The non-perturbative part of the plaquette in quenched QCD

Abstract

We define the non-perturbative 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 non-perturbative part can be parametrized as A (lambda)^B exp{-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 non-perturbative part scales like (a/r_0)^4 with a/r_0 defined with the force method. We discuss the large uncertainties associated with this statement. We propose a parametrization of ln((a/r_0)) as the two-loop universal terms plus a constant and exponential corrections. These corrections are consistent with a_{1-loop}^2 and play an important role when beta<6. We briefly discuss the possibility of calculating them semi-classically at large beta.

arXiv comment13 pages, 16 figures, uses revtex, contains a new section with the uncertainties on the extrapolations, refs. added

References in corpus (14)

• Instantons in QCD
• Thermodynamics of SU(3) Lattice Gauge Theory
• On the Viability of Lattice Perturbation Theory
• The Nf=0 heavy quark potential from short to intermediate distances
• Precision computation of a low-energy reference scale in quenched lattice QCD
• Lambda^2-contribution to the condensate in lattice gauge theory
• Perturbative expansions from Monte Carlo simulations at weak coupling: Wilson loops and the static-quark self-energy
• Separating perturbative and non-perturbative contributions to the plaquette
• A consistency check for Renormalons in Lattice Gauge Theory: beta^(-10) contributions to the SU(3) plaquette
• Lattice gluodynamics at negative g^2
• The lattice scale at large beta in quenched QCD
• An example of optimal field cut in lattice gauge perturbation theory
• About a possible 3rd order phase transition at T=0 in 4D gluodynamics
• Asymptotic scaling corrections in QCD with Wilson fermions from the 3-loop average plaquette

Cited by in corpus (15)

• Model-independent determination of the gluon condensate in four-dimensional SU(3) gauge theory
• Wilson loops to 20th order numerical stochastic perturbation theory
• Fisher's zeros as boundary of renormalization group flows in complex coupling spaces
• Density of states and Fisher's zeros in compact U(1) pure gauge theory
• Renormalon Subtraction from the Average Plaquette and the Gluon Condensate
• Hyperasymptotic approximation to the plaquette and determination of the gluon condensate
• Series expansions of the density of states in SU(2) lattice gauge theory
• Extracting gluon condensate from the average plaquette
• Dyson instability for 2D nonlinear O(N) sigma models
• Phenomenology of renormalons and the OPE from lattice regularization: the gluon condensate and the heavy quark pole mass
• Convergent perturbation theory for lattice models with fermions
• Dyson's Instability in Lattice Gauge Theory
• Theoretical description of the plaquette with exponential accuracy
• Definition and parametrization of non-perturbative effects in quenched QCD
• Fisher's Zeros and Perturbative Series in Gluodynamics