Wilson-like fermions and the static B_B parameter with no chirality breaking mixings

TL;DR

This paper extends a chirally improved Wilson fermion method to static-light systems, enabling cleaner calculations of the B_B parameter by avoiding operator mixing issues, with a simplified renormalization pattern similar to Ginsparg-Wilson fermions.

Contribution

It introduces a novel extension of a chirally improved Wilson fermion approach to static-light systems, simplifying the renormalization process for B_B parameter calculations.

Findings

Achieves operator mixing exclusion in static-light systems.

Provides a simplified renormalization pattern akin to Ginsparg-Wilson fermions.

Extends the method to static approximation for B_B parameter computation.

Abstract

I consider the recent proposal by R. Frezzotti and G. Rossi to chirally improve Wilson fermions in such a way that mixings among operators of different chirality can be excluded. The method, which is based on the use of twisted mass QCD with several replica of valence quarks, is extended here to static-light systems. The operators relevant for the computation of the B_B parameter (in the static approximation) are discussed. In this case the same renormalization pattern as for Ginsparg-Wilson fermions is obtained by a simple modification of the discretization of the action for valence quarks.