Updated determination ofαsfromτdecays

Abstract

Employing our previous framework to treat non-perturbative effects selfconsistently, including duality violations, we update the determination of the strong coupling, α s , using a modified version of the 1998 OPAL data, updated to reflect current values of exclusive mode hadronic τ decay branching fractions. To account for non-perturbative effects, non-linear, multi-parameter fits are necessary. We have, therefore, investigated the posterior probability distribution of the model parameters underlying our fits in more detail. We find that OPAL data alone provide only weak constraints on some of the parameters needed to model duality violations, especially in the case of fits involving axial vector channel data, making additional prior assumptions on the expected size of these parameters necessary at present. We provide evidence that this situation could be greatly improved if hadronic spectral functions based on the high-statistics BaBar and Belle data were to be made available.2

Determination ofαsfrom the QCD static energy: An update

“…Non-lattice determinations from τ decays in Refs. [45,46]; from thrust in e + e − collisions in Refs. [4,47]; the recent H1 re-analysis of Ref.…”

τ − →K − η (′) ν τ decays in Chiral Perturbation Theory with resonances

“…[76] the multi-channel Muskelishivili-Omnès problem for three channels (Kπ, Kη, Kη for i = 1, 2, 3) is solved. Each of the scalar form factors f i 0 (s) is then coupled to the others via 12) where s i is the threshold for channel i and t i→j 0 are partial wave T -matrix elements for the i → j scattering. The unitarized form factors are obtained solving the coupled dispersion relations arising from eq.…”

“…At the (semi-)inclusive level this allows to extract fundamental parameters of the Standard Model, most importantly the strong coupling α S [9][10][11][12]. Tau decays containing Kaons have been split into the Cabibbo-allowed and suppressed decays [13,14] rendering possible determinations of the quark-mixing matrix element |V us | [15,16] and the mass of the strange quark [17][18][19][20][21][22][23][24][25] at high precision.…”

Tau Decays and αs

“…Most of these other determinations [14,[18][19][20][21][22][23][24] were based directly or indirectly on the earlier versions of the spectral functions from ALEPH. Only two recent determinations [25,26] were obtained using the spectral functions of OPAL. One major difference of the latter determinations with the others is the introduction of duality violation with a model containing four additional parameters.…”