Role of quark-interchange processes in evolution of mesonic matter

We divide the cross section for a meson-meson reaction into three parts. The first part is for the quark-interchange process, the second for quark-antiquark annihilation processes and the third for resonant processes. Master rate equations are established to yield time dependence of fugacities of pions, rhos, kaons and vetor kaons. The equations include cross sections for inelastic scattering of pions, rhos, kaons and vector kaons. Cross sections for quark-interchange-induced reactions, that were obtained in a potential model, are parametrized for convenient use. The number densities of pion and rho (kaon and vector kaon) are altered by quark-interchange processes in equal magnitudes but opposite signs. The master rate equations combined with the hydrodynamic equations for longitudinal and transverse expansion are solved with many sets of initial meson fugacities. Quark-interchange processes are shown to be important in the contribution of the inelastic meson-meson scattering to evolution of mesonic matter.Comment: 28 pages, 1 figure, 8 table

The geometric correlations of leptonic mixing parameters

Leptonic mixing patterns are usually extracted on the basis of groups or algebraic structures. In this paper, we introduce an alternative geometric method to study the correlations between the leptonic mixing parameters. At the 3{\sigma} level of the recent global fit data of neutrino oscillations, the distribution of the scatter points of the angles between the vectors of the magnitude of the leptonic mixing matrix is analysed. We find that the scatter points are concentrated on several special regions. Using the data in these regions, correlations of the leptonic mixing angles and the Dirac CP violating phase are obtained. The implications of the correlations are shown through the predicted flavor ratio of high-energy astrophysical neutrinos (HANs) at Earth.Comment: 15 pages, 7 figure