Four loop stochastic perturbation theory in 3d SU(3)

Abstract

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.

Non-perturbative plaquette in 3d pure SU(3)

“…This can be accomplished by a 4-loop matching computation, with the techniques discussed in ref. [11]. The full QCD pressure of order g 6 T 4 can be obtained by a further 4-loop matching computation.…”

“…We can, however, determine the non-perturbative input needed for it. In order to evaluate c ′ 4 a 4-loop lattice perturbation theory calculation is required; alternatively, it can be evaluated non-diagrammatically by means of numerical stochastic perturbation theory [11].…”

Plaquette expectation value and lattice free energy of three-dimensional SU(Nc) gauge theory

“…There are ultraviolet divergences up to 4-loop level only [7]. Terms required in the conversion have been determined up to 3-loop level [8,9]. Infrared divergences cause an additional complication in the 4-loop level.…”

Two and three loops computations of renormalization constants for lattice QCD

“…It has been shown to be very powerful in the quenched approximation, but the technique is quite general and can be in principle applied to any theory [2]. In particular, it can be generalized to actually carry on unquenched QCD calculations [3].…”

“…Numerical Stochastic Perturbation Theory (NSPT) is a numerical method [1] to perform Lattice Perturbation calculations. It has been shown to be very powerful in the quenched approximation, but the technique is quite general and can be in principle applied to any theory [2]. In particular, it can be generalized to actually carry on unquenched QCD calculations [3].…”