Size measurement of dynamically generated resonances with finite boxes

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.

14 pages, 8 figures, version accepted for publication in Phys. Rev. C

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• Effective Kbar N interaction based on chiral SU(3) dynamics
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• Structure of Lambda(1405) and construction of KbarN local potential based on chiral SU(3) dynamics
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• Constraint on K Kbar compositeness of the a0(980) and f0(980) resonances from their mixing intensity
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• Determination of exotic hadron structure by constituent-counting rule for hard exclusive processes
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• Determination of compositeness of the Lambda(1405) resonance from its radiative decay
• Bound states on the lattice with partially twisted boundary conditions
• Possible interpretation of the complex expectation values associated with resonances
• Double-pole nature of $\Lambda (1405)$ studied with coupled-channel complex scaling method using complex-range Gaussian basis
• Mirror symmetry breaking in He isotopes and their mirror nuclei
• Is two-poles' $\Lambda (1405)$ one state or two?
• Recent developments in antikaon-nucleon dynamics
• Compositeness of hadrons, nuclei, and atomic systems
• Compositeness of hadron resonances in finite volume
• Determining Compositeness of Hadronic Resonances: the $\Lambda (1405)$ Radiative Decay and the $a_0(980)$-$f_0(980)$ Mixing
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• Size measurement of dynamically generated hadronic resonances with finite volume effect
• Compositeness of Hadrons and Near-Threshold Dynamics
• Two-body Wave Functions, Compositeness, And The Internal Structure Of Dynamically Generated Resonances