The $DN$, $\pi \Sigma_c$ interaction in finite volume and the $\Lambda_c(2595)$ resonance

TL;DR

This paper extends a chiral unitary model of the $DN$ and $\pi \Sigma_c$ interactions to finite volume, demonstrating how to extract accurate phase shifts and resonance positions from lattice-like energy levels, emphasizing the importance of coupled-channel effects.

Contribution

It provides a method to determine infinite-volume phase shifts and resonance properties from finite-volume energy levels considering coupled channels, improving lattice QCD analysis techniques.

Findings

Accurate $\pi \Sigma_c$ phase shifts can be obtained from finite-volume data.

The $\Lambda_c(2595)$ resonance position can be reliably extracted.

Some energy levels are linked to closed channels, affecting phase shift extraction.

Abstract

In this work the interaction of the coupled channels $DN$ and $\pi \Sigma_c$ in an SU(4) extrapolation of the chiral unitary theory, where the $\Lambda_c(2595)$ resonance appears as dynamically generated from that interaction, is extended to produce results in finite volume. Energy levels in the finite box are evaluated and, assuming that they would correspond to lattice results, the inverse problem of determining the phase shifts in the infinite volume from the lattice results is solved. We observe that it is possible to obtain accurate $\pi \Sigma_c$ phase shifts and the position of the $\Lambda_c(2595)$ resonance, but it requires the explicit consideration of the two coupled channels. We also observe that some of the energy levels in the box are attached to the closed $DN$ channel, such that their use to induce the $\pi \Sigma_c$ phase shifts via L\"uscher's formula leads to incorrect results.