Renormalization-Scheme Dependence of Pade Summation in QCD

Details Renormalization-Scheme Dependence of Pade Summation in QCD Renormalization-Scheme Dependence of Pade Summation in QCD

1996-07-23

arxiv.org/abs/hep-ph/9607404v1

Phys.Rev.D54:6986-6996,1996

Physics

High Energy Physics

High Energy Physics - Phenomenology

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

Scientific paper

10.1103/PhysRevD.54.6986

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 $Q^2=3 GeV^2$ to estimate $\alpha_s(M_Z) = 0.117^{+0.004}_{-0.007} \pm 0.002$, where the first error is experimental, and the second is theoretical.

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