Three Topics in Renormalization and Improvement

TL;DR

This paper discusses three specific topics in lattice QCD: chiral symmetry loss and recovery, mass independent renormalization schemes, and the twisted mass formulation for improved scaling and normalization.

Contribution

It provides an in-depth analysis of the consequences of chiral symmetry breaking, details on non-perturbative renormalization schemes, and introduces twisted mass QCD for better physical quantity scaling.

Findings

Chiral symmetry is lost in Wilson fermions but recovered in the continuum limit.

Mass independent renormalization schemes facilitate non-perturbative operator renormalization.

Twisted mass QCD improves normalization and scaling properties of physical observables.

Abstract

This is an expanded version of lecture notes, delivered at the XCIII Les Houches Summer School (August 2009). Our aim is to present three very specific topics: (i) The consequences of the loss of chiral symmetry in the Wilson lattice regularization of the fermionic action and its recovery in the continuum limit. The treatment of these arguments involves lattice Ward identities. (ii) The definition and properties of mass independent renormalization schemes, which are suitable for a non-perturbative computation of various operator renormalization constants. (iii) The modification of the Wilson fermion action, by the introduction of a chirally twisted mass term (known as twisted mass QCD - tmQCD), which results to improved (re)normalization and scaling properties for physical quantities of interest.