Four- and Five-Body Scattering Calculations

TL;DR

This paper performs detailed five- and four-quark scattering calculations using the Gaussian Expansion Method, finding no five-quark resonance below 1.85 GeV except for a predicted state at 1.9 GeV, and also analyzing the X(3872).

Contribution

It introduces a precise multi-quark scattering calculation method explicitly including scattering channels, revealing the absence of low-energy five-quark resonances.

Findings

No five-quark resonance below 1.85 GeV around Θ+(1540).

Predicted a five-quark resonance at 1.9 GeV with a narrow width.

Analyzed the four-quark system related to X(3872).

Abstract

We study the five-quark system $uudd{\bar s}$ in the standard non-relativistic quark model by solving the scattering problem. Using the Gaussian Expansion Method (GEM), we perform the almost precise multi-quark calculations by treating a very large five-body modelspace including the NK scattering channel explicitly. Although a lot of pseudostates (discretized continuum states) with $J^\pi={1/2}^\pm$ and $J^\pi={3/2}^\pm$ are obtained within the bound-state approximation, all the states in $1.4-1.85$ GeV in mass around ${\rm {\rm \Theta}}^+(1540)$ melt into non-resonant continuum states through the coupling with the NK scattering state in the realistic case, i.e., there is no five-quark resonance below 1.85GeV. Instead, we predict a five-quark resonance state of $J^\pi={1/2}^-$ with the mass of about 1.9GeV and the width of $\Gamma \simeq$ 2.68MeV. Similar calculation is done for the four-quark system $c{\bar c}q{\bar q}$ ($q=u,d$) in connection with X$^0$(3872).