Lattice QCD with a chirally twisted mass term
Roberto Frezzotti, Pietro Antonio Grassi, Stefan Sint, Peter Weisz
TL;DR
The paper introduces twisted mass QCD (tmQCD) with Wilson quarks as an effective regularization that avoids unphysical zero modes and establishes a precise mapping between tmQCD and standard QCD through axial rotations. By employing Ginsparg-Wilson quarks, it derives exact bare relations and shows how renormalized correlators can be related under suitable renormalization schemes, with an analytic differential equation in the rotation angle $\alpha$ guiding the connection. It demonstrates that renormalized tmQCD Ward identities reproduce standard QCD Ward identities for appropriate linear combinations of correlators, and provides practical recipes to define the angle $\alpha$ and to choose renormalization conditions that simplify operator renormalization, including applications to the $\Delta S=2$ sector. The work argues that tmQCD offers computational and conceptual advantages, such as reduced renormalization complexity at $\alpha=\pi/2$, while noting lattice artifacts at finite spacing and the need for careful treatment of the continuum limit; the framework opens avenues for improved simulations and extensions to heavier flavors.
Abstract
Lattice QCD with Wilson quarks and a chirally twisted mass term represents a promising alternative regularization of QCD, which does not suffer from unphysical fermion zero modes. We show how the correlation functions of the renormalized theory are related to the theory with a standard parameterization of the mass term. In particular we discuss the conditions under which these relations take the same form as obtained from naive continuum considerations. We discuss in detail some applications and comment on potential benefits and problems of this framework.