String Junction Model, Cluster Hypothesis, Penta-Quark Baryon and Tetra-Quark Meson

Abstract

Thirty years ago we proposed string junction model of hadrons and examined structure and reaction of hadrons including exotic ones. Mass m of exotic hadrons of light quarks is roughly given by m ∼ NJ · mB ,w hereNJ is the total number of junctions and mB ∼ 1 GeV is the ordinary light baryon mass. In this paper we introduce “cluster hypothesis” into the model by which mass of a complex hadron is given by the sum of masses of clusters composing it. The hypothesis guarantees the established picture that mass differences of hadrons of the same string junction structure are due to those of the constituent quarks. A candidate for penta-quark baryon Θ (1530 MeV, S = +1) including a strange antiquark s and that for tetra-quark meson Z + (4430 MeV) recently reported by the Belle collaboration are examined in parallel. Θ is considered to have non-strange partners, which are lighter by the mass difference Δs between strange and non-strange quarks. Mass of such light penta-quark baryons with NJ = 3 is expected to be about 3 GeV. Several parameters of the model are estimated such as mass of junction of mJ ∼ O(10) MeV. While mass of light tetra-quark meson with NJ = 2 is expected to be about 2 GeV, Z + (4430 MeV) containing (u, c, d, c) gives a clue to determine some parameters of the model, e.g., inter-junction string energy mIJ.