Towards the understanding of $Z_c(3900)$ from lattice QCD
Chuan Liu, Liuming Liu, Ke-Long Zhang
TL;DR
This paper develops theoretical constraints and strategies for lattice QCD studies of the $Z_c(3900)$ resonance, focusing on multi-channel analysis and effective range theory near threshold energies.
Contribution
It introduces new constraint relations within the three-channel Ross-Shaw effective range theory for narrow near-threshold resonances like $Z_c(3900)$ and discusses their application in lattice QCD.
Findings
Derived constraints among parameters for narrow near-threshold resonances.
Outlined strategies for applying multi-channel Lüscher formula in lattice QCD.
Provided theoretical framework for analyzing $Z_c(3900)$ structure.
Abstract
Within the framework of three-channel Ross-Shaw effective range theory, we derive the constraints among different parameters of the theory in the case of a narrow resonance close to the threshold of the third channel, which is relevant for the resonance-like structure . The usage of these constraint relations, together with the multi-channel L\"uscher formula in lattice QCD calculations are also discussed and the strategies are outlined.
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