High-order perturbative expansions in massless gauge theories with NSPT

Luigi Del Debbio,Gianluca Filaci,Francesco Di Renzo,M Della Morte,P Fritzsch,C Pena Ruano,E Gámiz Sánchez

doi:10.1051/epjconf/201817511023

Luigi Del Debbio, Gianluca Filaci + Show 5 more

Open Access

https://doi.org/10.1051/epjconf/201817511023

Copy DOI

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.

Highlights

Numerical stochastic perturbation theory (NSPT) is a technique which allows to perform perturbative expansions numerically in a quantum theory
In particular, we are interested in applying NSPT to a S U(Nc) lattice gauge theory in four dimensions with massless Wilson fermions in the fundamental representation, see [1] for a review
An idea, proposed in [6], to overcome this problem is to introduce a new quantum number so that fermions exist in different copies, or smells, which transform into each other according to the antifundamental representation of S U(Nc)

Summary

Introduction

Numerical stochastic perturbation theory (NSPT) is a technique which allows to perform perturbative expansions numerically in a quantum (field) theory. In particular, we are interested in applying NSPT to a S U(Nc) lattice gauge theory in four dimensions with massless Wilson fermions in the fundamental representation, see [1] for a review. When sufficient high orders are reached, it is possible to study the divergent behaviour of a perturbative series: the pattern of divergence (e.g. renormalons) gives information on non-perturbative physics (e.g. power corrections in the OPE). There are wellestablished results in lattice gauge theories only for gluodynamics [2,3,4]. Fermions are a handle on the beta function, they affect the running of the coupling and should control and determine the high-order perturbative behaviour

Twisted boundary conditions and smell

Critical mass

Zero-momentum extrapolation and valence twist

Conclusion