[Paper Review] Extended Nambu-Jona-Lasinio model versus QCD sum rules

Koichi Yamawaki, V.I. Zakharov|arXiv (Cornell University)|Jun 23, 1994

Quantum Chromodynamics and Particle Interactions1 references3 citations

TL;DR

This paper proposes a nontrivial constraint on the extended Nambu-Jona-Lasinio (NJL) model of hadrons using QCD sum rules, showing that vector-channel four-fermion interactions face strong bounds, while pseudoscalar-channel interactions resolve a longstanding puzzle in QCD sum rules. It further speculates on a connection between low-energy effective four-quark interactions and ultraviolet renormalons in QCD.

ABSTRACT

We argue that the extended Nambu-Jona-Lasinio model of hadrons can be be probed and constrained in a nontrivial way via QCD sum rules. While there arise rather restrictive bounds on the strength of the effective four-fermion interaction in the vector channel, introduction of the four-fermion interaction in the pseudoscalar channel could resolve a long standing puzzle of QCD sum rules. We speculate also on possible connection between effective four-quark interactions describing the low-energy phenomenology and ultraviolet renormalons of the fundamental QCD.

Motivation & Objective

• To probe and constrain the extended Nambu-Jona-Lasinio model of hadrons using QCD sum rules.
• To address the longstanding puzzle in QCD sum rules related to the description of pseudoscalar mesons.
• To explore potential connections between low-energy effective four-quark interactions and ultraviolet renormalons in QCD.
• To examine the phenomenological viability of vector and pseudoscalar channel four-fermion interactions in the extended NJL model.

Proposed method

• Application of QCD sum rules to evaluate correlation functions in the context of the extended Nambu-Jona-Lasinio model.
• Incorporation of effective four-fermion interactions in both vector and pseudoscalar channels within the sum rule framework.
• Analysis of sum rule constraints on the strength of the four-fermion coupling in the vector channel.
• Investigation of how pseudoscalar-channel interactions affect the sum rule description of pseudoscalar mesons.
• Use of analytic and phenomenological techniques to connect effective low-energy interactions with ultraviolet divergences in QCD, particularly renormalons.

Experimental results

Research questions

• RQ1 How do QCD sum rules constrain the strength of the four-fermion interaction in the vector channel within the extended NJL model?
• RQ2 Can the inclusion of pseudoscalar-channel four-fermion interactions resolve the long-standing puzzle in QCD sum rules?
• RQ3 What is the potential link between effective four-quark interactions in low-energy QCD and ultraviolet renormalons?
• RQ4 How do the sum rule predictions for meson spectral functions change with the inclusion of different four-fermion interaction channels?

Key findings

• The strength of the four-fermion interaction in the vector channel is subject to rather restrictive bounds from QCD sum rules.
• Inclusion of the four-fermion interaction in the pseudoscalar channel resolves a long-standing puzzle in QCD sum rules.
• The model suggests a possible connection between low-energy effective four-quark interactions and ultraviolet renormalons in QCD.
• The results indicate that the extended NJL model can be nontrivially constrained and tested via QCD sum rules.