Renormalization-Scheme Dependence of Pade Summation in QCD

Abstract

We study the renormalization-scheme (RS) dependence of Pade Approximants (PA's), and compare them with the Principle of Minimal Sensitivity (PMS) and the Effective Charge (ECH) approaches. Although the formulae provided by the PA, PMS and ECH predictions for higher-order terms in a QCD perturbation expansion differ in general, their predictions can be very close numerically for a wide range of renormalization schemes. Using the Bjorken sum rule as a test case, we find that Pade Summation (PS) reduces drastically the RS dependence of the Bjorken effective charge. We use these results to estimate the theoretical error due to the choice of RS in the extraction of ${\alpha }_s$ from the Bjorken sum rule, and use the available data at $Q^2=3Ge{V}^2$ to estimate ${\alpha }_s(M_Z)=0.117_{-0.007}^{+0.004}\pm 0.002$, where the first error is experimental, and the second is theoretical.

12 pages (latex), including 6 embedded figures; uses epsfig.sty

References in corpus (5)

• Estimates of the higher-order QCD corrections to R(s), R_τ and deep-inelasstic scattering sum rules
• Comparison of the Pade Approximation Method to Perturbative QCD Calculations
• Pade Approximants, Borel Transforms and Renormalons: the Bjorken Sum Rule as a Case Study
• QCD Sum Rule Calculation of Twist-4 Corrections to Bjorken and Ellis-Jaffe Sum Rules
• QCD Renormalons and Higher Twist Effects

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