The $DN$, $\pi {\Sigma }_c$ interaction in finite volume and the ${\Lambda }_c(2595)$ resonance

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 Lüscher's formula leads to incorrect results.

10 pages, 13 figures, accepted for publication in Eur. Phys. J. A

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Cited by in corpus (7)

• Moving Multi-Channel Systems in a Finite Volume with Application to Proton-Proton Fusion
• Generalized Lüscher Formula in Multi-channel Baryon-Meson Scattering
• Chiral study of the $a_0(980)$ resonance and $\pi \eta$ scattering phase shifts in light of a recent lattice simulation
• Emergence of molecular-type characteristic spectrum of hidden-charm pentaquark with strangeness embodied in the $P_{\psi s}^{\Lambda }(4338)$ and $P_{cs}(4459)$
• The pion-pion Interaction in the rho Channel in Finite Volume
• Production of charmed baryon ${\Lambda }_c(2940)$ by kaon-induced reaction on a proton target
• K-pi interaction in finite volume and the K* resonance