Pion photoproduction of nucleon excited states with Hamiltonian effective field theory

Abstract

Over the past few years, Hamiltonian effective field theory has been successfully applied to studies of nucleon and hyperon excited states. By discretizing the Hamiltonian in a finite volume, one can obtain the energy spectrum and compare it with the results calculated from lattice QCD. Through the analysis of experimental data, Hamiltonian effective field theory provides a framework that connects the finite-volume spectra from lattice QCD to infinite-volume scattering observables. The model independence of the approach is well preserved under the combined constraints from lattice QCD and experimental data. Building on these developments, recent works have attempted to extend HEFT to electromagnetic processes. Meanwhile, lattice QCD has also gradually advanced into the study of electromagnetic interactions. The combination of these analyses will undoubtedly deepen our understanding of light resonances.

Figures (3)

• Figure 1: Tree-level diagrams for the pure electromagnetic amplitude of the $\gamma N\to \alpha$ process without FSI: (a) s channel, (b) u channel, (c) t channel, (d) the contact term. The solid, wiggly, and dashed lines represent the baryons, photons and mesons, respectively.
• Figure 2: (a) The amplitudes $E_{0+}$ in units of attometer (am) for a proton target. (b) The amplitudes $M_{1-}$ in units of attometer (am) for a proton target. The data points are from SAID. The solid and dashed lines refer to the cases whether turning on or off the electromagnetic transition couplings between the bare nucleon resonances and nucleons, respectively.
• Figure 3: The multipole amplitude $E_{0+}$ (in attometers, am) at the $\pi N$ threshold with the isospin $I_{\pi N}=1/2$. The data points are from lattice QCD simulations Gao:2025loz, and the red dashed line represent the extended results with HEFT.