Two-Baryon Systems with Twisted Boundary Conditions

TL;DR

This paper derives a general quantization condition for two-baryon systems with twisted boundary conditions, demonstrating how to reduce finite-volume effects and improve accuracy in lattice QCD calculations of the deuteron.

Contribution

It introduces a comprehensive framework for applying twisted boundary conditions to two-baryon systems, enhancing precision in finite-volume lattice QCD studies.

Findings

Twisted boundary conditions significantly reduce finite-volume corrections.

Proper boundary condition choices enable sub-percent accuracy in deuteron binding energy.

Results facilitate more precise lattice QCD calculations of nuclear systems.

Abstract

I derive the most general quantization condition for energy eigenvalues of two interacting baryons in a finite cubic volume when arbitrary twisted boundary conditions are imposed on their finite-volume wavefunctions. These quantization conditions are used, along with experimentally known scattering parameters of two-nucleon systems in the coupled 3S1-3D1 channels, to demonstrate the expected effect of a selection of twisted boundary conditions on the spectrum of the deuteron. It is shown that an order of magnitude reduction in the finite-volume corrections to the deuteron binding energy arise in moderate volumes with a proper choice of boundary conditions on the proton and the neutron, or by averaging the result of periodic and anti-periodic boundary conditions. These observations mean that a sub-percent accuracy can be achieved in the determination of the deuteron binding energy at (spatial) volumes as small as ~(9[fm])^3 in upcoming lattice QCD calculations of this nucleus with physical light-quark masses. The results reviewed in this talk are presented in details in Ref. [1].