Lattice QCD with a chiral twist

Abstract

In these lectures I explain how chiral symmetry of continuum QCD naturally leads to a class of lattice regularisations known as twisted mass QCD (tmQCD). As compared to standard Wilson quarks, its advantages are the absence of unphysical zero modes, the possibility to circumvent lattice renormalisation problems and automatic O(a) improvement. On the other hand, the physical parity and flavour symmetries are explicitly broken. I discuss these aspects and then turn to the theory in a finite space-time volume with Schroedinger functional boundary conditions. Again, chiral transformations of the continuum theory may be used as a guide to formulate an alternative lattice regularisation of the Schrödinger functional, with interesting applications to renormalization problems in QCD.

40 pages, 7 figures; lectures presented at the School "Perspectives in Lattice Gauge Theories", Nara, Japan, October 31 - November 14, 2005, to appear in the proceedings

Cited by in corpus (15)

• High precision renormalization of the flavour non-singlet Noether currents in lattice QCD with Wilson quarks
• The running coupling of QCD with four flavors
• The chirally rotated Schrödinger functional with Wilson fermions and automatic O(a) improvement
• Phase Diagram of Dynamical Twisted Mass Wilson Fermions at Finite Isospin Chemical Potential
• Flavour symmetry restoration and kaon weak matrix elements in quenched twisted mass QCD
• How perturbative are heavy sea quarks?
• Determination of ${\alpha }_s(m_Z)$ by the non-perturbative decoupling method
• Past, present, and future of precision determinations of the QCD coupling from lattice QCD
• Logarithmic corrections to O($a$) and O($a^2$) effects in lattice QCD with Wilson or Ginsparg-Wilson quarks
• Varieties and properties of central-branch Wilson fermions
• Effect of r averaging on Chiral Anomaly in Lattice QCD with Wilson Fermion: Finite volume and cutoff effects
• One-loop lattice artifacts of a dynamical charm quark
• A tmQCD mixed-action approach to flavour physics
• Matching of $N_f=2+1$ CLS ensembles to a tmQCD valence sector
• Wilson chiral perturbation theory for dynamical twisted mass fermions vs lattice data - a case study