Abstract
We re-examine recent determinations of power corrections from τ-decay and confront the results with the existing ones from QCD spectral sum rules (QSSR). We conclude that contrary to the QSSR analysis, which lead to 〈αsG2〉=(6.8±1.3)10−2 GeV4, τ-decay is not a good place for extracting the gluon condensate due to its extra αs2 coefficient which suppresses its contribution in this process. Results from e+e− sum rules and τ-decay: ραs〈u¯u〉2=(4.5±0.3)10−4 GeV6, where ρ=3.0±0.2 confirm the deviation from the vacuum saturation estimate of the four-quark condensate. “Non-standard” power corrections (direct instantons, duality violation and tachyonic gluon mass) beyond the SVZ-expansion, partially cancel out in the V+A hadronic τ-decay channel, which gives at order αs4: αs(Mτ)=0.3249 (29)ex(75)th leading to αs(MZ)|τ=0.1192 (4)ex(9)th, in remarkable agreement with (but more accurate than) αs(MZ)|Z=0.1191 (27) obtained at the same αs4 order from the Z-width and the global fit of electroweak data. Finally, the rôle of the tachyonic gluon mass in the determinations of |Vus| from τ-decay and of m¯s from τ decay, e+e− and (pseudo)scalar channels is emphasized.
Highlights
Hadronic V + A τ -decay is expected to provide the most accurate determination of αs once its value obtained at the τ -mass is runned until the Z-mass [1,2,3,4,5]
ΑsG2 is better determined from QCD spectral sum rules (QSSR) [7,8,24] than from τ -decay with the robust estimate in Eq (12)
In the V channel, τ -decay and e+e− sum rules lead to a value of the four–quark condensate ραs uu 2 in Eq (16) which violates the vacuum saturation estimate by a factor 3 [Eq (17)] and confirms previous QSSR results from different hadronic channels [7,8,9,10,17,18,19,20]
Summary
Hadronic V + A τ -decay is expected to provide the most accurate determination of αs once its value obtained at the τ -mass is runned until the Z-mass [1,2,3,4,5]. The extraction of αs, at this relatively low scale Mτ , can become feasible, as theoretically, the V + A channel is less sensitive to the QCD non-perturbative effects than the individual V and A channel (if one uses the OPEa la SVZ [6]) and to the values of the quark and gluon condensates obtained from an overall fit of the hadronic channels [6,7], e+e− [8,9,10,11,12] and τ -decay [13,14,15,16,17,18,19] data, light baryon sum rules [20], heavy quarkonia sum rules [6,21,22,23] and heavy-quarkonia mass-splittings [24].
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