Cross sections for inelastic meson-meson scattering via quark-antiquark annihilation

TL;DR

This paper investigates inelastic meson-meson scattering via quark-antiquark annihilation and creation, deriving formulas and calculating cross sections at various temperatures to understand their temperature dependence.

Contribution

It introduces a detailed theoretical framework for meson-meson scattering involving quark-antiquark annihilation and computes temperature-dependent cross sections.

Findings

Cross sections show significant temperature dependence.

Formulas for transition amplitudes and potentials are derived.

Reactions include various meson combinations such as pion-pion and kaon-antikaon.

Abstract

We study inelastic meson-meson scattering that is governed by quark-antiquark annihilation and creation involving a quark and an antiquark annihilating into a gluon, and subsequently the gluon creating another quark-antiquark pair. The resultant hadronic reactions include for I=1: pion + pion to rho + rho, kaon + antikaon to kaon* + antikaon*, kaon + antikaon* to kaon* + antikaon*, kaon* + antikaon to kaon* + antikaon*, as well as pion + pion to kaon + antikaon, pion + rho to kaon + antikaon*, pion + rho to kaon* + antikaon, and kaon + antikaon to rho + rho. In each reaction, one or two Feynman diagrams are involved in the Born approximation. We derive formulas for the unpolarized cross section, the transition amplitude, and the transition potential for quark-antiquark annihilation and creation. The unpolarized cross sections for the reactions are calculated at six temperatures, and prominent temperature dependence is found. It is due to differences among mesonic temperature dependence in hadronic matter.