Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2006-09-05
Phys.Rev.D74:096005,2006
Physics
High Energy Physics
High Energy Physics - Lattice
13 pages, 16 figures, uses revtex, contains a new section with the uncertainties on the extrapolations, refs. added
Scientific paper
10.1103/PhysRevD.74.096005
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.
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