Determination of $$\alpha _s(m_Z)$$ by the non-perturbative decoupling method

Abstract We present the details and first results of a new strategy for determination $$\alpha _s(m_Z)$$ α s ( m Z ) (ALPHA Collaboration et al. in Phys. Lett. B 807:135571, 2020). By simultaneously decoupling 3 fictitious heavy quarks we establish relation between $$\Lambda $$ Λ -parameters three-flavor QCD pure gauge theory. Very precise recent theory (Dalla Brida Ramos Eur. J. C 79(8):720, 2019; Nada Eur Phys J 81(1):1, 2021) can thus be leveraged to obtain three-flavour -parameter units common scale. Connecting this scale hadronic physics 3-flavour leads our result physical units, ^{(3)}_{\overline{\textrm{MS}}} = 336(12)\, {\textrm{MeV}}$$ MS ¯ 3 = 336 12 MeV , which translates _s(m_Z) 0.11823(84)$$ 0.11823 84 . This is compatible with both FLAG average (Aoki review 2021. arXiv:2111.09849 [hep-lat]) previous ALPHA al., Rev. 119(10):102001, 2017), comparable, yet still statistics dominated, error. constitutes highly non-trivial check, as conceptually very different from step-scaling method, so are their systematic errors. These include uncertainties combined continuum limits, discuss some detail. also quantify correlation results, due elements, such definition energy where apply decoupling.