Applications of Chiral Perturbation theory to lattice QCD

Abstract

These lectures describe the use of effective field theories to extrapolate results from the parameter region where numerical simulations of lattice QCD are possible to the physical parameters (physical quark masses, infinite volume, vanishing lattice spacing, etc.). After a brief introduction and overview, I discuss three topics: 1) Chiral perturbation theory in the continuum; 2) The inclusion of discretization effects into chiral perturbation theory, focusing on the application to Wilson and twisted-mass lattice fermions; 3) Extending chiral perturbation theory to describe partially quenched QCD.

arXiv comment86 pages, 48 figures. Lectures given at ILFTN Workshop on "Perspectives in Lattice QCD", Nara, Japan, Oct 31-Nov 11 2005; typos corrected and references updated

References in corpus (56)

• Chiral perturbation theory
• Chiral symmetry and O(a) improvement in lattice QCD
• On the Foundations of Chiral Perturbation Theory
• Chiral Perturbation Theory for the Quenched Approximation of QCD
• Light pseudoscalar decay constants, quark masses, and low energy constants from three-flavor lattice QCD
• Quenched Chiral Logarithms
• Spontaneous Flavor and Parity Breaking with Wilson Fermions
• Partially Quenched Gauge Theories and a Application to Staggered Fermions
• Non-perturbative renormalization of lattice QCD at all scales
• Finite volume effects for meson masses and decay constants
• The Low Energy $\pi \pi$ Amplitude to One and Two Loops
• The Microscopic Spectral Density of the QCD Dirac Operator
• Twisted-mass lattice QCD with mass non-degenerate quarks
• Chiral Perturbation Theory Beyond One Loop
• Enhanced chiral logarithms in partially quenched QCD
• The quark condensate from K_{e_4} decays
• Non-perturbative Heavy Quark Effective Theory
• Improved bilinears in lattice QCD with non-degenerate quarks
• Partially Quenched Chiral Perturbation Theory and the Replica Method
• Staggered Chiral Perturbation Theory and the Fourth-Root Trick
• Simulations with different lattice Dirac operators for valence and sea quarks
• Chiral Logs in the Presence of Staggered Flavor Symmetry Breaking
• Observations on staggered fermions at non-zero lattice spacing
• Pion mass splitting and phase structure in Twisted Mass QCD
• Chiral Loops and Ghost States in the Quenched Scalar Propagator
• Scalar meson in dynamical and partially quenched two-flavor QCD: lattice results and chiral loops
• Electromagnetic and spin polarisabilities in lattice QCD
• Chiral perturbation theory with Wilson-type fermions including $a^2$ effects: $N_f=2$ degenerate case
• The phase structure of lattice QCD with two flavours of Wilson quarks and renormalization group improved gluons
• Spontaneous violation of CP symmetry in the strong interactions
• Finite-volume two-pion energies and scattering in the quenched approximation
• Quenched Scaling of Wilson twisted mass fermions
• Spectrum of quenched twisted mass lattice QCD at maximal twist
• Flavour Breaking Effects of Wilson twisted mass fermions
• Three-Flavor Partially Quenched Chiral Perturbation Theory at NNLO for Meson Masses and Decay Constants
• Lattice Spacing Dependence of the First Order Phase Transition for Dynamical Twisted Mass Fermions
• Observations on discretization errors in twisted-mass lattice QCD
• Light quarks with twisted mass fermions
• Discretization errors in the spectrum of the Hermitian Wilson-Dirac operator
• Partially Quenched Chiral Condensates from the Replica Method
• Effective theory for quenched lattice QCD and the Aoki phase
• Chiral perturbation theory at non-zero lattice spacing
• Unphysical Operators in Partially Quenched QCD
• Numerical simulations with two flavours of twisted-mass Wilson quarks and DBW2 gauge action
• Exploring twisted mass Lattice QCD with the Clover term
• Nucleon and Delta masses in twisted mass chiral perturbation theory
• Automatic O(a) improvement for twisted-mass QCD in the presence of spontaneous symmetry breaking
• Pseudo scalar meson masses in Wilson Chiral Perturbation Theory for 2+1 flavors
• Introduction to Chiral Perturbation Theory
• Chiral Meson Physics at Two Loops
• Predictions from Lattice QCD
• Dynamical twisted mass fermions
• Quenched penguins and the Delta I=1/2 rule
• The eta mass and NNLO Three-Flavor Partially Quenched Chiral Perturbation Theory
• Twisted mass fermions: neutral pion masses from disconnected contributions
• Determining the low energy parameters of Wilson Chiral Perturbation Theory

Cited by in corpus (14)

• FLAG Review 2019
• Full nonperturbative QCD simulations with 2+1 flavors of improved staggered quarks
• Inverse magnetic catalysis and the Polyakov loop
• Rooted staggered fermions: good, bad or ugly?
• Phase structure of thermal lattice QCD with N_f=2 twisted mass Wilson fermions
• Chiral behavior of the B(s,d)-Bbar(s,d) mixing amplitude in the Standard Model and beyond
• Two-loop Sunset Integrals at Finite Volume
• Connected and Disconnected Contractions in Pion-Pion Scattering
• Vector and Axial Currents in Wilson Chiral Perturbation Theory
• Scaling test of two-flavor O(a)-improved lattice QCD
• Exotic open and hidden charm states
• The finite-temperature phase structure of lattice QCD with twisted-mass Wilson fermions
• Chiral perturbation theory for three-flavour lattice QCD with isospin splitting
• Extracting the low-energy constant $L_0^r$ at three flavors from pion-kaon scattering