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Scheme variations of the QCD coupling and hadronic $\tau$ decays
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abstract
The Quantum Chromodynamics (QCD) coupling, $\alpha_s$, is not a physical observable of the theory since it depends on conventions related to the renormalization procedure. We introduce a definition of the QCD coupling, denoted by $\hat\alpha_s$, whose running is explicitly renormalization scheme invariant. The scheme dependence of the new coupling $\hat\alpha_s$ is parameterized by a single parameter $C$, related to transformations of the QCD scale $\Lambda$. It is demonstrated that appropriate choices of $C$ can lead to substantial improvements in the perturbative prediction of physical observables. As phenomenological applications, we study $e^+e^-$ scattering and decays of the $\tau$ lepton into hadrons, both being governed by the QCD Adler function.
Forward citations
Cited by 3 Pith papers
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On divergences in a four-derivative scalar field theory
The renormalisation of a four-derivative scalar theory is computed to three loops, IR finiteness and non-renormalisation theorems are proven, and the perfect-square theory's beta function is shown to agree with O(2) p...
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Hadronic tau decays at higher orders in QCD
Sequence transformations applied to the fixed-order QCD series for hadronic tau decays produce estimates c5,1 = 298 ± 15, c6,1 = 3431 ± 256, c7,1 = 2.29 ± 0.29 × 10^4 and a predicted δ^(0)_FOPT = 0.2119 ± 0.0040.
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Higher-order perturbative coefficients in QCD from series acceleration by conformal mappings
The paper predicts the six-, seven-, and eight-loop Adler function coefficients in MS QCD as c5,1=287±40, c6,1=2948±208, c7,1=(1.89±0.75)×10^4 by reexpanding conformal-mapping accelerated Borel series.
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