Renormalon-free definition of the gluon condensate within the large-$\beta_0$ approximation

TL;DR

This paper introduces a renormalon-free definition of the gluon condensate within the large-$eta_0$ approximation, enabling a systematic and unambiguous extraction of the condensate from lattice data.

Contribution

It proposes a new renormalon-free formulation of the gluon condensate, improving the precision of its determination and consistency across observables.

Findings

Renormalon uncertainty is separated from perturbative calculations.

The gluon condensate is defined to be renormalon-free and scale-independent.

Numerical extraction from lattice data is demonstrated.

Abstract

We propose a clear definition of the gluon condensate within the large-$\beta_0$ approximation as an attempt toward a systematic argument on the gluon condensate. We define the gluon condensate such that it is free from a renormalon uncertainty, consistent with the renormalization scale independence of each term of the operator product expansion (OPE), and an identical object irrespective of observables. The renormalon uncertainty of $\mathcal{O}(\Lambda^4)$, which renders the gluon condensate ambiguous, is separated from a perturbative calculation by using a recently suggested analytic formulation. The renormalon uncertainty is absorbed into the gluon condensate in the OPE, which makes the gluon condensate free from the renormalon uncertainty. As a result, we can define the OPE in a renormalon-free way. Based on this renormalon-free OPE formula, we discuss numerical extraction of the gluon condensate using the lattice data of the energy density operator defined by the Yang--Mills gradient flow.