Twenty-first Century Lattice Gauge Theory: Results from the QCD Lagrangian

Abstract

Quantum chromodynamics (QCD) reduces the strong interactions, in all their variety, to a simple nonabelian gauge theory. It clearly and elegantly explains hadrons at short distances, which has led to its universal acceptance. Since its advent, however, many of its long-distance, emergent properties have been believed to be true, without having been demonstrated to be true. This paper reviews a variety of results in this regime that have been established with lattice gauge theory, directly from the QCD Lagrangian. This body of work sheds light on the origin of hadron masses, its interplay with dynamical symmetry breaking, as well as on other intriguing features such as the phase structure of QCD. In addition, nonperturbative QCD is quantitatively important to many aspects of particle physics (especially the quark flavor sector), nuclear physics, and astrophysics. This review also surveys some of the most interesting connections to those subjects.

arXiv commentinvited review for Annual Reviews of Nuclear and Particle Science (2012); 21 pp., 4 tables, 6 figures. v2: Figures 2 and 5 updated; references added; many minor wording changes and clarifications; conforms closely to accepted version

References in corpus (102)

• Parton distributions for the LHC
• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• The chiral and deconfinement aspects of the QCD transition
• The glueball spectrum from an anisotropic lattice study
• On the Viability of Lattice Perturbation Theory
• Ab-initio Determination of Light Hadron Masses
• Equation of state and QCD transition at finite temperature
• The Schrödinger Functional - a Renormalizable Probe for Non-Abelian Gauge Theories
• Hadronic Z- and tau-Decays in Order alpha_s^4
• 2+1 Flavor Lattice QCD toward the Physical Point
• Full nonperturbative QCD simulations with 2+1 flavors of improved staggered quarks
• Review of lattice results concerning low energy particle physics
• Excited state baryon spectroscopy from lattice QCD
• The 2009 World Average of ${\alpha }_s$
• Weak transition matrix elements from finite-volume correlation functions
• Light hadrons with improved staggered quarks: approaching the continuum limit
• Quark confinement and the bosonic string
• High Precision determination of the pi, K, D and D_s decay constants from lattice QCD
• High-Precision c and b Masses, and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD
• Bound H-dibaryon in Flavor SU(3) Limit of Lattice QCD
• Fine Structure of the QCD String Spectrum
• Probing Novel Scalar and Tensor Interactions from (Ultra)Cold Neutrons to the LHC
• Charm and Bottom Quark Masses: an Update
• Nucleon structure from mixed action calculations using 2+1 flavors of asqtad sea and domain wall valence fermions
• Chiral expansion of baryon masses and $\sigma$-terms
• Evidence for a Bound H-dibaryon from Lattice QCD
• Numerical Evidence for the Observation of a Scalar Glueball
• Octet baryon masses and sigma terms from an SU(3) chiral extrapolation
• The Upsilon spectrum and m_b from full lattice QCD
• Update: Precision D_s decay constant from full lattice QCD using very fine lattices
• Lattice QCD inputs to the CKM unitarity triangle analysis
• Neutral B Meson Mixing in Unquenched Lattice QCD
• Physical Results from Unphysical Simulations
• B Meson Semileptonic Form Factors from Unquenched Lattice QCD
• Isoscalar meson spectroscopy from lattice QCD
• Semileptonic decays of $D$ mesons in three-flavor lattice QCD
• Possible Indications of New Physics in Bd-mixing and in sin(2 beta) Determinations
• The Deuteron and Exotic Two-Body Bound States from Lattice QCD
• Flavour blindness and patterns of flavour symmetry breaking in lattice simulations of up, down and strange quarks
• Charmed meson decay constants in three-flavor lattice QCD
• Lattice QCD at the physical point: light quark masses
• Nucleon sigma term and strange quark content from lattice QCD with exact chiral symmetry
• The Upsilon spectrum and the determination of the lattice spacing from lattice QCD including charm quarks in the sea
• Study of B --> pi l nu and B --> rho l nu Decays and Determination of |V_ub|
• High-Precision Charm-Quark Mass and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD
• The Two Higgs Doublet of Type II facing flavour physics data
• Hyperon-Nucleon Scattering from Fully-Dynamical Lattice QCD
• Electromagnetic mass splittings of the low lying hadrons and quark masses from 2+1 flavor lattice QCD+QED
• The B -> pi l nu semileptonic form factor from three-flavor lattice QCD: A model-independent determination of |V(ub)|
• The chiral critical point of Nf=3 QCD at finite density to the order (mu/T)^4
• Sigma term and strangeness content of octet baryons
• Observation of the Decay $B_c^{\pm }\to J/\psi {\pi }^{\pm }$ and Measurement of the $B_c^{\pm }$ Mass
• Measurement of the decay $B^0\to {\pi }^{-}{\ell }^{+}\nu$ and determination of $|V_{ub}|$
• QCD Thermodynamics from the Lattice
• Effects of right-handed charged currents on the determinations of |V_ub| and |V_cb|
• Accumulating evidence for nonstandard leptonic decays of D_s mesons
• $D\to K,l\nu$ Semileptonic Decay Scalar Form Factor and $|V_{cs}|$ from Lattice QCD
• The strange quark condensate in the nucleon in 2+1 flavor QCD
• Precision computation of the kaon bag parameter
• Four-loop moments of the heavy quark vacuum polarization function in perturbative QCD
• Precise charm to strange mass ratio and light quark masses from full lattice QCD
• Testing non-perturbative strong interaction effects via the Adler function
• Nucleon isovector structure functions in (2+1)-flavor QCD with domain wall fermions
• Accurate Determinations of ${\alpha }_s$ from Realistic Lattice QCD
• Mass of the B_c Meson in Three-Flavor Lattice QCD
• The $K\to (\pi \pi {)}_{I=2}$ Decay Amplitude from Lattice QCD
• Evidence for the exclusive decay Bc+- to J/psi pi+- and measurement of the mass of the Bc meson
• The $\eta$ and ${\eta }^{\prime }$ mesons from Lattice QCD
• The B -> D* l nu form factor at zero recoil from three-flavor lattice QCD: A model independent determination of |V_cb|
• Quarkonium mass splittings in three-flavor lattice QCD
• Hyperon sigma terms for 2+1 quark flavours
• Building the International Lattice Data Grid
• Continuum Limit of $B_K$ from 2+1 Flavor Domain Wall QCD
• Update: Accurate Determinations of alpha_s from Realistic Lattice QCD
• Precise B, B_s and B_c meson spectroscopy from full lattice QCD
• Excited State Nucleon Spectrum with Two Flavors of Dynamical Fermions
• D and D_s meson spectroscopy
• $D\to \pi ,l\nu$ Semileptonic Decays, $|V_{cd}|$ and 2${}^{nd}$ Row Unitarity from Lattice QCD
• Charm quark system at the physical point of 2+1 flavor lattice QCD
• The ratio FK/Fpi in QCD
• The neutral kaon mixing parameter B_K from unquenched mixed-action lattice QCD
• The Realistic Lattice Determination of alpha_s(M_Z) Revisited
• A Prediction of the B*_c mass in full lattice QCD
• The Origins of Lattice Gauge Theory
• Meson-Baryon Scattering Lengths from Mixed-Action Lattice QCD
• Nucleon strange quark content from two-flavor lattice QCD with exact chiral symmetry
• Glueball mass measurements from improved staggered fermion simulations
• $K$ to $\pi \pi$ Decay amplitudes from Lattice QCD
• Quark condensate in two-flavor QCD
• K->pi form factors with reduced model dependence
• Determination of the chiral condensate from QCD Dirac spectrum on the lattice
• Tuning Fermilab Heavy Quarks in 2+1 Flavor Lattice QCD with Application to Hyperfine Splittings
• K -> pion Semileptonic Form Factors from Two-Flavor Lattice QCD
• Lower Higgs boson mass bounds from a chirally invariant lattice Higgs-Yukawa model with overlap fermions
• Determination of the chiral condensate from 2+1-flavor lattice QCD
• The phase diagram of quantum chromodynamics
• Effect of H^\pm on B^\pm\to τ^\pmν_τand D^\pm_s\to μ^\pmν_μ,τ^\pmν_τ
• The bottomonium spectrum from lattice QCD with 2+1 flavors of domain wall fermions
• Staggered fermions, zero modes, and flavor-singlet mesons
• Update on the Direct Detection of Dark Matter in MSSM Models with Non-Universal Higgs Masses
• Determination of the renormalized heavy-quark mass in Lattice QCD
• QCD String formation and the Casimir Energy

Cited by in corpus (53)

• Non-Standard Heavy Mesons and Baryons, an Experimental Review
• QCD and strongly coupled gauge theories: challenges and perspectives
• Simulating Lattice Gauge Theories within Quantum Technologies
• Nuclear effective field theory: status and perspectives
• NuSTEC White Paper: Status and Challenges of Neutrino-Nucleus Scattering
• SU(N) gauge theories at large N
• The Status of Glueballs
• 50 Years of Quantum Chromodynamics
• Accurate evaluation of hadronic uncertainties in spin-independent WIMP-nucleon scattering: Disentangling two- and three-flavor effects
• Loop, String, and Hadron Dynamics in SU(2) Hamiltonian Lattice Gauge Theories
• Viability of carbon-based life as a function of the light quark mass
• SU(2) lattice gauge theory on a quantum annealer
• Varying the light quark mass: impact on the nuclear force and Big Bang nucleosynthesis
• Mesons in large-N QCD
• Improved predictions for $\mu \to e$ conversion in nuclei and Higgs-induced lepton flavor violation
• Digitizing Gauge Fields: Lattice Monte Carlo Results for Future Quantum Computers
• Two-Baryon Systems with Twisted Boundary Conditions
• Light stops, blind spots, and isospin violation in the MSSM
• Light-Meson Spectroscopy with COMPASS
• $B\to \pi \ell \ell$ form factors for new-physics searches from lattice QCD
• Framework for simulating gauge theories with dipolar spin systems
• α_S from $F_{\pi }$ and Renormalization Group Optimized Perturbation
• Searching for the rules that govern hadron construction
• Introduction to Big Bang Nucleosynthesis and Modern Cosmology
• Binary neutron star mergers as a probe of quark-hadron crossover equations of state
• Recent Results in Bottomonium
• Leptonic decay-constant ratio f_{K^+}/f_{pi^+} from lattice QCD with physical light quarks
• Digital quantum simulation of a (1+1)D SU(2) lattice gauge theory with ion qudits
• Lattice QCD Calculation of the Pion Mass Splitting
• Oklo reactors and implications for nuclear science
• Probing hadronization with flavor correlations of leading particles in jets
• Generalized linear sigma model with two glueballs
• The QCD Running Coupling and its Measurement
• Spinless mesons and glueballs mixing patterns in SU(3) flavor limit
• Lattice regularisation and entanglement structure of the Gross-Neveu model
• Ken Wilson: Solving the Strong Interactions
• Quark and glue spectroscopy of scalars and pseudoscalars in SU(3) flavor limit
• Critical exponents and transport properties near the QCD critical endpoint from the statistical bootstrap model
• Nuclear Physics from Lattice Quantum Chromodynamics
• Effective scalar four-fermion interaction for Ge-phobic exothermic dark matter and the CDMS-II Silicon excess
• Equation of state for hyperonic neutron-star matter in SU(3) flavor symmetry
• Review of Neutral Naturalness
• Quark Flavor Physics Review
• Neutron Star Mergers and the Quark Matter Equation of State
• Thermodynamic potential for quark-gluon plasma with finite quark masses and chemical potential
• Multiquark States in the Thomas-Fermi Quark Model and on the Lattice
• Recent progress on hadron spectroscopy from lattice QCD
• Emergence of the $\pi (1300)$ Resonance from Lattice QCD
• Theoretical Perspective of Charm Physics
• Updates of the nuclear equation of state for core-collapse supernovae and neutron Stars: effects of 3-body forces, QCD, and magnetic fields
• Nuclear Forces from Lattice Quantum Chromodynamics
• Non-Abelian basis tensor gauge theory
• 't Hooft model in the temporal gauge