Abstract: We propose a generalized mu-tau reflection symmetry to constrain the lepton flavor mixing parameters. We obtain a new correlation between the atmospheric mixing angle theta(23) and the “Dirac” CP violation phase delta(CP). Only in a specific limit our proposed CP transformation reduces to standard mu-tau reflection, for which theta(23) and delta(CP) are both maximal. The “Majorana” phases are predicted to lie at their CP-conserving values with important implications for the neutrinoless double beta decay rates. We also study the phenomenological implications of our scheme for present and future neutrino oscillation experiments including T2K, NO nu A and DUNE.

Abstract: Starting from a molecular picture for the X(3872) resonance, this state and its J(PC) = 2(++) heavy-quark spin symmetry partner [X-2(4012)] are analyzed within a model which incorporates possible mixings with 2P charmonium (c (c) over bar) states. Since it is reasonable to expect the bare chi(c1)(2P) to be located above the D (D) over bar* threshold, but relatively close to it, the presence of the charmonium state provides an effective attraction that will contribute to binding the X(3872), but it will not appear in the 2(++) sector. Indeed in the latter sector, the chi(c2)(2P) should provide an effective small repulsion, because it is placed well below the D*(D) over bar* threshold. We show how the 1(++) and 2(++) bare charmonium poles are modified due to the D-(*)(D) over bar ((*)) loop effects, and the first one is moved to the complex plane. The meson loops produce, besides some shifts in the masses of the charmonia, a finite width for the 1(++) dressed charmonium state. On the other hand, X(3872) and X-2(4012) start developing some charmonium content, which is estimated by means of the compositeness Weinberg sum rule. It turns out that in the heavy-quark limit, there is only one coupling between the 2P charmonia and the D-(*)(D) over bar ((*)) pairs. We also show that, for reasonable values of this coupling, leading to X(3872) molecular probabilities of around 70-90%, the X2 resonance destabilizes and disappears from the spectrum, becoming either a virtual state or one being located deep into the complex plane, with decreasing influence in the D*(D) over bar* scattering line. Moreover, we also discuss how around 10-30% charmonium probability in the X(3872) might explain the ratio of radiative decays of this resonance into psi(2S) gamma and J/psi gamma Finally, we qualitatively discuss within this scheme, the hidden bottom flavor sector, paying a special attention to the implications for the X-b and Xb(2) states, heavy-quark spin-flavor partners of the X(3872).

Abstract: We impose an S-3 symmetry on the quark fields under which two of three quarks transform like a doublet and the remaining one as singlet, and use a scalar sector with the same structure of SU(2) doublets. After gauge symmetry breaking, a Z(2) subgroup of the S-3 remains unbroken. We show that this unbroken subgroup can explain the approximate block structure of the CKM matrix. By allowing soft breaking of the S-3 symmetry in the scalar sector, we show that one can generate the small elements, of quadratic or higher order in the Wolfenstein parametrization of the CKM matrix. We also predict the existence of exotic new scalars, with unconventional decay properties, which can be used to test our model experimentally.