Internal structure of the resonantΛ(1405) state in chiral dynamics

Abstract

The internal structure of the resonant (1405) state is investigated based on meson-baryon coupled-channels chiral dynamics by evaluating density distributions obtained from the form factors of the (1405) state. The form factors are defined as an extension of the ordinary stable particles and are directly evaluated from the currentcoupled meson-baryon scattering amplitude, paying attention to the charge conservation of the probe interactions. For the resonant (1405) state we calculate the density distributions in two ways. One is on the pole position of the (1405) in the complex energy plane, which evaluates the resonant (1405) structure without contamination from nonresonant backgrounds, and another is on the real energy axis around the (1405) resonance energy, which may be achieved in experiments. Using several probe interactions and channel decomposition, we separate the various contributions to the internal structure of the (1405). As a result, we find that the resonant (1405) state is composed of widely spreadK around N , which gives dominant component inside the (1405), with escaping π component. Furthermore, we considerKN bound state without decay channels, with which we can observe the internal structure of the bound state within real numbers. We also study the dependence of the form factors on the binding energy and meson mass. This verifies that the form factor defined through the current-coupled scattering amplitude serves as a natural generalization of the form factor for the resonance state. The relation between the interaction strength and the meson mass shows that the physical kaon mass appears to be within the suitable range to form a molecular bound state with the nucleon through the chiral SU(3) interaction.

Reanalysis of lattice QCD spectra leading to the D s0 ∗ (2317) and D s1 ∗ (2460)

“…The compositeness condition was extended leading to a new sum rule in an arbitrary number of coupled channels [13], which is reformulated in [14][15][16][17][18] for the case of energy dependent potentials. The sum rule contains two terms (see eq.…”

Constraint onKK¯compositeness of thea0(980)andSekihara1, Kumano2 2015Phys. Rev. D

“…[65]. Based on this normalization, we propose to interpret the compositeness X i and elementariness Z for a certain class of resonances on the basis of the similarity to the bound state case.…”

“…In fact, the spatial size of exotic hadron candidates was theoretically measured in a meson-meson and meson-baryon scatterings in, e.g., Refs. [65][66][67][68], and it was found that f 0 (980) and Λ(1405), whose KK andKN compositeness are close to unity, respectively, has spatial size exceeding largely the typical hadronic scale 0.8 fm.…”

Estimation of the Spatial Structure of \(\Lambda \)(1405) with Energy-Dependent Complex \(\bar{K}N\) Potential

“…For the confirmation of the dominance of such aKN molecular component in the Λ(1405), the concept of the compositeness has been used in recent works [9,10]. The spatial structure of the Λ(1405) has been discussed with the form factors and finite volume effect [11][12][13]. As an alternative way for the confirmation, in this work, we study the spatial extent of the Λ(1405) from theKN wave function, considering that the hadronic molecular states would have the relatively larger size than usual hadrons [14].…”