RG/Pade Estimate of the Three-Loop Contribution to the QCD Static Potential Function

Details RG/Pade Estimate of the Three-Loop Contribution to the QCD Static Potential Function RG/Pade Estimate of the Three-Loop Contribution to the QCD Static Potential Function

2001-07-05

arxiv.org/abs/hep-ph/0107052v3

Phys.Lett. B521 (2001) 434-440

Physics

High Energy Physics

High Energy Physics - Phenomenology

13 pages, LaTeX, additional discussion on the results

Scientific paper

10.1016/S0370-2693(01)01256-4

The three renormalization-group-accessible three-loop coefficients of powers of logarithms within the \bar{MS} series momentum-space for the QCD static potential are calculated and compared to values obtained via asymptotic Pad\'e-approximant methods. The leading and next-to-leading logarithmic coefficients are both found to be in exact agreement with their asymptotic Pad\'e-predictions. The predicted value for the third RG-accessible coefficient is found to be within 7% relative |error| of its true value for n_f leq 6, and is shown to be in exact agreement with its true value in the n_f \to \infty limit. Asymptotic Pad\'e estimates are also obtained for the remaining (RG-inaccessible) three-loop coefficient. Comparison is also made with recent estimates of the three-loop contribution to the configuration-space static-potential function.

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