The nucleon and Delta(1232) form factors at low momentum-transfer and small pion masses

TL;DR

This paper develops a covariant effective field theory framework to analyze the electromagnetic form factors of the nucleon and Delta(1232) at low momentum transfer and pion masses, providing new predictions and insights into their chiral behavior.

Contribution

It introduces a manifestly covariant chiral perturbation theory approach including Delta(1232) degrees of freedom, with next-to-leading order calculations for form factors, radii, and moments.

Findings

Predicted the second derivative of the proton electric form factor.

Compared chiral behavior with lattice QCD and heavy-baryon results.

Identified cusps and singularities at the Delta decay threshold.

Abstract

An expansion of the electromagnetic form factors of the nucleon and Delta(1232) in small momentum transfer and pion mass is performed in a manifestly-covariant EFT framework consistent with chiral symmetry and analyticity. We present the expressions for the nucleon and Delta(1232) electromagnetic form factors, charge radii, and electromagnetic moments in the framework of SU(2) baryon chiral perturbation theory, with nucleon and Delta(1232)-isobar degrees of freedom, to next-to-leading order. Motivated by the results for the proton electric radius obtained from the muonic-hydrogen atom and electron-scattering process, we extract values for the second derivative of the electric form factor which is a genuine prediction of the p^3 BChPT. The chiral behavior of radii and moments is studied and compared to that obtained in the heavy-baryon framework and lattice QCD. The chiral behavior of Delta(1232)-isobar properties exhibits cusps and singularities at the threshold of Delta->pi N decay, and their physical significance is discussed.