Research On Meson-meson Inelastic Scatterings In Hadronic Matter

Lattice QCD predicts that at high energy density, hadronic matter will turn into a plasma of deconfined quarks and gluons (QGP). Relativistic heavy-ion collisions is considered as a significant mean of generating quark-gluon plasma in controllable laboratory environment. Quark-gluon plasma at a critical temperature transits into hadronic matter which contains a large number of pions and a certain portion ofρ,ω, K and K~* mesons in relativistic heavy-ion collisions. Whether the quark-gluon plasma is formed or not, hot hadronic matter with high density would come into being when colliding. Hence, the research on the quality of hot hadronic matter has the practical significance of independent study, and on the other hand it can serve for the background of the signal of quark-gluon plasma formation. Hadronic matter endures for a long time before thermal freeze-out and the evolution of hadronic matter considerably affects productions of hadrons. To understand the evolution of hadronic matter, meson-meson scatterings as basic processes must be studied. Meson-meson inelastic scatterings are crucial to study chemical equilibrium of hadronic matter but unknown.First, the relevant research backgrounds are reviewed and generalized in the introduction of this thesis. The research objectives and research contents are also given in the same part. Then the present researches are addressed in the following chapters systemically. The main researches and innovations of this thesis are divided into three sections: cross sections for meson-meson inelastic scatterings, master rate equations and photon from hadronic matter.Meson-meson nonresonant reactions governed by the quark-interchange mechanism are studied in the extended Buchmuller Tye potential. Buchmuller-Tye potential that arises from color confinement and one gluon exchange plus one- and two-loop corrections, is nonrelativistic, central and spin-independent. The extended Buchmuller-Tye potential includes a central spin-independent term, spin-spin interaction, spin-orbit and tensor terms. The Schrodinger equation with the central spin-independent potential produces a radial wave function for the quark-antiquark relative motion of mesons. The agreement between our theoretical values of S-wave elastic phase shifts for I = 2ππand I = 3/2 Kπscattering and the experimental data is reasonable. Then the quark-antiquark relative motion wave functions are reliable. We studied inelastic scatterings of the mesons both in the ground-state pseudoscalar octet and in the ground-state vector nonet, and derived new and useful results that include cross sections for the nonresonant reactions of I = 2ππ(?)ρρ, I = 2πρ(?)ρρ, I = 1 KK (?) K~*K~*, I = 1 KK~* (?) K~*K~*, I = 3/2πK (?)ρK~*, I = 3/2πK~*(?)ρK~*, I = 3/2ρK (?)ρK~* and I = 3/2πK~* (?)ρK. These cross sections unknown both in experiment and in theory have been first performed in this research. While the post-prior equivalence holds for the elastic scattering, the post-prior discrepancy of the inelastic scatterings relies on the spin-dependent terms of quark-antiquark potential. Cross sections for reactions involvingπ,ρ, K and K~* indicate that mesonic interactions in matter consisting of only K and K~* can be stronger than mesonic interactions in matter consisting of only p and ? and the reaction of I = 3/2πK~*→ρK is most important among the endothermic non-resonant reactions. It is found from the (?)-dependences of cross sections thatρand K~* creation cross sections can be larger than their absorption cross sections, respectively. To help understand the behavior ofφmeson in hadronic matter, we first study the hadron-phi cross sections in the attempt of quark level. By the quark-interchange mechanism we calculate cross sections for the nonresonant reactions of I = 1πφ→KK~* (or K~*K), I = 1πφ→K~*K~*, I = 1ρφ→KK, I = 1ρφ→KK~* (or K~*K) and I = 1ρφ→K~*K~*. Then we can offer (?)-dependences ofφabsorption cross sections in collisions withπandρmesons.The first study on the role of quark-interchange processes in evolution of hadronic matter is performed in this thesis. Master rate equations are established to get time dependences of fugacities of pions, rhos, kaons and vector kaons. The equations include cross sections for inelastic scatterings of pions, rhos, kaons and vector kaons. We divide the cross section for a meson-meson inelastic scattering into three parts. The first part is for a quark-interchange process, the second for quark-antiquark annihilation processes and the third for resonant processes. Cross sections for quark-interchange-induced reactions are parametrized for convenient use. The master rate equations combined with the hydrodynamic equation for longitudinal expansion are solved with a set of initial fugacities of mesons by numerical integration using a fourth order Runge-Kutta method. Numerical results of the master rate equations show that the variations of fugacities of pions, rhos, kaons and vector kaons are governed by both meson-meson reactions and expansion of hadronic matter. In most reactions quark-interchange processes take place. The number densities ofπandρ(K and K~*) are altered by quark-interchange processes in equal magnitudes but opposite signs. Quark-interchange processes increase or decrease fugacities and are shown to be important in the contribution of meson-meson inelastic scatterings to evolution of hadronic matter.The effect on photon of hadronic matter from chemical nonquilibrium is studied with the fugacities of mesons from the master rate equations. Direct photon production has been proposed as a promising signature to identify the existence of quark-gluon plasma in relativistic heavy-ion collisions. We studied photon emission from a chemically non-equilibrated hadronic matter, describable by the Jiittner distribution with nonequilibrium fugacity, formed in relativistic heavy-ion collisions. The photon spectrum is obtained by integrating the photon rate over the space-time evolution of hadronic matter. Results are discussed. Compared to chemical equilibrium, photon yield from chemical nonequilibrium hadronic matter is suppressed. The photon spectrum of hadronic matter is dominated by its early times corresponding to high temperatures, especially for large photon energies.