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

TL;DR

This paper extends the string junction model of hadrons by introducing a cluster hypothesis, enabling mass predictions for exotic hadrons like penta-quarks and tetra-quarks, and analyzing recent experimental candidates.

Contribution

It introduces a cluster hypothesis into the string junction model to predict masses of exotic hadrons and examines recent experimental candidates within this framework.

Findings

Mass of penta-quark baryons with N_J=3 estimated around 3 GeV.

Mass of tetra-quark mesons with N_J=2 estimated around 2 GeV.

Analysis of Z+(4430) provides parameter constraints for the model.

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 $m \sim N_J\cdot m_B$, where $N_J$ is the total number of junctions and $m_B \sim 1$ 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 $\Theta$(1530 MeV, $S=+1)$ including a strange anti-quark ${\sb}$ and that for tetra-quark meson $Z^+$(4430 MeV) recently reported by the Bell collaboration are examined in parallel. $\Theta $ is considered to have non-strange partners, which are lighter by the mass difference $\Delta_s$ between strange and non-strange quarks. Mass of such light penta-quark baryons with $N_J=3$ is expected to be about 3 GeV. Several parameters of the model are estimated such as mass of junction of $m_J \sim O(10)$ MeV. While mass of light tetra-quark meson with $N_J=2$ is expected to be about 2 GeV, $Z^+$(4430 MeV) containing $(u,c,{\db},{\cb})$ gives a clue to determine some parameters of the model, e.g., inter-junction string energy $m_{IJ}$.