Threshold $\pi^0$ photoproduction in relativistic chiral perturbation theory

TL;DR

This paper calculates neutral pion photoproduction on protons using relativistic chiral perturbation theory up to order q^4, analyzing experimental data, comparing with heavy-baryon results, and predicting polarization observables.

Contribution

It provides a comprehensive relativistic chiral perturbation theory analysis of $$ photoproduction, including wave contributions, data fitting, and predictions for polarization observables.

Findings

Good agreement with Mainz Microtron data near threshold.

Comparison shows relativistic and heavy-baryon approaches yield consistent results.

Predictions for polarization observables to guide future experiments.

Abstract

We present a calculation of $\pi^0$ photoproduction on the proton in manifestly Lorentz-invariant baryon chiral perturbation theory up to and including chiral order $q^4$. With the results we analyze the latest $\pi^0$ photoproduction data in the threshold region obtained at the Mainz Microtron. In the calculation of observables and the fit of the low-energy constants, we take $S$, $P$, and $D$ waves into account. We compare the results for the multipoles with the corresponding single-energy analysis. Furthermore, we also fit the $O(q^4)$ heavy-baryon chiral perturbation theory calculation and compare both results. We provide predictions for several polarization observables for future experiments. Finally, we discuss the $\beta$ parameter of the unitarity cusp which is related to the breaking of isospin symmetry.