Amplitude determination for $M M \to M M$, $M = \pi, K$ and cross-sections for $\gamma \gamma \to \pi^+ \pi^-, \pi^0 \pi^0, \pi^0 \eta$ in a chiral model

TL;DR

This paper compares chiral perturbation theory predictions with experimental data on meson pair production in two-photon collisions, providing insights into low-energy QCD interactions and the validity of theoretical models.

Contribution

It introduces a comparison between chiral perturbation theory calculations and model-independent experimental amplitude extractions for meson pair production.

Findings

Chiral perturbation theory results agree well with experimental amplitudes.

Theoretical cross-sections match experimental data within the low-energy range.

The analysis enhances understanding of meson-meson interactions in QCD.

Abstract

Dai and Pennington have performed a comprehensive analysis of essentially all pion and kaon pair production data from two-photon collisions below 1.5 GeV, including all high statistics results from Belle, as well as the older data from Mark II at SLAC, CELLO at DESY, and Crystal Ball at SLAC. Imposing the basic constraints required by analyticity, unitarity, and crossing symmetry and making use of Low's low-energy theorem for QED, they were able to extract the final-state, strong-interaction scattering amplitudes for the intermediate $\pi \pi \to \pi \pi$ and $\pi \pi \to K \overline{K}$ reactions in a model-independent fashion. In addition, they provided good fits to the respective $\gamma \gamma \to \pi \pi$ cross-sections that are known in the low-energy sector in the restricted angular range, $| \cos \theta | < 0.6 - 0.8$. Using the parameters obtained in this fashion, these authors constructed the $\gamma \gamma \to \pi \pi$ cross-sections integrated over the full angular range. In the present work, we use a version of chiral perturbation theory developed by Oller and Oset to evaluate the final-state, strong-interaction amplitudes theoretically, and we compare our low-energy QCD-based results with the amplitudes extracted by Dai and Pennington. We also calculate the $\gamma \gamma \to \pi \pi$ cross-sections (integrated over the full angular range) and compare them with those obtained by Dai and Pennington. These calculations give a more detailed insight into the fit of chiral perturbation theory, not just to the measured $\gamma \gamma \to \pi \pi$ cross-sections, as is usually presented, but rather to a higher level of detail through the available analysis of the experimental data for the underlying final-state, strong-interaction, meson-meson scattering amplitudes $\pi \pi \to \pi \pi$ and $\pi \pi \to K \overline{K}$ themselves. The fits appear to be sensible.