Tetraquark-adequate QCD sum rules for quark-exchange processes

TL;DR

This paper develops specialized QCD sum rules for exotic tetraquark states, highlighting the importance of four-quark singularities and proposing a sum rule that starts at order O(α_s^2).

Contribution

It introduces tetraquark-adequate QCD sum rules that differ from traditional ones by focusing on diagrams with four-quark singularities and the order of the operator product expansion.

Findings

Sum rules split into two non-overlapping relations.

Only diagrams with four-quark singularities contribute to tetraquark formation.

The relevant sum rule begins with diagrams of order O(α_s^2).

Abstract

We consider quark-hadron duality relations and QCD sum rules for correlators involving exotic tetraquark currents, here specializing to the case of quark-exchange processes. We point out the differences they exhibit with respect to the cases involving ordinary bilinear quark currents. Based on the observation that only diagrams possessing at least four-quark singularities can contribute to the formation of tetraquark states, we show that the quark-hadron duality relations and the corresponding sum rules split into two non-overlapping relations. The ultimate tetraquark-adequate QCD sum rule is concerned only with one of these relations, in which the operator product expansion starts with diagrams of order $O(\alpha_s^2)$.