Abstract
Recently, a framework has been developed to study form factors of two-hadron states probed by an external current. The method is based on relating finite-volume matrix elements, computed using numerical lattice QCD, to the corresponding infinite-volume observables. As the formalism is complicated, it is important to provide non-trivial checks on the final results and also to explore limiting cases in which more straightforward predications may be extracted. In this work we provide examples on both fronts. First, we show that, in the case of a conserved vector current, the formalism ensures that the finite-volume matrix element of the conserved charge is volume-independent and equal to the total charge of the two-particle state. Second, we study the implications for a two-particle bound state. We demonstrate that the infinite-volume limit reproduces the expected matrix element and derive the leading finite-volume corrections to this result for a scalar current. Finally, we provide numerical estimates for the expected size of volume effects in future lattice QCD calculations of the deuteron's scalar charge. We find that these effects completely dominate the infinite-volume result for realistic lattice volumes and that applying the present formalism, to analytically remove an infinite-series of leading volume corrections, is crucial to reliably extract the infinite-volume charge of the state.
Highlights
One of the overarching goals of modern-day nuclear physics is the characterization and fundamental understanding of the low-lying strongly interacting spectrum
We provide numerical estimates for the expected size of volume effects in future lattice quantum chromodynamics (QCD) calculations of the deuteron’s scalar charge. We find that these effects completely dominate the infinite-volume result for realistic lattice volumes and that applying the present formalism, to analytically remove an infinite series of leading volume corrections, is crucial to reliably extract the infinite-volume charge of the state
The formalism predicts that the charge of a two-hadron finite-volume state is exactly equal to the sum of the constituent charges and independent of L. This relies on nontrivial relations between various L-dependent geometric functions, and a relation between the 2 → 2 and 2 þ J → 2 amplitudes that follows from the Ward-Takahashi identity
Summary
One of the overarching goals of modern-day nuclear physics is the characterization and fundamental understanding of the low-lying strongly interacting spectrum. One of the leading methods to overcome this issue is to derive and apply nonperturbative mappings between finite-volume energies and matrix elements (directly calculable via numerical LQCD) and infinitevolume scattering and transition amplitudes.. One of the leading methods to overcome this issue is to derive and apply nonperturbative mappings between finite-volume energies and matrix elements (directly calculable via numerical LQCD) and infinitevolume scattering and transition amplitudes.2 This approach was first introduced by Lüscher [13,14], in seminal work relating the spectrum of two-particle states in a cubic volume with periodicity L, to the corresponding infinite-volume amplitudes. This article includes three Appendixes, providing proofs of various technical results used in the main text
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