1211.4316 (Gauhar Abbas et al.)

Perturbative expansion of the QCD Adler function improved by
renormalization-group summation and analytic continuation in the Borel plane    [PDF]

Gauhar Abbas, B. Ananthanarayan, Irinel Caprini, Jan Fischer

We examine the large-order behaviour of a recently proposed renormalization group (RG)-improved expansion of the Adler function in perturbative QCD, which sums in an analytically closed form the leading logarithms accessible from RG-invariance. The expansion is first written as an effective series in powers of the one-loop coupling, and its leading singularities in the Borel plane are shown to be identical to those of the standard "contour-improved" (CI) expansion. Applying the technique of conformal mappings for the analytic continuation in the Borel plane, we define a class of improved expansions, which implement both the RG-invariance and the knowledge about the large order behaviour of the series. Detailed numerical studies of specific models for the Adler function indicate that the new expansions have remarkable convergence properties up to high orders. Using these expansions for the theoretical analysis of the hadronic decay width of the $\tau$ lepton, we obtain for the strong coupling the value $\alpha_s(M_\tau^2)= 0.3189^{+0.0145}_{-0.0115}$, which translates to $\alpha_s(M_Z^2)= 0.1184^{+0.0018}_{-0.0015}$.

View original: http://arxiv.org/abs/1211.4316