Three topics in renormalization and improvement
This chapter is a detailed presentation of three specific topics: (1) 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, through which we establish the normalization properties of lattice partially conserved currents and the relation between renormalized composite fields, like the scalar and pseudoscalar densities, which belong to the same chiral multiplet. We also discuss the consequences of the loss of chiral symetry for the chiral condensate. (2) The definition and properties of mass independent renormalization schemes, which are suitable for a non-perturbative computation of various operator renormalization constants. In particular we present in detail the RI/MOM scheme. (3) 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.
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