Strong Coupling From the Tau Hadronic Width by Non-Power QCD Perturbation Theory

Abstract

Starting from the divergent character of the perturbative expansions in QCD and using the technique of series acceleration by the conformal mappings of the Borel plane, I define a novel, non-power perturbative expansion for the Adler function, which simultaneously implements renormalization-group summation and has a tamed large-order behaviour. The new expansion functions, which replace the standard powers of the coupling, are singular at the origin of the coupling plane and have divergent perturbative expansions, resembling the expanded function itself. Confronting the new perturbative expansions with the standard ones on specific models investigated recently in the literature, I show that they approximate in an impressive way the exact Adler function and the spectral function moments. Applied to the τ hadronic width, the contour-improved and the renormalization-group summed non-power expansions in the MS scheme lead to the prediction αs(M

Determination of the Strong Coupling From Hadronic Tau Decays Using Renormalization Group Summed Perturbation Theory

“…The special features of this latter expansion will be discussed elsewhere in these proceedings [34].…”

“…The non-power expansions show remarkable convergence properties for the Adler function, which is the crucial input in the determination of α s from hadronic τ decays. This is reviewed elsewhere in these proceedings [34].…”

“…This provides a new class of expansions, which simultaneously implement the RG invariance and the large-order summation by the analytic continuation in the Borel plane. The details may be found elsewhere in these proceedings [34].…”

Expansions ofτhadronic spectral function moments in a nonpower QCD perturbation theory with tamed large order behavior

“…The hadronic decays of the τ lepton allow for one of the most precise determinations of the strong coupling and also provide a beautiful experimental test of the predicted QCD running [1,3]. Indeed, the recent calculation of the QCD Adler function to five loops in massless QCD [4] motivated a large number of new determinations of α s from these processes [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. It may however be noted that τ decays involve the strong coupling at a rather low scale, where the theoretical ambiguities inherent to perturbative QCD are expected to be large.…”

“…It has been recently pointed out [15,16,19,20] that an alternative to FOPT and CIPT, which is placed somewhat between the two, but in practice is closer to CIPT, is one that sums the leading logarithms thereby accounting for the renormalization-group invariance. In Refs.…”