Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The strong coupling from a nonperturbative determination of the
  $\Lambda$ parameter in three-flavor QCD   We present a lattice determination of the $\Lambda$ parameter in three-flavor
QCD and the strong coupling at the Z pole mass. Computing the nonperturbative
running of the coupling in the range from $0.2\,$GeV to $70\,$GeV, and using
experimental input values for the masses and decay constants of the pion and
the kaon, we obtain $\Lambda_{\overline{\rm MS}}^{(3)}=341(12)\,$MeV. The
nonperturbative running up to very high energies guarantees that systematic
effects associated with perturbation theory are well under control. Using the
four-loop prediction for $\Lambda_{\overline{\rm
MS}}^{(5)}/\Lambda_{\overline{\rm MS}}^{(3)}$ yields
$\alpha^{(5)}_{\overline{\rm MS}}(m_{\rm Z}) = 0.11852(84)$.

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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
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The categories of this paper are: stat
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int