Toward a unified description of hadro- and photoproduction: S-wave pi- and eta-photoproduction amplitudes

TL;DR

This paper extends the Chew-Mandelstam parameterization to electromagnetic interactions, enabling unified analysis of hadro- and photoproduction S-wave amplitudes from pion threshold to 1.61 GeV, with implications for global data fits.

Contribution

It introduces a generalized, unitary parameterization for electromagnetic amplitudes within the SAID framework, integrating hadronic and photoproduction data analysis.

Findings

Qualitative agreement with MAID parameterization

Differences observed in numerical solutions

Potential for improved global data fits

Abstract

The Chew-Mandelstam parameterization, which has been used extensively in the two-body hadronic sector, is generalized in this exploratory study to the electromagnetic sector by simultaneous fits to the pion- and eta-photoproduction S-wave multipole amplitudes for center-of-mass energies from the pion threshold through 1.61 GeV. We review the Chew-Mandelstam parameterization in detail to clarify the theoretical content of the SAID hadronic amplitude analysis and to place the proposed, generalized SAID electromagnetic amplitudes in the context of earlier employed parameterized forms. The parameterization is unitary at the two-body level, employing four hadronic channels and the gamma-N electromagnetic channel. We compare the resulting fit to the MAID parameterization and find qualitative agreement though, numerically, the solution is somewhat different. Applications of the extended parameterization to global fits of the photoproduction data and to global fits of the combined hadronic and photoproduction data are discussed.