Estimation of potential radius based on momentum distribution of a constituent particle

Abstract

We propose using the potential radius as a probe of the structure of hadrons, particularly to classify exotic hadrons as hadronic or quark composite states.In this study, we focus on the radius of the effective potential felt by each constituent particle. Using a simple model with a square-well potential, we demonstrate that the potential radius can be estimated from the momentum distribution of a constituent particle not only for deeply bound states but also for shallowly bound states.We find that the momentum-based quantity provides a more robust estimate of the potential radius in the shallow-binding regime.This is because the momentum-based length scale decreases to zero as the potential radius vanishes, whereas the RMS radius approaches a finite value set by the binding energy.As a result, the momentum distribution avoids the finite-intercept problem that can make the inverse estimate of the potential radius ill-defined.With future experimental data on the momentum distribution of the constituent nucleon in $\overline{K}NNN$ production at J-PARC, the potential radius may be determined within the present framework.