Hybrids and Quark Confinement

Abstract

It has become traditional to assume that the Dirac structure of the phenomenological quark confinement potential is scalar $\otimes$ scalar. We use the heavy quark expansion of the Coulomb gauge QCD Hamiltonian and the Flux Tube model to demonstrate that this is true but in the effective sense only. The demonstration contains some surprises: confinement is actually vector $\otimes$ vector and it is nonperturbative mixing between ordinary and hybrid $Q \bar Q$ states which generates the scalar-like spin dependent potential at order $1/m_q^2$. Thus the existence of hybrids is crucial to establishing well-known spin splitting phenomenology. Finally, the resolution also indicates that the gluonic degrees of freedom in a hybrid must be of a collective nature.