The strong coupling from a nonperturbative determination of the $\Lambda$ parameter in three-flavor QCD

Abstract

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 ${\Lambda }_{\overline{\mathrm{MS}}}^{(3)}=341(12)$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 ${\Lambda }_{\overline{\mathrm{MS}}}^{(5)}/{\Lambda }_{\overline{\mathrm{MS}}}^{(3)}$ yields ${\alpha }_{\overline{\mathrm{MS}}}^{(5)}(m_{\mathrm{Z}})=0.11852(84)$.

Correction in the comparison to the LHC value for alpha(1.5TeV) which was given by CMS in the 5-flavor theory. The agreement is improved. Also 1 Reference added and a few typos corrected

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