Renormalization-group analysis of the validity of staggered-fermion QCD with the fourth-root recipe

Abstract

I develop a renormalization-group blocking framework for lattice QCD with staggered fermions. Under plausible, and testable, assumptions, I then argue that the fourth-root recipe used in numerical simulations is valid in the continuum limit. The taste-symmetry violating terms, which give rise to non-local effects in the fourth-root theory when the lattice spacing is non-zero, vanish in the continuum limit. A key role is played by reweighted theories that are local and renormalizable on the one hand, and that approximate the fourth-root theory better and better as the continuum limit is approached on the other hand.

arXiv commentMinor corrections. Revtex, 58 pages

References in corpus (51)

• Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation
• The Schrödinger Functional - a Renormalizable Probe for Non-Abelian Gauge Theories
• Locality properties of Neuberger's lattice Dirac operator
• High-Precision Lattice QCD Confronts Experiment
• A Precise Determination of the Running Coupling in the SU(3) Yang-Mills Theory
• Non-perturbative quark mass renormalization in quenched lattice QCD
• Light pseudoscalar decay constants, quark masses, and low energy constants from three-flavor lattice QCD
• On the Schroedinger functional in QCD
• Partially Quenched Gauge Theories and a Application to Staggered Fermions
• Flavor-Symmetry Restoration and Symanzik Improvement for Staggered Quarks
• Pion and Kaon masses in Staggered Chiral Perturbation Theory
• Partial Flavor Symmetry Restoration for Chiral Staggered Fermions
• Semileptonic decays of $D$ mesons in three-flavor lattice QCD
• Charmed meson decay constants in three-flavor lattice QCD
• Pseudoscalar Decay Constants in Staggered Chiral Perturbation Theory
• Staggered eigenvalue mimicry
• First determination of the strange and light quark masses from full lattice QCD
• One-loop renormalization of the QCD Schrödinger functional
• Partially Quenched Chiral Perturbation Theory and the Replica Method
• Accurate Determinations of ${\alpha }_s$ from Realistic Lattice QCD
• Staggered Chiral Perturbation Theory and the Fourth-Root Trick
• Scaling tests with dynamical overlap and rooted staggered fermions
• Chiral Logs in the Presence of Staggered Flavor Symmetry Breaking
• The Index Theorem and Universality Properties of the Low-lying Eigenvalues of Improved Staggered Quarks
• Observations on staggered fermions at non-zero lattice spacing
• Localization in Lattice QCD
• High-precision determination of the light-quark masses from realistic lattice QCD
• Staggered versus overlap fermions: a study in the Schwinger model with $N_f=0,1,2$
• Effects of staggered fermions and mixed actions on the scalar correlator
• Perturbative Improvement for Lattice QCD: An Update
• Locality of the fourth root of the Staggered-fermion determinant: renormalization-group approach
• Actions for dynamical fermion simulations: are we ready to go?
• Breakdown of staggered fermions at nonzero chemical potential
• Lattice fermions with complex mass
• $B_K$ Using Staggered Fermions: An Update
• The running quark mass in the SF scheme and its two-loop anomalous dimension
• On the fourth root prescription for dynamical staggered fermions
• Localization properties of lattice fermions with plaquette and improved gauge actions
• Algorithms for Lattice QCD with Dynamical Fermions
• Order of the Chiral and Continuum Limits in Staggered Chiral Perturbation Theory
• Mobility edge in lattice QCD
• Validity of the Rooted Staggered Determinant in the continuum limit
• Perfect Lattice Actions for Staggered Fermions
• Improvement of the Staggered Fermion Operators
• Improving the staggered quark action to reduce flavour symmetry violations
• Lattice QCD at the end of 2003
• Lattice Regularization and Symmetries
• The Schrödinger functional running coupling with staggered fermions
• Localization in lattice QCD (with emphasis on practical implications)
• Fixed Point Actions for Lattice Fermions
• The continuum limit of the quark mass step scaling function in quenched lattice QCD

Cited by in corpus (62)

• FLAG Review 2019
• Full nonperturbative QCD simulations with 2+1 flavors of improved staggered quarks
• Lattice QCD ensembles with four flavors of highly improved staggered quarks
• $B$- and $D$-meson leptonic decay constants from four-flavor lattice QCD
• Flavor Physics in the Quark Sector
• B- and D-meson decay constants from three-flavor lattice QCD
• Neutral B Meson Mixing in Unquenched Lattice QCD
• Light hadron spectroscopy using domain wall valence quarks on an Asqtad sea
• $B_{(s)}^0$-mixing matrix elements from lattice QCD for the Standard Model and beyond
• Nuclear Physics from Lattice QCD
• Light Hadron Masses from Lattice QCD
• Charmed and light pseudoscalar meson decay constants from four-flavor lattice QCD with physical light quarks
• Lattice QCD at non-zero temperature
• Update of $|V_{cb}|$ from the $\bar{B}\to D^{\ast }\ell \bar{\nu }$ form factor at zero recoil with three-flavor lattice QCD
• $B\to K{l}^{+}{l}^{-}$ decay form factors from three-flavor lattice QCD
• Multi-Pion States in Lattice QCD and the Charged-Pion Condensate
• The B -> pi l nu semileptonic form factor from three-flavor lattice QCD: A model-independent determination of |V(ub)|
• Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD
• Precise Determination of the I=2 pipi Scattering Length from Mixed-Action Lattice QCD
• Calculating the hadronic vacuum polarization and leading hadronic contribution to the muon anomalous magnetic moment with improved staggered quarks
• The B -> D* l nu form factor at zero recoil from three-flavor lattice QCD: A model independent determination of |V_cb|
• Semileptonic form factors for $B\to D^{\ast }\ell \nu$ at nonzero recoil from 2 + 1-flavor lattice QCD
• Scalar Meson Spectroscopy with Lattice Staggered Fermions
• The neutral kaon mixing parameter B_K from unquenched mixed-action lattice QCD
• Lattice QCD and the anomalous magnetic moment of the muon
• The K+K+ Scattering Length from Lattice QCD
• Meson-Baryon Scattering Lengths from Mixed-Action Lattice QCD
• f_K/f_pi in Full QCD with Domain Wall Valence Quarks
• $B_K$ using HYP-smeared staggered fermions in $N_f=2+1$ unquenched QCD
• Comment on "Chiral anomalies and rooted staggered fermions"
• Effective field theories for QCD with rooted staggered fermions
• QCD thermodynamics with 2+1 flavors at nonzero chemical potential
• Tuning Fermilab Heavy Quarks in 2+1 Flavor Lattice QCD with Application to Hyperfine Splittings
• Determination of $|V_{us}|$ from a lattice-QCD calculation of the $K\to \pi \ell \nu$ semileptonic form factor with physical quark masses
• Heavy-Light Semileptonic Decays in Staggered Chiral Perturbation Theory
• Hadronic Interactions from Lattice QCD
• Lattice computation of the electromagnetic contributions to kaon and pion masses
• Mixed Meson Masses with Domain-Wall Valence and Staggered Sea Fermions
• 't Hooft vertices, partial quenching, and rooted staggered QCD
• Kaon semileptonic vector form factor and determination of |V_{us}| using staggered fermions
• Staggered fermions, zero modes, and flavor-singlet mesons
• Neutral B-meson mixing from three-flavor lattice QCD: Determination of the SU(3)-breaking ratio ξ
• Rooted staggered fermions: good, bad or ugly?
• Leptonic decay-constant ratio f_{K^+}/f_{pi^+} from lattice QCD with physical light quarks
• Möbius domain-wall fermions on gradient-flowed dynamical HISQ ensembles
• Physics of eta-prime with rooted staggered quarks
• Quark Hadron Duality at Finite Temperature
• The rooting issue for a lattice fermion formulation similar to staggered fermions but without taste mixing
• Chiral Perturbation Theory for All-Staggered Heavy-Light Mesons
• Staggered Baryon Operators with Flavor SU(3) Quantum Numbers
• One-loop matching of improved four-fermion staggered operators with an improved gluon action
• Neutral B Mixing in Staggered Chiral Perturbation Theory
• Staggered Heavy Baryon Chiral Perturbation Theory
• Semileptonic Kaon Decay in Staggered Chiral Perturbation Theory
• Brief Review of Saturation Physics
• Staggered chiral perturbation theory in the two-flavor case
• Two Lectures on QCD at Short Distances: Jets and Factorization
• Quark Confinement and the Renormalization Group
• Impossibility of spontaneous vector flavor symmetry breaking on the lattice
• A 0-dimensional counter-example to rooting?
• The rooted staggered determinant in the Schwinger model
• Strong-Isospin Breaking in the Neutron-Proton Mass Difference