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Nonperturbative part of the plaquette in pure gauge theory
Journal article   Open access   Peer reviewed

Nonperturbative part of the plaquette in pure gauge theory

Y Meurice
Physical review. D, Particles and fields, Vol.74(9), 096005
11/01/2006
DOI: 10.1103/PHYSREVD.74.096005
url
https://arxiv.org/pdf/hep-lat/0609005View
Open Access

Abstract

We define the nonperturbative 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 nonperturbative part can be parametrized as A{lambda}{sup B}e{sup -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 nonperturbative part scales like (a/r{sub 0}){sup 4} with a/r{sub 0} defined with the force method. We discuss the large uncertainties associated with this statement. We propose a parametrization of ln(a/r{sub 0}) as the two-loop universal terms plus a constant and exponential corrections. These corrections are consistent with a{sub 1-loop}{sup 2} and play an important role when {beta}<6. We briefly discuss the possibility of calculating them semiclassically at large {beta}.
 ANHARMONIC OSCILLATORS APPROXIMATIONS CORRECTIONS COUPLING EXTRAPOLATION GAUGE INVARIANCE LATTICE FIELD THEORY PHYSICS OF ELEMENTARY PARTICLES AND FIELDS POTENTIALS QUANTUM CHROMODYNAMICS SINGULARITY

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