Joint description of the e+e- annihilation into both four-pion channels

TL;DR

This paper extends a model of e+e- annihilation into four charged pions to include neutral channels, incorporating omega and h_1 mesons, achieving a good fit to experimental cross section data for both reactions.

Contribution

The authors develop a combined model for e+e- annihilation into both four-pion channels, including additional intermediate states, and demonstrate its effectiveness in fitting experimental data.

Findings

Inclusion of omega(782) is essential for fitting the data.

Adding h_1(1170) improves the fit further.

Unified model successfully describes both reaction channels.

Abstract

The e+e- --> pi+pi-pi0pi0 reaction cross section as a function of the incident energy is calculated using a model that is an extension of our recently published model of the e+e- annihilation into four charged pions. The latter considered the intermediate states with the pi, rho, and a_1 mesons and fixed the mixing angle of the a_1-rho-pi Lagrangian and other parameters by fitting the cross section data. Here we supplement the original intermediate states with those containing omega(782) and h_1(1170), but keep unchanged the values of those parameters that enter both charged and mixed channel calculations. The inclusion of omega is vital for obtaining a good fit to the cross section data, while the intermediate states with h_1 further improve it. Finally, we merge our models of the e+e- --> pi+pi-pi0pi0 and e+e- --> pi+pi-pi+pi- reactions and obtain a simultaneous good fit.