Abstract
We review the current status of the determination of the strong coupling from tau decay. Using the most recent release of the ALEPH data, a very comprehensive phenomenological analysis has been performed, exploring all strategies previously considered in the literature and several complementary approaches. Once their actual uncertainties are properly assessed, the results from all adopted methodologies are in excellent agreement, leading to a very robust and reliable value of the strong coupling, \alpha_s^{(n_f=3)}(m_\tau^2) = 0.328\pm 0.013αs(nf=3)(mτ2)=0.328±0.013, which implies \alpha_s^{(n_f=5)}(M_Z^2) = 0.1197\pm 0.0015αs(nf=5)(MZ2)=0.1197±0.0015.
Highlights
The inclusive hadronic decay width of the τ lepton is a very clean observable to determine the strong coupling with high precision [1,2,3,4]
Using the analyticity properties of the correlators, this experimental information can be related with theoretical QCD predictions through moments of the type [4, 9]
For large-enough values of s0, this contour integral can be predicted as an expansion in inverse powers of s0, using the operator product expansion (OPE) of the current correlators: ΠJ(0+1)(s) OPE =
Summary
The inclusive hadronic decay width of the τ lepton is a very clean observable to determine the strong coupling with high precision [1,2,3,4]. The measured invariant-mass distribution of the final hadrons determines the spectral functions ρJ (s). For large-enough values of s0, this contour integral can be predicted as an expansion in inverse powers of s0, using the operator product expansion (OPE) of the current correlators: ΠJ(0+1)(s) OPE =. Differences between the physical values of the integrated moments AωJ (s0) and their OPE approximations are known as quark-hadron duality violations. They are very efficiently minimized by taking “pinched” weight functions which vanish at s = s0, suppressing in this way the contributions from the region near the real axis where the OPE is not valid [4, 9]
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