Probabilities in nonorthogonal basis: Four--quark systems

TL;DR

This paper develops an analytical method to expand four-quark wave functions in nonorthogonal color bases, enabling the evaluation of their physical components and aiding in classifying four-quark states as molecular or compact.

Contribution

It introduces a formalism for expanding four-quark wave functions in nonorthogonal color bases and evaluates their physical components for state classification.

Findings

Method to expand four-quark wave functions in nonorthogonal bases

Formalism to evaluate probabilities of physical components

Application to classify bound and unbound four-quark states

Abstract

Four-quark states may exist as colorless meson-meson molecules or compact systems with two-body colored components. We derive an analytical procedure to expand an arbitrary four--quark wave function in terms of nonorthogonal color singlet--singlet vectors. Using this expansion we develop the necessary formalism to evaluate the probability of physical components with an arbitrary four-quark wave function. Its application to characterize bound and unbound four--quark states as meson-meson, molecular or compact systems is discussed