Tri-bimaximal neutrino mixing from A4 and θ13∼θC

It is a common believe that, if the tri-bimaximal mixing (TBM) pattern is explained by vacuum alignment in an $A_4$ model, only a very small reactor angle, say ${\theta }_{13}～O({\lambda }_C^2)$ being ${\lambda }_C\equiv {\theta }_C$ the Cabibbo angle, can be accommodated. This statement is based on the assumption that all the flavon fields acquire VEVs at a very similar scale and the departures from exact TBM arise at the same perturbation level. From the experimental point of view, however, a relatively large value ${\theta }_{13}～O({\lambda }_C)$ is not yet excluded by present data. In this paper, we propose a seesaw $A_4$ model in which the previous assumption can naturally be evaded. The aim is to describe a ${\theta }_{13}～O({\lambda }_C)$ without conflicting with the TBM prediction for ${\theta }_{12}$ which is rather close to the observed value (at ${\lambda }_C^2$ level). In our model the deviation of the atmospherical angle from maximal is subject to the sum-rule: ${\sin }^2{\theta }_{23}\approx 1/2+\sqrt{2}/2\cos \delta \sin {\theta }_{13}$ which is a next-to-leading order prediction of our model.     

Temperature-dependent cross sections for meson–meson nonresonant reactions in hadronic matter

We present a potential of which the short-distance part is given by one gluon exchange plus perturbative one- and two-loop corrections and of which the large-distance part exhibits a temperature-dependent constant value. The Schrödinger equation with this temperature-dependent potential yields a temperature dependence of the mesonic quark–antiquark relative-motion wave function and of meson masses. The temperature dependence of the potential, the wave function and the meson masses brings about temperature dependence of cross sections for the nonresonant reactions $\pi \pi \to \rho \rho$ for $I=2$, $KK\to K^{*}{K}^{*}$ for $I=1$, $K{K}^{*}\to K^{*}{K}^{*}$ for $I=1$, $\pi K\to \rho K^{*}$ for $I=3/2$, $\pi K^{*}\to \rho K^{*}$ for $I=3/2$, $\rho K\to \rho K^{*}$ for $I=3/2$ and $\pi K^{*}\to \rho K$ for $I=3/2$. As the temperature increases, the rise or fall of peak cross sections is determined by the increased radii of initial mesons, the loosened bound states of final mesons, and the total-mass difference of the initial and final mesons. The temperature-dependent cross sections and meson masses are parametrized.