Statistical Inference of Scattering Parameters for Exotic Hadronic States in the $J/\psi\,p$ Spectrum

Abstract

We present a global two-channel Flatt\'e amplitude analysis of the hidden-charm pentaquark candidates observed by the LHCb collaboration in the J/{\psi}p invariant-mass spectrum using the Run 1+2 dataset. We simultaneously fit the three pentaquark amplitudes to the full spectrum, including a polynomial background and complex coupling phases. The scattering length and effective range are extracted from the fitted amplitudes using the effective range expansion, with uncertainties determined through non-parametric bootstrap resampling. While real couplings yield scattering parameters compatible with a molecular interpretation, this conclusion becomes less robust when coupling phases are included. We further find that interference effects are important for the closely spaced Pc(4440)+ and Pc(4457)+ states, demonstrating the limitations of the incoherent-sum approximation.