Cluster reducibility of multiquark operators

TL;DR

This paper demonstrates that multiquark gauge-invariant operators can be decomposed into products of hadronic operators, revealing their cluster reducibility and impacting the understanding of exotic states and multiquark bound states.

Contribution

It provides a formal proof of the cluster reducibility of multiquark operators, unifying multiquark and molecular approaches at the gauge-invariant operator level.

Findings

Multiquark operators decompose into hadronic operator products.

Cluster reducibility inhibits fully compact multiquark bound states.

Multiquark operators are crucial near hadronic cluster proximity.

Abstract

It is shown that the multiquark gauge-invariant operators can, in general, be decomposed into combinations of products of ordinary hadronic operators, exhibiting their cluster reducibility. The latter property inhibits the formation of completely compact multiquark bound states. Multiquark operators still play a crucial role in the description of exotic states in regions of configuration space where the hadronic clusters are close to each other. Our proof gives a foundation for a unified viewpoint, where the multiquark-type and the molecular-type approaches play complementary roles, at the gauge-invariant nonlocal operator level.