Abstract: We propose to relate dark matter stability to the possible Dirac nature of neutrinos. The idea is illustrated in a simple scheme where small Dirac neutrino masses arise from a type-I seesaw mechanism as a result of a Z(4) discrete lepton number symmetry. The latter implies the existence of a viable WIMP dark matter candidate, whose stability arises from the same symmetry which ensures the Diracness of neutrinos.

Abstract: Using the latest global determination of neutrino oscillation parameters from [1] we examine the status of the simplest revamped version of the BMV (Babu-Ma-Valle) model, proposed in [2]. The model predicts a striking correlation between the “poorly determined” atmospheric angle 623 and CP phase Sep, leading to either maximal CP violation or none, depending on the preferred 623 octants. We determine the allowed BMV parameter regions and compare with the general three-neutrino oscillation scenario. We show that in the BMV model the higher octant is possible only at 99% C. L., a stronger rejection than found in the general case. By performing quantitative simulations of forthcoming DUNE and T2HK experiments, using only the four “well-measured” oscillation parameters and the indication for normal mass ordering, we also map out the potential of these experiments to corner the model. The resulting global sensitivities are given in a robust form, that holds irrespective of the true values of the oscillation parameters.

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: We propose two schemes for the lepton mixing matrix U = (U1U nu)-U-dagger, where U = U-1 refers to the charged sector, and U-v denotes the neutrino diagonalization matrix. We assume U-nu to be CP conserving and its three angles to be connected with the Cabibbo angle in a simple manner. CP violation arises solely from the U-1, assumed to have the CKM form, U-1 similar or equal to V-CKM, suggested by unification. Oscillation parameters depend on a single parameter, leading to narrow ranges for the “solar” and “accelerator” angles theta(12) and theta(23), as well as for the CP phase, predicted as delta(CP) similar to +/- 1.3 pi.

Abstract: We propose an A(4) extension of the Standard Model with a Lepton Quarticity symmetry correlating dark matter stability with the Dirac nature of neutrinos. The flavor symmetry predicts (i) a generalized bottom-tau mass relation involving all families, (ii) small neutrino masses are induced a la seesaw, (iii) CP must be significantly violated in neutrino oscillations, (iv) the atmospheric angle theta(23) lies in the second octant, and (v) only the normal neutrino mass ordering is realized.