Review of lattice results concerning low energy particle physics

Abstract

We review lattice results relevant for pion and kaon physics with the aim of making them easily accessible to the particle physics community. Specifically, we review the determination of the light-quark masses, the form factor f_+(0), relevant for the semileptonic K -> pi transition at zero momentum transfer as well as the ratio f_K/f_pi of decay constants and discuss the consequences for the elements V_{us} and V_{ud} of the CKM matrix. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU(2)_LxSU(2)_R and SU(3)_LxSU(3)_R Chiral Perturbation Theory and review the determination of the B_K parameter of neutral kaon mixing. We introduce quality criteria and use these when forming averages. Although subjective and imperfect, these criteria may help the reader to judge different aspects of current lattice computations. Our main results are summarized in section 1.2, but we stress the importance of the detailed discussion that underlies these results and constitutes the bulk of the present review.

126 pages, 11 figures. Plain Latex. Review provided by the FLAG (Flavianet Lattice Averaging Group) working group. Updated to February 28, 2011. To appear in EPJ

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• High Precision determination of the pi, K, D and D_s decay constants from lattice QCD
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• Light hadrons from lattice QCD with light (u,d), strange and charm dynamical quarks
• An improved calculation of the isospin-symmetry-breaking corrections to superallowed Fermi beta decay
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• Lattice QCD at the physical point: Simulation and analysis details
• alpha_s and the tau hadronic width: fixed-order, contour-improved and higher-order perturbation theory
• Lattice QCD at the physical point: light quark masses
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• High-Precision Charm-Quark Mass and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD
• Epsilon_K at Next-to-Next-to-Leading Order: The Charm-Top-Quark Contribution
• Electromagnetic mass splittings of the low lying hadrons and quark masses from 2+1 flavor lattice QCD+QED
• Chiral symmetry breaking and the Banks--Casher relation in lattice QCD with Wilson quarks
• Isospin corrections for superallowed Fermi beta decay in self-consistent relativistic random phase approximation approaches
• $\eta \to 3\pi$ at Two Loops In Chiral Perturbation Theory
• Non-perturbative renormalization of quark bilinear operators and B_K using domain wall fermions
• Determination of light quark masses from the electromagnetic splitting of pseudoscalar meson masses computed with two flavors of domain wall fermions
• The pion form factor from lattice QCD with two dynamical flavours
• Rationale for UV-filtered clover fermions
• A note on isospin violation in Pl2(gamma) decays
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• Average up/down, strange and charm quark masses with Nf=2 twisted mass lattice QCD
• Electromagnetic form factor of the pion from twisted-mass lattice QCD at Nf=2
• Continuum Limit of $B_K$ from 2+1 Flavor Domain Wall QCD
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• K->pi form factors with reduced model dependence
• Determination of the chiral condensate from QCD Dirac spectrum on the lattice
• BK-parameter from Nf = 2 twisted mass lattice QCD
• S-parameter and pseudo-Nambu-Goldstone boson mass from lattice QCD
• Vector form factor in K_l3 semileptonic decay with two flavors of dynamical domain-wall quarks
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• The Chiral Condensate in a Finite Volume
• The Kl3 scalar form factors in the standard model
• Lattice study of meson correlators in the epsilon-regime of two-flavor QCD
• Unquenched determination of the kaon parameter B_K from improved staggered fermions
• On the pion decay constant
• Results for light pseudoscalar mesons
• Three-Flavor Partially Quenched Chiral Perturbation Theory at NNLO for Meson Masses and Decay Constants
• SU(2) chiral perturbation theory for Kl3 decay amplitudes
• Equivalence of QCD in the epsilon-regime and chiral Random Matrix Theory with or without chemical potential
• Parameters of the lowest order chiral Lagrangian from fermion eigenvalues
• Decay Constants of Charged Pseudoscalar Mesons
• Non-perturbative renormalization of quark mass in Nf=2+1 QCD with the Schroedinger functional scheme
• Topology, the Wilson flow and the HMC algorithm
• The epsilon regime with Wilson fermions
• Mixed Action Effective Field Theory: an Addendum
• Probing the chiral regime of Nf=2 QCD with mixed actions
• The condensate for two dynamical chirally improved quarks in QCD
• Chiral dynamics with strange quarks in the light of recent lattice simulations
• Pion in a Box
• Integrating out strange quarks in ChPT: terms at order p^6
• Chiral logs in twisted mass lattice QCD with large isospin breaking
• Flavour symmetry restoration and kaon weak matrix elements in quenched twisted mass QCD
• On the determination of alpha_s from hadronic tau decays with contour-improved, fixed order and renormalon-chain perturbation theory
• Chiral extrapolation and determination of low-energy constants from lattice data
• Status of the Hadronic Tau Determination of V_us
• Finite volume effects in $B_K$ with improved staggered fermions
• A Mixed Tau-Electroproduction Sum Rule for V_us
• The rotator spectrum in the delta-regime of the O(n) effective field theory in 3 and 4 dimensions
• Status of the Hadronic tau Decay Determination of |V_{us}|
• Pseudoscalar decay constants from N_f=2+1+1 twisted mass lattice QCD
• Algorithms for lattice QCD: progress and challenges
• Geometry dependence of RMT-based methods to extract the low-energy constants Sigma and F
• Light quark masses from QCD sum rules with minimal hadronic bias
• Non-Perturbative Study of the Light Pseudoscalar Masses in Chiral Dynamics
• Staggered chiral perturbation theory in the two-flavor case and SU(2) analysis of the MILC data
• The QCD rotator with a light quark mass
• Improved analysis of the scalar and vector form factors of kaon semileptonic decays with N_f = 2 twisted-mass fermions
• Theoretical progress on the V_us determination from tau decays
• Electromagnetic Corrections in Staggered Chiral Perturbation Theory
• Chiral extrapolation of SU(3) amplitudes

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