Absence of even-integer ζ-function values in Euclidean physical quantities in QCD

At order alpha(4)(s) in perturbative quantum chromodynamics, even-integer zeta-function values are present in Euclidean physical correlation functions like the scalar quark correlation function or the scalar gluonium correlator. We demonstrate that these contributions cancel when the perturbative expansion is expressed in terms of the so-called C-scheme coupling (alpha) over cap (s) which has recently been introduced in Ref. [1]. It is furthermore conjectured that a zeta(4) term should arise in the Adler function at order alpha(5)(s) in the (MS) over bar -scheme, and that this term is expected to disappear in the C-scheme as well. (C1 2018 The Authors. Published by Elsevier B.V.