The continuum limit of perturbative coefficients calculated with a large field cutoff

TL;DR

This paper presents Monte Carlo calculations of perturbative coefficients in lattice scalar field theory with a large field cutoff, demonstrating convergence of series and relevance as a UV regulator, with implications for QCD.

Contribution

It introduces a method to compute perturbative coefficients with a field cutoff, showing convergence and UV regulation, extending previous asymptotic series approaches.

Findings

Perturbative series become convergent with a large field cutoff.

Accurate calculations are feasible even in crossover regions.

Field cutoff acts as a UV regulator.

Abstract

We report MC calculations of perturbative coefficients for lattice scalar field theory in dimensions 1, 2 and 3, where the large field contributions are cutoff. This produces converging (instead of asymptotic) perturbative series. We discuss the statistical errors and the lattice effects and show that accurate calculations are possible even in a crossover region where no approximation works. We show that the field cutoff is also a UV regulator. We point out the relevance for QCD questions discussed by Tomboulis and Trottier at this conference.