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Numerical Stochastic Perturbation Theory (NSPT) allows for perturbativecomputations in quantum field theory. We present an implementation of NSPT thatyields results for high orders in the perturbative expansion of lattice gaugetheories coupled to fermions. The zero-momentum mode is removed by imposingtwisted boundary conditions; in turn, twisted boundary conditions require us tointroduce a smell degree of freedom in order to include fermions in thefundamental representation. As a first application, we compute the criticalmass of two flavours of Wilson fermions up to order $O(\beta^{-7})$ in a${\mathrm{SU}}(3)$ gauge theory. We also implement, for the first time,staggered fermions in NSPT. The residual chiral symmetry of staggered fermionsprotects the theory from an additive mass renormalisation. We compute theperturbative expansion of the plaquette with two flavours of massless staggeredfermions up to order $O(\beta^{-35})$ in a ${\mathrm{SU}}(3)$ gauge theory, andinvestigate the renormalon behaviour of such series. We are able to subtractthe power divergence in the Operator Product Expansion (OPE) for the plaquetteand estimate the gluon condensate in massless QCD. Our results confirm thatNSPT provides a viable way to probe systematically the asymptotic behaviour ofperturbative series in QCD and, eventually, gauge theories with fermions inhigher representations.

Large-order NSPT for lattice gauge theories with fermions: the plaquette in massless QCD