$Z_c(3900)$: Confronting theory and lattice simulations

TL;DR

This paper compares theoretical models and lattice QCD simulations to understand the nature of the $Z_c(3900)$ state, highlighting the difficulty in distinguishing between resonance and virtual state scenarios.

Contribution

It applies a coupled-channel $T$-matrix formalism to lattice volumes to analyze the $Z_c(3900)$, proposing volume dependence as a key to identifying its true nature.

Findings

Energy levels for both scenarios match lattice results, making distinction difficult.

Volume dependence analysis suggests multiple-volume lattice simulations could clarify the state’s nature.

The formalism provides a unified approach to compare theory with lattice data.

Abstract

We consider a recent $T$-matrix analysis by Albaladejo {\it et al.}, [Phys.\ Lett.\ B {\bf 755}, 337 (2016)] which accounts for the $J/\psi\pi$ and $D^\ast\bar{D}$ coupled--channels dynamics, and that successfully describes the experimental information concerning the recently discovered $Z_c(3900)^\pm$. Within such scheme, the data can be similarly well described in two different scenarios, where the $Z_c(3900)$ is either a resonance or a virtual state. To shed light into the nature of this state, we apply this formalism in a finite box with the aim of comparing with recent Lattice QCD (LQCD) simulations. We see that the energy levels obtained for both scenarios agree well with those obtained in the single-volume LQCD simulation reported in Prelovsek {\it et al.} [Phys.\ Rev.\ D {\bf 91}, 014504 (2015)], making thus difficult to disentangle between both possibilities. We also study the volume dependence of the energy levels obtained with our formalism, and suggest that LQCD simulations performed at several volumes could help in discerning the actual nature of the intriguing $Z_c(3900)$ state.