Abstract
We study the pair description of heavy tetraquark systems $|QQ\bar Q \bar Q\rangle$ in the frame of a non-relativistic potential model. By taking the two heavy quark pairs $(Q\bar Q)$ as colored clusters, the four-quark Schr\"odinger equation is reduced to a two-pair equation, when the inner motion inside the pairs can be neglected. Taking into account all the Casimir scaling potentials between two quarks and using the lattice QCD simulated mixing angle between the two color-singlet states for the tetraquark system, we extracted a detailed pair potential between the two heavy quark pairs.
Highlights
Among the studies of exotic hadrons which cannot be explained as normal mesons and baryons, there are many theoretical works focusing on heavy tetraquark systems QQQ Q (Q means charm quark c or bottom quark b)
The molecular picture is an often used mechanism to understand the properties of multiquark states, for instance the phenomenon that some of the tetraquark states locate below the threshold of the corresponding two mesons
The key quantity to control the molecular structure of heavy tetraquark states is the interaction potential between the two molecules
Summary
Among the studies of exotic hadrons which cannot be explained as normal mesons and baryons, there are many theoretical works focusing on heavy tetraquark systems QQQ Q (Q means charm quark c or bottom quark b). We study a colored pair description for general heavy tetraquark systems in the frame of a nonrelativistic potential model. Since the Cornell potential depends only on the distance between two interacting quarks, the four-body Schrödinger equation can be divided into a center-of-mass part and a relative part Ψ 1⁄4 Θψ.
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