Strong coupling from an improved τ vector isovector spectral function

Abstract

We perform a precise extraction of the QCD coupling at the τ-mass scale, α s (m τ ), from a new vector isovector spectral function which combines ALEPH and OPAL distributions for the dominant channels, τ → ππ 0 ν τ , τ → 3ππ 0 ν τ and τ → π3π 0 ν τ , with estimates of subleading contributions obtained from electroproduction cross-sections using CVC, as well as BaBar results for τ → K − K 0 ν τ . The fully inclusive spectral function thus obtained is entirely based on experimental data, without Monte Carlo input. From this new data set, we obtain α s (m τ ) = 0.3077 ± 0.0075, which corresponds to α s (m Z ) = 0.1171 ± 0.0010. This analysis can be improved on the experimental side with new measurements of the dominant ππ 0 , π3π 0 , and 3ππ 0 τ decay modes.

On the difference between FOPT and CIPT for hadronic tau decays

“…either by multiplication of the proper Γ (n) factors or by using the inverse Borel integral in Eq. (11). Likewise the form of Eq.…”

“…(12) in the entire complex u-plane can be uniquely determined from summing the absolute convergent Taylor series (13) within its radius of convergence (which is 1 due to the p = −1 poles) and using analytic continuation. The poles for negative p are the so-called UV renormalons and are related to signalternating divergence patterns which can be formally summed in the Borel representation (11). In QCD the UV renormalons arise from the large-momentum behavior of the loop diagrams.…”

“…(1). Using the 5-loop results [3][4][5] an impressive precision of about 5% has been achieved for α s (m 2 τ ) (corresponding to an uncertainty of 1.5% for α s (m 2 Z )), where the uncertainty is dominated by the perturbative error in δ (0) W (s 0 ) [8,9,11,12]. A major limitation of α s determinations from the moments A W (s 0 ) arises from the fact that two different expansion approaches to evaluate δ (0) W (s 0 ), called contour-improved perturbation theory (CIPT) and fixedorder perturbation theory (FOPT) yield systematic numerical differences that do not seem to be covered by the conventional perturbative uncertainty estimates related to renormalization scale variations.…”

“…( 1 ). Using the 5-loop results [ 3 – 5 ] an impressive precision of about has been achieved for (corresponding to an uncertainty of for ), where the uncertainty is dominated by the perturbative error in [ 8 , 9 , 11 , 12 ].…”

Determination of perturbative QCD coupling from ALEPH $$\tau $$ decay data using pinched Borel–Laplace and Finite Energy Sum Rules

“…In a recent work [99], the mentioned DV-model strategy was used in FOPT-evaluated FESRs of semihadronic τ -decays, using an experimental spectral V-channel function based on data from various experiments (ALEPH, OPAL, BABAR, and supplemented by e + e − → hadrons data), and they obtained the result α s (m 2 τ ) = 0.3077 ± 0.0075, which is very close to our result α s (m 2 τ ) = 0.3075 +0.0066 −0.0069 obtained from Borel-Laplace sum rule global fit with FOPT method, cf. Eq.…”