Decoupling of heavy quarks in the minimal subtraction scheme

Decoupling constant for α s and the effective gluon-Higgs coupling to three loops in supersymmetric QCD

“…This allows us to consider in Fig. 2(b) both the exact result for ζ (2) αs (solid line) and the approximations (dahed lines) based on the hierarchies (h1), (h2) and (h3). The latter are obtained from the (naive) averages over the various representations, i.e., the different choices of m R according to Eq.…”

“…Within QCD the beta function is known to four-loop accuracy [32,33], however, the supersymmetric analogue only to three loops [19,34,35]. 2 As a consequence for the four-loop curve in Fig. 4 we only use three-loop running above µ dec .…”

“…It is tightly connected to the construction of an effective theory containing only the light active degrees of freedom in the dynamical part of the Lagrange density. Within the framework of QCD decoupling constants for the strong coupling α s are known at two- [2][3][4], three [4] and even four-loop order [5,6]. Recently also the expression for the simultaneous decoupling of two heavy quarks has been computed at the three-loop level [7].…”

The determination of α s by the ALPHA collaboration

“…It has long been known how to connect these theories perturbatively [29,30] and we now have 4-loop precision [31,32] where m * = m MS (m * ) is the mass of the decoupled quark. Together with eq.…”

The Strong Coupling Constant

“…Measurements of α s obtained at different energy scales can be compared, either by evolving backwards to the point Λ where α s diverges, or by evolving to a common reference energy, which in recent years has become the Z mass. In the evolution [1] α s is continous at flavour thresholds, which, within the still comparatively large uncertainties of the quark masses, can be taken at the MS-running mass of the respective quark flavour. As an example consider the evolution of an α s -measurement with n f = 3 from the scale µ = m τ to µ = M Z .…”