Bound states on the lattice with partially twisted boundary conditions

TL;DR

This paper introduces a lattice simulation method to analyze exotic hadrons by examining how their spectrum depends on twisting angles, offering an alternative to traditional volume-dependence studies, with applications to $DK$ bound states.

Contribution

It presents a novel approach using partially twisted boundary conditions to study hadron bound states, simplifying the analysis of their nature on the lattice.

Findings

Spectrum dependence on twisting angle can reveal bound state properties.

Partial twisting is effectively equivalent to full twisting for certain cases.

Method applied to $DK$ bound state demonstrates its practical utility.

Abstract

We propose a method to study the nature of exotic hadrons by determining the wave function renormalization constant $Z$ from lattice simulations. It is shown that, instead of studying the volume-dependence of the spectrum, one may investigate the dependence of the spectrum on the twisting angle, imposing twisted boundary conditions on the fermion fields on the lattice. In certain cases, e.g., the case of the $DK$ bound state which is addressed in detail, it is demonstrated that the partial twisting is equivalent to the full twisting up to exponentially small corrections.