Comment on "$Z_c$-like spectra from QCD Laplace sum rules at NLO"

TL;DR

This paper critically examines the methods used in a previous study on tetraquark molecular states, focusing on operator product expansion and Borel window issues, to assess the reliability of the reported large mass gaps.

Contribution

It provides a detailed analysis of the methodological aspects in QCD sum rule calculations for tetraquark states, highlighting potential issues affecting the results.

Findings

Identifies problems in the operator product expansion approach.

Highlights issues with Borel window selection.

Questions the reliability of large mass gap results.

Abstract

In Phys. Rev. {\bf D103} (2021) 074015 (arXiv:2101.07281), huge (or largest) mass gaps between the ground states and first radial excited states for the tetraquark molecular states are obtained, $\Delta=1.70\sim 2.35\,\rm{GeV}$. We explore the problems in the operator product expansion, Borel windows, etc, in details.