Tests of the Z_c-like Laplace Sum Rule (LSR) results using FESR at NLO

TL;DR

This paper tests the validity of Laplace sum rule results for Z_c-like states using Finite Energy Sum Rules at NLO, confirming the existence of a (D^*D)_1 excitation around 5700 MeV and discussing the coupling and masking effects of other states.

Contribution

It introduces a FESR-based validation method for LSR results on Z_c-like states and clarifies the estimates and interpretations of these exotic states.

Findings

Confirmed a (D^*D)_1 radial excitation at ~5700 MeV

Identified coupling strengths of the states to the current

Discussed potential masking of the Z_c(4430) candidate

Abstract

In this note, we use local duality Finite Energy Sum Rule (FESR) to test the validity of the Laplace sum rules (LSR) results truncated at the dimension-six condensates for the estimates of the masses and couplings of the Z_c-like ground states in Ref.1 by taking the example of the D^*D molecule configuration. We confirm the existence of an eventual (D^*D)_1 radial excitation with a mass around 5700 MeV and coupling of 197(25) keV to the current which may mask the eventual Z_c(4430) radial excitation candidate (named (D^*D)_0 in Ref.1) having a relatively small coupling f_{(D^*D)_0}=46(56) keV. We add more explanations on the estimates in Ref.1 from LSR and comment the results in Ref.2.