Nucleon form factors and the pion-nucleon sigma term

TL;DR

This paper reviews recent progress in lattice QCD calculations of nucleon form factors and the pion-nucleon sigma term, focusing on excited state contributions and their impact on extracting ground state matrix elements.

Contribution

It advances understanding of multihadron excited state effects in lattice calculations and extends chiral perturbation theory analysis of the sigma term to include the Delta resonance.

Findings

Multihadron excited states significantly affect axial/pseudoscalar form factors.

New data supports previous trends in nucleon form factors.

Nπ and Nππ states each contribute about 10 MeV to σπN.

Abstract

This talk summarizes the progress made since Lattice 2021 in understanding and controlling the contributions of towers of multihadron excited states with mass gaps starting lower than of radial excitations, and in increasing our confidence in the extraction of ground state nucleon matrix elements. The most clear evidence for multihadron excited state contributions (ESC) is in axial/pseudoscalar form factors that are required to satisfy the PCAC relation between them. The talk examines the broader question--which and how many of the theoretically allowed positive parity states $N(\textbf p)\pi(-\textbf p)$, $N(\textbf 0)\pi(\textbf 0)\pi(\textbf 0)$, $N(\textbf p)\pi(\textbf 0)$, $N(\textbf 0)\pi(\textbf p),\ \ldots$ make significant contributions to a given nucleon matrix element? New data for the axial, electric and magnetic form factors are presented. They continue to show trends observed in Ref[1]. The N${}^2$LO $\chi$PT analysis of the ESC to the pion-nucleon sigma term, $\sigma_{\pi N}$, has been extended to include the $\Delta$ as an explicit degree of freedom [2]. The conclusion reached in Ref [3] that $N \pi$ and $N \pi \pi$ states each contribute about 10 MeV to $\sigma_{\pi N}$, and the consistency between the lattice result with $N \pi$ state included and the phenomenological estimate is not changed by this improvement.