Applications of the Feynman-Hellmann theorem in hadron structure

TL;DR

This paper explores the use of the Feynman-Hellmann theorem to compute hadron structure properties, including disconnected contributions and form factors at high momentum, providing new computational approaches and preliminary results.

Contribution

It introduces a FH-motivated method for calculating disconnected contributions and high-momentum form factors, extending the theorem to finite momentum transfers in hadron physics.

Findings

Discovered a non-negative disconnected quark contribution of about -5% at heavy pion mass.

Calculated nucleon and pion electromagnetic form factors up to 8 GeV^2.

Results do not confirm a sign change in the G_E/G_M ratio, suggesting further studies at lighter pion masses.

Abstract

The Feynman-Hellmann (FH) relation offers an alternative way of accessing hadronic matrix elements through artificial modifications to the QCD Lagrangian. In particular, a FH-motivated method provides a new approach to calculations of disconnected contributions to matrix elements and high-momentum nucleon and pion form factors. Here we present results for the total nucleon axial charge, including a statistically significant non-negative total disconnected quark contribution of around $-5\%$ at an unphysically heavy pion mass. Extending the FH relation to finite-momentum transfers, we also present calculations of the pion and nucleon electromagnetic form factors up to momentum transfers of around 7-8 GeV$^2$. Results for the nucleon are not able to confirm the existence of a sign change for the ratio $\frac{G_E}{G_M}$, but suggest that future calculations at lighter pion masses will provide fascinating insight into this behaviour at large momentum transfers.