Improving the Volume Dependence of Two-Body Binding Energies Calculated with Lattice QCD

TL;DR

This paper extends finite-volume correction techniques from nonrelativistic quantum mechanics to quantum field theory, specifically for two-body bound states in lattice QCD, to reduce systematic uncertainties in binding energy calculations.

Contribution

It generalizes Luscher's and related methods to boosted two-body systems in quantum field theory, improving the accuracy of lattice QCD binding energy computations.

Findings

Exponential reduction of volume dependence from ~ e^{-kappa L}/L to ~ e^{-2 kappa L}/L

Relativistic corrections to the volume dependence are identified and quantified

Analysis of lattice QCD calculations for the deuteron demonstrates practical applicability

Abstract

Volume modifications to the binding of two-body systems in large cubic volumes of extent L depend upon the total momentum and exponentially upon the ratio of L to the size of the boosted system. Recent work by Bour et al determined the momentum dependence of the leading volume modifications to nonrelativistic systems with periodic boundary conditions imposed on the single-particle wavefunctions, enabling them to numerically determine the scattering of such bound states using a low-energy effective field theory and Luscher's finite-volume method. The calculation of bound nuclear systems directly from QCD using Lattice QCD has begun, and it is important to reduce the systematic uncertainty introduced into such calculations by the finite spatial extent of the gauge-field configurations. We extend the work of Bour et al from nonrelativistic quantum mechanics to quantum field theory by generalizing the work of Luscher and of Gottlieb and Rummukainen to boosted two-body bound states. The volume modifications to binding energies can be exponentially reduced from ~ e^{-kappa L}/L to ~ e^{-2 kappa L}/L in nonrelativistic systems (where kappa is the binding momentum of the state) by forming particular combinations of the binding energies determined in the four lowest-lying boosted systems. Relativistic corrections to this combination, and others, that violate the exponential reduction are determined. An analysis of what can be expected from Lattice QCD calculations of the deuteron is performed, the results of which are representative of a generic loosely bound system.