The non-perturbative part of the plaquette in quenched QCD

TL;DR

This paper investigates the non-perturbative contributions to the average plaquette in quenched lattice QCD, proposing extrapolation methods and parametrizations to understand their scaling and relation to perturbative series behavior.

Contribution

It introduces new extrapolation techniques for the perturbative series and proposes a parametrization of non-perturbative effects in quenched QCD.

Findings

Non-perturbative part scales like (a/r_0)^4.

Extrapolations are consistent up to order 20-25.

Corrections are compatible with two-loop universal terms.

Abstract

We define the non-perturbative part of a quantity as the difference between its numerical value and the perturbative series truncated by dropping the order of minimal contribution and the higher orders. For the anharmonic oscillator, the double-well potential and the single plaquette gauge theory, the non-perturbative part can be parametrized as A (lambda)^B exp{-C/lambda} and the coefficients can be calculated analytically. For lattice QCD in the quenched approximation, the perturbative series for the average plaquette is dominated at low order by a singularity in the complex coupling plane and the asymptotic behavior can only be reached by using extrapolations of the existing series. We discuss two extrapolations that provide a consistent description of the series up to order 20-25. These extrapolations favor the idea that the non-perturbative part scales like (a/r_0)^4 with a/r_0 defined with the force method. We discuss the large uncertainties associated with this statement. We propose a parametrization of ln((a/r_0)) as the two-loop universal terms plus a constant and exponential corrections. These corrections are consistent with a_{1-loop}^2 and play an important role when beta<6. We briefly discuss the possibility of calculating them semi-classically at large beta.