Signatures of S-wave bound-state formation in finite volume

TL;DR

This paper analyzes how S-wave bound states manifest in finite volume systems, showing that their signatures can be detected through phase-shift formulas and sign changes in scattering length, despite finite size effects.

Contribution

It demonstrates that the formation of S-wave bound states can be identified in finite volume using phase-shift analysis and sign change of scattering length, with finite size effects being exponentially suppressed.

Findings

Bound-state pole condition is modified by finite size corrections exponentially suppressed by L.

Appearance of bound states causes an abrupt sign change in the scattering length.

Sign change can help distinguish bound states from scattering states in finite volume simulations.

Abstract

We discuss formation of an S-wave bound-state in finite volume on the basis of L\"uscher's phase-shift formula.It is found that although a bound-state pole condition is fulfilled only in the infinite volume limit, its modification by the finite size corrections is exponentially suppressed by the spatial extent $L$ in a finite box $L^3$. We also confirm that the appearance of the S-wave bound state is accompanied by an abrupt sign change of the S-wave scattering length even in finite volume through numerical simulations. This distinctive behavior may help us to discriminate the loosely bound state from the lowest energy level of the scattering state in finite volume simulations.