Investigation of New Methods for Numerical Stochastic Perturbation Theory in ${\phi }^4$ Theory

Abstract

Numerical stochastic perturbation theory is a powerful tool for estimating high-order perturbative expansions in lattice field theory. The standard algorithms based on the Langevin equation, however, suffer from several limitations which in practice restrict the potential of this technique. In this work we investigate some alternative methods which could in principle improve on the standard approach. In particular, we present a study of the recently proposed Instantaneous Stochastic Perturbation Theory, as well as a formulation of numerical stochastic perturbation theory based on Generalized Hybrid Molecular Dynamics algorithms. The viability of these methods is investigated in ${\phi }^4$ theory.

45 pages, 12 figures. Added new section on cost comparison with Langevin NSPT. Matches published version

References in corpus (7)

• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Locally smeared operator product expansions in scalar field theory
• SMD-based numerical stochastic perturbation theory
• Triviality of ${\varphi }_4^4$ theory: small volume expansion and new data
• Non-renormalizability of the HMC algorithm
• Asymptotics of Fixed Point Distributions for Inexact Monte Carlo Algorithms
• Instantaneous stochastic perturbation theory

Cited by in corpus (8)

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• Short flow-time coefficients of CP-violating operators
• Past, present, and future of precision determinations of the QCD coupling from lattice QCD
• Large-order NSPT for lattice gauge theories with fermions: the plaquette in massless QCD
• Universal Renormalons in Principal Chiral Models
• Numerical stochastic perturbation theory applied to the twisted Eguchi-Kawai model
• Perturbative study of large $N$ principal chiral model with twisted reduction
• NSPT estimate of the improvement coefficient $c_A$ to two loops