Dynamical effects of QCD in $q^2 \bar{q}^{2}$ systems

TL;DR

This paper investigates the impact of a gluonic potential matrix on tetraquark systems, revealing angle-dependent phase shifts and higher angular momentum components, which suggest orbital excitations influence meson-meson interactions.

Contribution

It introduces a potential matrix model based on lattice data that incorporates a minimal-area gluonic potential, leading to new insights into meson-meson scattering and orbital effects.

Findings

Phase shifts develop angle dependence with the new potential.

D-wave and higher angular momentum components are revealed.

Orbital excitations may influence meson-meson molecular properties.

Abstract

We study the coupling of a tetraquark system to an exchanged meson-meson channel, using a pure gluonic theory based four-quark potential {\em matrix} model which is known to fit well a large number of data points for lattice simulations of different geometries of a four-quark system. We find that if this minimal-area-based potential matrix replaces the earlier used simple Gaussian form for the gluon field overlap factor $f$ in its off-diagonal terms, the resulting $T$-matrix and phase shifts develop an angle dependence whose partial wave analysis reveals $D$ wave and higher angular momentum components in it. In addition to the obvious implications of this result for the meson-meson scattering, this new feature indicates the possibility of orbital excitations influencing properties of meson-meson molecules through a polarization potential. We have used a formalism of the resonating group method, treated kinetic energy and overlap matrices on model of the potential matrix, but decoupled the resulting complicated integral equations through the Born approximation. In this exploratory study we have used a quadratic confinement and not included the spin-dependence; we also used the approximation of equal constituent quark masses.