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Resolving the structure of bound states using lattice quantum field theories

Joseph Moscoso1,2,3,4,*, Felipe G. Ortega-Gama3,4,†, Raúl A. Briceño3,4,‡, Andrew W. Jackura5,§, Charles Kacir2,∥, and Amy N. Nicholson2,4,¶

  • *Contact author: jmoscoso@umd.edu
  • †Contact author: fgortegagama@berkeley.edu
  • ‡Contact author: rbriceno@berkeley.edu
  • §Contact author: awjackura@wm.edu
  • ∥Contact author: ckacir@unc.edu
  • Contact author: annichol@email.unc.edu
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Phys. Rev. D 114, 054505 – Published 18 September, 2026

DOI: https://doi.org/10.1103/nhbl-t2hv

Abstract

This work presents the first calculation of a two-to-two particle matrix element of a local current within a lattice-regularized quantum field theory. This exploratory calculation is performed using a leading-order pionless effective field theory of two nucleons in a finite 3D spatial volume, where the Hamiltonian can be diagonalized exactly for moderate volumes. By considering a range of couplings where the theory supports a deuteronlike bound state, we determine the finite-volume spectra and matrix elements of the conserved local vector current. Using the Lüscher formalism, we constrain the infinite-volume, purely hadronic amplitude for this theory. Using previously derived formalism, we then map the finite-volume matrix elements to scattering amplitudes describing a reaction coupling two-particle states via a current insertion, 2+J→2. We then use a recently derived relation between this class of amplitudes and the bound-state elastic form factor to directly constrain the infinite-volume form factor. By varying over a range of values of the coupling of the theory, we explore the effects of this analysis for deep- and shallow-bound states. We reproduce the expected result that, for deep-bound states, the finite-volume formalism is largely unnecessary, while for shallow-bound states, it is absolutely critical to obtain a sensible result. We present a detailed outline of the analysis of this class of matrix elements, including the determination of the charge radius of the bound state. In the shallow-bound-state limit, we find good agreement with the prediction stemming from the anomalous threshold.

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Phys. Rev. D 114, 054505– Published 18 September, 2026
  • Received 10 March 2026
  • Accepted 6 July 2026
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