were observed following one-neutron and one-neutron-one-proton removal from Sn-136 and Sb-137 beams, respectively, on a beryllium target at relativistic energies. Based on the analogy to 133Sn populated via one-neutron removal from Sn-134, an excitation energy of 695(15) keV is assigned to the 3/2(-) state with strongest single-particle character in 135Sn. This result provides the first direct information about the evolution of the neutron shell structure beyond N = 82 and thus allows for a crucial test of shellmodel calculations in this region. The experimental findings are in full agreement with calculations performed employing microscopic effective two-body interactions derived from CD-Bonn and N3LO nucleon-nucleon potentials, which do not predict a pronounced subshell gap at neutron number N=90. The occurrence of such a gap in Sn-140, i.e., when the 1f(7/2) orbital is completely filled, had been proposed in the past, in analogy to the magicity of Ca-48, featuring a completely filled 0f(7/2) orbital one harmonic oscillator shell below.