Asymptotic Scaling and Monte Carlo Data

TL;DR

The paper investigates the discrepancy between perturbative predictions and Monte Carlo data in asymptotically free theories like QCD, proposing that lattice artifacts explain the observed deviations and demonstrating this with fits to recent data.

Contribution

It introduces the Lattice-Distorted Perturbation Theory as an alternative explanation for asymptotic scaling discrepancies and confirms its validity through data fitting.

Findings

Lattice artifacts significantly affect asymptotic scaling observations.

Fitting functions with cut-off effects reproduce Monte Carlo data well.

Lattice data align with g_0-PT when including O(a^n) terms.

Abstract

It is a generally known problem that the behaviour predicted from perturbation theory for asymptotically free theories like QCD, i.e. asymptotic scaling, has not been observed in Monte Carlo simulations when the series is expressed in terms of the bare coupling g_0. This discrepancy has been explained in the past with the poor convergence properties of the perturbative series in the g_0. An alternative point of view, called Lattice-Distorted Perturbation Theory proposes that lattice artifacts due to the finiteness of the lattice spacing, a, cause the disagreement between Monte Carlo data and perturbative scaling. Following this alternative scenario, we fit recent quenched data from different observables to fitting functions that include these cut-off effects, confirming that the lattice data are well reproduced by g_0-PT with the simple addition of terms O(a^n).