QCD sum rules for the nucleon and the non-locality of quark condensates

TL;DR

This paper investigates how the x dependence of quark condensates, influenced by instanton zero modes, impacts QCD sum rules for the nucleon, revealing significant effects on traditional approximations used in the field.

Contribution

It demonstrates that the non-locality of quark condensates due to instanton effects can substantially alter nucleon sum rule results, challenging conventional local condensate assumptions.

Findings

Non-local quark condensates significantly affect sum rule calculations.

Instanton size scale (~600 MeV) is comparable to Borel mass (~1 GeV).

Traditional local condensate approximations may be inadequate.

Abstract

We emphasize the role of the x dependence of the quark condensate <|\bar q(0)q(x)|> originated by the zero fermion modes in the instanton vacuum. The effect is not negligible since the inverse size of the instanton 1/\rho~600MeV is comparable with the value of Borel mass M~1GeV. Using as an example the sum rules for the nucleon we show that this "non-locality" may strongly affected the conventional results obtained under the <|\bar q(0)q(x)|>=<|\bar q(0)q(0)|> approximation.