Renormalon-free definition of the gluon condensate within the large-${\beta }_0$ approximation

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.

24 pages, 7 figures. The final version to appear in PTEP

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Cited by in corpus (5)

• Renormalons beyond the Borel plane
• Formulation for renormalon-free perturbative predictions beyond large-${\beta }_0$ approximation
• Infrared renormalon in $SU(N)$ QCD(adj.) on ${\mathbb{R}}^3\times S^1$
• Spectral sum of current correlators from lattice QCD
• Renormalon effect of quasi-PDF in gradient flow formalism