Nucleon QCD sum rules in instanton vacuum

TL;DR

This paper calculates the nucleon polarization operator within an instanton-based QCD vacuum model, demonstrating that a realistic nucleon mass emerges when considering a specific instanton size distribution.

Contribution

It introduces a combined instanton vacuum model with large and small instantons and solves the QCD sum rules to match the physical nucleon mass.

Findings

Solution with nucleon mass close to physical value at w_s ≈ 2/3

Large instantons described by local scalar condensate

Small instantons interpreted as nonlocal scalar condensate

Abstract

We calculate the polarization operator of the nucleon current in the instanton medium. The medium (QCD vacuum) is assumed to be a composition of the instantons of large and small sizes. The former are described in terms of the local scalar condensate, while the latter can be interpreted as the nonlocal scalar condensate. We solve the corresponding QCD sum rules equations and demonstrate that there is a solution with the value of the nucleon mass close to the physical one if the fraction of the small size instantons w_s \approx 2/3.