Resummation of the hadronic tau decay width with the modified Borel transform method

Abstract

A modified Borel transform of the Adler function is used to resum the hadronic tau decay width ratio. In contrast with the ordinary Borel transform, the integrand of the Borel integral is renormalization-scale invariant. We use an ansatz which explicitly accounts for the structure of the leading infrared renormalon. Further, we use judiciously chosen conformal transformations for the Borel variable, in order to map sufficiently away from the origin the other ultraviolet and infrared renormalon singularities. In addition, we apply Padé approximants for the corresponding truncated perturbation series of the modified Borel transform, in order to further accelerate the convergence. Comparing the results with the presently available experimental data on the tau hadronic decay width ratio, we obtain α s (M 2 z ) = 0.1192± 0.0007 exp. ± 0.0010 EW+CKM ± 0.0009 th. ± 0.0003 evol. . These predictions virtually agree with those of our previous resummations where we used ordinary Borel transforms instead. PACS number(s): 13.35. Dx, 11.15.Tk

Extraction ofαsfrom the Gross–Llewellyn Smith sum rule using Borel resummation

“…This PA choice of the beta function has reasonable behavior in the region of large x ≡ α s /π and has been used in Refs. [9,11,38] in the analyses of low energy QCD observables. We will comment later on how the results change when we use N 3 L TPS of the β MS (x), and when we change the RSch even more drastically.…”

“…These techniques were applied to the hadronic tau decay width [9][10][11] and to the hadronic contribution to the muon anomalous magnetic moment [12]. In this work we apply them to the GLS sum rule.…”

Calculations of binding energies and masses of heavy quarkonia using renormalon cancellation

“…The coefficients h (σ) k in Eq. (35) differ from h k 's of the bilocal case (34), and are determined by the requirement that the power expansion of expression (35) reproduce the known N 3 LO TPS of the Borel transform of F s (26). If σ parameter increases (i.e., σ 1), formula (35) is expected to gradually reduce to the bilocal formula (33).…”

“…The comparison of the various methods is more reasonable if the same central input value of (MS) α s (M Z ) is taken. Our central value was α s (m τ ) = 0.3254 [⇒ α s (M Z ) = 0.1192] since such [34], or similar [20,64], values follow from the (nonstrange) semihadronic τ decay data which are very precise [65]. On the other hand, the world average as of September 2002 is α s (M Z ) = 0.1183 ± 0.0027 [66].…”

“…When c 4 is varied according to (9), the variation is about ∓2 and ∓1 MeV for m b , m t , respectively. The uncertainty in α s can be taken as α s (m τ ) = 0.3254 ± 0.0125 [34], corresponding to α s (M Z ) = 0.1192 ± 0.0015. This uncertainty is by far the major source in the variation of the pole masses: (δm b ) αs = +135 −148 MeV for bilocal method ( +137 −150 MeV for R-method), and (δm t ) αs = +161 −171 MeV for bilocal method ( +161…”