I disagree with the use of Gaussian parametrization (8) – a resonance must represent a pole on the complex energy plane, otherwise the extracted sigma is not related to the inverse lifetime of a state and cannot be compared with the width of psi(4660). In a previous version of this analysis in arXiv 2005.06306 by the same authors, a relativistic Breit-Wigner parametrization was used. This was more justified (a relativistic generalization of BW distribution is not unique and the authors did not explain why they applied the simplest one, but this is a minor problem). However, the resonance in question lies close to a threshold energy E_thr. The use of a constant partial width Gamma_r for a resonance in an analysis is then justified only, if
k = 2(M_r-E_thr)/ Gamma_r >> 1. In the given analysis this is not the case, k=1.6. Hence, it is necessary to build in the appropriate threshold behavior, that was not done. I would advice to consult the review 49 “Resonance” in Particle Data,
https://pdg.lbl.gov/2021/reviews/rpp2020-rev-resonances.pdf
namely, the section 49.3.1 (page 6), where it is described what should be done.