Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Precision physics with QCD   The four-loop determination of the strong coupling from fully inclusive
observables is reviewed. Special attention is given to the low-energy
measurement extracted from the hadronic $\tau$ decay width. A recent exhaustive
analysis of the ALEPH data, exploring several complementary methodologies with
very different sensitivities to inverse power corrections and duality
violations, confirms the strong suppression of non-perturbative contributions
to $R_\tau$. It gives the value $\alpha_s(m_\tau^2)= 0.328 \pm 0.013$, which
implies $\alpha_s(M_Z^2)= 0.1197 \pm 0.0015$. The excellent agreement with the
direct measurement at the $Z$ peak, $\alpha_s(M_Z^2)= 0.1196 \pm 0.0030$,
provides a beautiful test of asymptotic freedom. Together with the most recent
lattice average from FLAG and the NNLO determinations from $e^+e^-$, PDFs and
collider data quoted by the PDG, these two inclusive determinations imply a
world average value $\alpha_s(M_Z^2)= 0.1180 \pm 0.0010$.

28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga