Photon-fusion reactions from the chiral Lagrangian with dynamical light vector mesons

TL;DR

This paper develops a chiral Lagrangian model with dynamical light vector mesons to analyze photon fusion reactions, fitting parameters to experimental data and predicting cross sections for various meson pairs.

Contribution

It introduces a novel chiral Lagrangian framework with dynamical vector mesons, fitted to photon fusion data, and predicts unmeasured cross sections.

Findings

Good agreement with experimental data up to 0.9 GeV for two-pion final states.

Dynamical generation of the $a_0$ meson in the $ ext{π}^0 ext{η}$ channel.

Predictions for $ ext{K}^0ar{ ext{K}}^0$, $ ext{K}^+ ext{K}^-$, and $ ext{η}η$ cross sections.

Abstract

We study the reactions $\gamma\gamma\rightarrow \pi^0\pi^0$, $\pi^+\pi^-$, $K^0\bar{K}^0$, $K^+K^-$, $\eta \eta$ and $\pi^0\eta$ based on a chiral Lagrangian with dynamical light vector mesons as formulated within the hadrogenesis conjecture. At present our chiral Lagrangian contains 5 unknown parameters that are relevant for the photon fusion reactions. They parameterize the strength of interaction terms involving two vector meson fields. These parameters are fitted to photon fusion data $\gamma\gamma\rightarrow \pi^0\pi^0$, $\pi^+\pi^-, \pi^0\eta$ and to the decay $\eta\rightarrow\pi^0\gamma\gamma$. In order to derive gauge invariant reaction amplitudes in the resonance region constraints from micro-causality and exact coupled-channel unitarity are used. Our results are in good agreement with the existing experimental data from threshold up to about 0.9 GeV for the two-pion final states. The $a_0$ meson in the $\pi^0\eta$ channel is dynamically generated and an accurate reproduction of the $\gamma\gamma\rightarrow \pi^0\eta$ data is achieved up to 1.2 GeV. Based on our parameter sets we predict the $\gamma\gamma\rightarrow $ $K^0\bar{K}^0$, $K^+K^-$, $\eta \eta$ cross sections.