SMD-based numerical stochastic perturbation theory

Abstract

The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously established and the use of higher-order symplectic integration schemes is shown to be highly profitable in this context. For illustration, the gradient-flow coupling in finite volume with Schrödinger functional boundary conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory. The scaling behaviour of the algorithm turns out to be rather favourable in this case, which allows the computations to be driven close to the continuum limit.

35 pages, 4 figures; v2: corrected typos, coincides with published version

References in corpus (4)

• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Slow running of the Gradient Flow coupling from 200 MeV to 4 GeV in $N_{\mathrm{f}}=3$ QCD
• The perturbative QCD gradient flow to three loops
• Step scaling and the Yang-Mills gradient flow

Cited by in corpus (25)

• FLAG Review 2019
• FLAG Review 2021
• An analysis of systematic effects in finite size scaling studies using the gradient flow
• FLAG Review 2024
• The two-loop energy-momentum tensor within the gradient-flow formalism
• Bootstrap for Lattice Yang-Mills theory
• Stochastic locality and master-field simulations of very large lattices
• Results and techniques for higher order calculations within the gradient-flow formalism
• The gradient flow coupling at high-energy and the scale of SU(3) Yang-Mills theory
• Short flow-time coefficients of CP-violating operators
• Non-perturbative determination of the $\Lambda$-parameter in the pure SU(3) gauge theory from the twisted gradient flow coupling
• Determination of ${\alpha }_s(m_Z)$ by the non-perturbative decoupling method
• Large-order NSPT for lattice gauge theories with fermions: the plaquette in massless QCD
• Past, present, and future of precision determinations of the QCD coupling from lattice QCD
• Investigation of New Methods for Numerical Stochastic Perturbation Theory in ${\phi }^4$ Theory
• Universal Renormalons in Principal Chiral Models
• openQ*D code: a versatile tool for QCD+QED simulations
• The twisted gradient flow coupling at one loop
• Numerical stochastic perturbation theory applied to the twisted Eguchi-Kawai model
• Short-flow-time expansion of quark bilinears through next-to-next-to-leading order QCD
• Strong CP problem in the quantum rotor
• Precision Determination of ${\alpha }_s$ from Lattice QCD
• Perturbative study of large $N$ principal chiral model with twisted reduction
• Applications of the Perturbative Gradient Flow
• NSPT estimate of the improvement coefficient $c_A$ to two loops