Quark currents renormalization constants can in principle be safely computed in lattice perturbation theory. In practice, traditional lattice perturbative computations are quite cumbersome, so that so far only the first loop results were available. By making use of Numerical Stochastic Perturbation Theory we reached three (and with less statistical precision even four) loops, both in quenched and in unquenched theory. Convergence properties of the series can be assessed and comparison with non perturbative results (where available) can be made: high loops computations of renormalization constants can be a valuable tool for lattice QCD.
Dimensional reduction is a key issue in finite temperature field theory. For example, when following the QCD Free Energy from low to high scales across the critical temperature, ultrasoft degrees of freedom can be captured by a 3d SU(3) pure gauge theory. For such a theory a complete perturbative matching requires four loop computations, which we undertook by means of Numerical Stochastic Perturbation Theory. We report on the computation of the pure gauge plaquette in 3d, and in particular on the extraction of the logarithmic divergence at order g 8 , which had already been computed in the continuum.
We present technical details of fermionic observables computations in NSPT. In particular we discuss the construction of composite operators starting from the inverse Dirac operator building block, the subtraction of UV divergences and the treatment of irrelevant contributions in extracting the continuum limit.
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