The pressure of QCD admits at high temperatures a factorization into purely perturbative contributions from “hard” thermal momenta, and slowly convergent as well as non-perturbative contributions from “soft” thermal momenta. The latter can be related to various eﬀective gluon condensates in a dimensionally reduced eﬀective ﬁeld theory, and measured there through lattice simulations. Practical measurements of one of the relevant condensates have suﬀered, however, from diﬃculties in extrapolating convincingly to the continuum limit. In order to gain insight on this problem, we employ Numerical Stochastic Perturbation Theory to estimate the problematic condensate up to 4-loop order in lattice perturbation theory. Our results seem to conﬁrm the presence of “large” discretization eﬀects, going like a ln(1/a), where a is the lattice spacing. For deﬁnite conclusions, however, it would be helpful to repeat the corresponding part of our study with standard lattice perturbation theory techniques.
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