Nonlocal Condensate Model for QCD Sum Rules

TL;DR

This paper introduces a nonlocal quark condensate model into QCD sum rules using the Källén-Lehmann representation, improving the description of the pion form factor up to high momentum transfers.

Contribution

It presents a novel formalism incorporating nonlocal condensates into QCD sum rules, revealing different Q^2 dependence than previous local models.

Findings

QSR results agree with experimental data up to Q^2 ≈ 10 GeV^2

Nonlocal condensate contribution decreases as 1/Q^2, unlike exponential decay

Contrasts with linear rise predicted by local-condensate approximation

Abstract

We include effects of nonlocal quark condensates into QCD sum rules (QSR) via the K$\ddot{\mathrm{a}}$ll$\acute{\mathrm{e}}$n-Lehmann representation for a dressed fermion propagator, in which a negative spectral density function manifests their nonperturbative nature. Applying our formalism to the pion form factor as an example, QSR results are in good agreement with data for momentum transfer squared up to $Q^2 \approx 10 $ GeV$^2$. It is observed that the nonlocal quark condensate contribution descends like $1/Q^2$, different from the exponential decrease in $Q^2$ obtained in the literature, and contrary to the linear rise in the local-condensate approximation.