A non-perturbative exploration of the high energy regime in N f = 3 QCD

Using continuum extrapolated lattice data we traceafamilyofrunningcouplingsinthree-flavourQCDover a large range of scales from about 4 to 128 GeV. The scale is set by the finite space time volume so that recursive finite size techniques can be applied, and Schrödinger functional (SF) boundary conditions enable direct simulations in the chiral limit. Compared to earlier studies we have improved on both statistical and systematic errors. Using the SF coupling to implicitly define a reference scale 1 / L 0 ≈ 4 GeV through ¯ g 2 ( L 0 ) = 2 . 012, we quote L 0 (cid:2) N f = 3 MS = 0 . 0791 ( 21 ) . This error is dominated by statistics; in particular, the remnant perturbative uncertainty is negligible and very well controlled, by connecting to infinite L , estimate of the requires g we We details and an extended

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