High-order perturbative expansions in massless gauge theories with NSPT

Abstract

Abstract. We investigate the possibility of using numerical stochastic perturbation theory (NSPT) to probe high orders in the perturbative expansion of lattice gauge theories with massless Wilson fermions. Twisted boundary conditions are used to regularise the gauge zero-mode; the extension of these boundary conditions to include fermions in the fundamental representation requires to introduce a smell degree of freedom. Moreover, the mass of Wilson fermions is affected by an additive renormalisation: we study how to determine the mass counterterms consistently in finite volume. The knowledge of the critical masses will enable high-order perturbative computations in massless QCD, e.g. (as a first application) for the plaquette.

Bootstrap for Lattice Yang-Mills theory

“…Nowadays, most of the non-perturbative computations in Yang-Mills theory are done by Monte Carlo (MC) simulations for the lattice Polyakov-Wilson formulation of YM theory. Combined with the perturbation theory [1][2][3][4][5] and RG tools, MC methods have had a huge success, especially in a recent couple of decades, due to the developments of supercomputers. It allowed, for the first time, to compute with a reasonable precision certain masses of hadrons and the S-matrix elements in QCD, reproducing the experimental data [6,7].…”