Size measurement of dynamically generated resonances with finite boxes

TL;DR

This paper develops a method to measure the size of dynamically generated resonances using finite volume effects, revealing the internal structure and dominant components of specific hadronic states like Lambda(1405) and f0(980).

Contribution

It introduces a novel approach to determine the spatial size of resonances from finite volume mass shifts, applicable to both bound and quasi-bound states with finite width.

Findings

Lambda(1405) is dominated by Kbar N scattering state.

f0(980) is dominated by KKbar scattering state.

Estimated sizes: Lambda(1405) ~1.8 fm, f0(980) ~2.8 fm.

Abstract

The structure of dynamically generated states is studied from a viewpoint of the finite volume effect. We establish the relation between the spatial size of a stable bound state and the finite volume mass shift. In a single-channel scattering model, this relation is shown to be valid for a bound state dominated by the two-body molecule component. We generalize this method to the case of a quasi-bound state with finite width in coupled-channel scattering. We define the real-valued size of the resonance in a given closed channel using the response to the finite volume effect on the channel. Applying this method to physical resonances we find that Lambda(1405) and f_{0}(980) are dominated by the Kbar N and K Kbar scattering states, respectively, and that the distance between Kbar N (K Kbar) inside Lambda(1405) [f_{0}(980)] is 1.7-1.9 fm (2.6-3.0 fm). The root mean squared radii of Lambda(1405) and f_0(980) are also estimated from the mean distance between constituents.