Construction of a local K¯N−πΣ−πΛ potential and composition of the Λ

Abstract

AKN -πΣ-πΛ coupled-channel potential is constructed on the basis of chiral SU(3) dynamics. Several matching conditions are introduced to formulate an equivalent local potential that reproduces the coupled-channel scattering amplitudes resulting from chiral SU(3)L×SU(3)R meson-baryon effective field theory. In contrast to a previously constructed effective single-channelKN potential, the explicit treatment of the πΣ channel yields a natural description of the low-mass pole as part of the two-pole structure of the Λ(1405) resonance. The energy dependence of the potential can now be parametrized with a minimum of polynomial orders. To study the properties of the Λ(1405) as a quantum-mechanical quasibound state, we derive the normalization condition of its wave function generated by the energy-dependent coupled-channel potential, using the Feshbach projection method. This framework provides an improved understanding of this system from the viewpoint of the compositeness of hadrons. With the properly normalized wave function, we demonstrate and confirm that the high-mass pole of the Λ(1405) is dominated by theKN component.

Hyperon II: Properties of excited hyperons

“…Most analyses find a twopole structure, with one narrow pole (Γ ≈ 20 − 30 MeV) at about 1420 MeV and one wider pole (Γ ≈ 160 MeV) [4,5]. These results were confirmed in a number of publications [9,44,45,46]. However, other analyses interpret the low-mass NK and πΣ spectra with a single resonance [47,48,49].…”

K−p Correlation Function from High-Energy Nuclear Collisions and Chiral SU(3) Dynamics

“…The starting point is chiral SU(3) dynamics at next-to-leading order [22] which successfully describes the set of existing K − p scattering data together with the SIDDHARTA kaonic hydrogen data [4]. An equivalent localKN -πΣ-πΛ coupled-channels potential has been constructed to reproduce the corresponding scattering amplitudes [21]. Fig.…”

Local Meson-Baryon Coupled-Channels Potential for the $$\varLambda (1405)$$

“…This is in sharp contrast to the single-channel version in Ref. [11] where one needs α max as large as 10 for sufficient accuracy. In other words, the explicit inclusion of the πY channels permits a parametrization of the potential strength with a more natural, much weaker energy dependence.…”

“…These parameters are determined by the matching conditions mentioned above, and the results are tabulated in Ref. [11]. One remarkable fact is that the energy dependence of V equiv ij can be accurately parametrized by a second-order polynomial (α max = 2).…”

“…When the potential is energy dependent, the sum of X i s does not become unity, and the elementarity Z is introduced. Using the Feshbach projection method, Z can be expressed by the expectation value of the energy derivative of the potential [11]. Originally, Z has been introduced as a field renormalization constant of the bare state representing the elementary component of the composite system [14].…”