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We review lattice results relevant for pion and kaon physics with the aim of making them easily accessible to the particle physics community.
1931
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[CP-PACS/JLQCD 07], T. Ishikawa, et. al
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M. Ademollo and R. Gatto, Nonrenormalization theorem for the strangeness violating vector currents
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R. H. Socolow, Departures from the Eightfold Way. 3. Pseudoscalar-meson electromagnetic masses
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G. Furlan, F. Lannoy, C. Rossetti, and G. Segré, Symmetry-breaking corrections to weak vector currents
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T. Das, G. S. Guralnik, V. S. Mathur, F. E. Low, and J. E. Young, Electromagnetic mass difference of pions
1967
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M. Gell-Mann, R. J. Oakes, and B. Renner, Behavior of current divergences under SU(3) × \times SU(3)
1968
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R. F. Dashen, Chiral SU(3) × \times SU(3) as a symmetry of the strong interactions
1969
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K. G. Wilson, Confinement of quarks
1974
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S. Weinberg, The problem of mass
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L. Susskind, Lattice fermions
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D. J. Gross, S. B. Treiman, and F. Wilczek, Light quark masses and isospin violation
1979
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1980
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T. Banks and A. Casher, Chiral symmetry breaking in confining theories
1980
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J. Gasser and H. Leutwyler, Quark masses
1982
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P. H. Ginsparg and K. G. Wilson, A remnant of chiral symmetry on the lattice
1982
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K. Symanzik, Continuum limit and improved action in lattice theories. 1. Principles and ϕ 4 \phi^{4} theory
1983
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K. Symanzik, Continuum limit and improved action in lattice theories. 2. O(N) nonlinear sigma model in perturbation theory
1983
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[GL 84], J. Gasser, and H. Leutwyler, Chiral perturbation theory to one loop
1984
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[LR 84], H. Leutwyler, and M. Roos, Determination of the elements V u s V_{us} and V u d V_{ud} of the Kobayashi-Maskawa matrix
1984
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[GL 85], J. Gasser, and H. Leutwyler, Chiral perturbation theory: expansions in the mass of the strange quark
1985
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J. Gasser and H. Leutwyler, η → 3 π \eta\to 3\pi to one loop
1985
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J. Gasser and H. Leutwyler, Low-energy expansion of meson form factors
1985
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M. E. Fisher and V. Privman, First-order transitions breaking O(n) symmetry: Finite-size scaling
1985
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E. Brezin and J. Zinn-Justin, Finite size effects in phase transitions
1985
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M. Lüscher and P. Weisz, On-shell improved lattice gauge theories
1985
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Y. Iwasaki, Renormalization group analysis of lattice theories and improved lattice action: two-dimensional nonlinear O(N) sigma model
1985
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1986
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S. R. Amendolia et. al
1986
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J. Gasser and H. Leutwyler, Light quarks at low temperatures
1987
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J. Gasser and H. Leutwyler, Thermodynamics of chiral symmetry
1987
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H. Leutwyler, Energy levels of light quarks confined to a box
1987
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J. Gasser and H. Leutwyler, Spontaneously Broken Symmetries: Effective Lagrangians at Finite Volume
1988
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P. Hasenfratz and H. Leutwyler, Goldstone boson related finite size effects in field theory and critical phenomena with O(N) symmetry
1990
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F. C. Hansen, Finite size effects in spontaneously broken SU(N) × \times SU(N) theories
1990
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J. F. Donoghue, J. Gasser, and H. Leutwyler, The decay of a light Higgs boson
1990
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F. C. Hansen and H. Leutwyler, Charge correlations and topological susceptibility in QCD
1991
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N. H. Fuchs, H. Sazdjian, and J. Stern, How to probe the scale of (anti-q q) in chiral perturbation theory
1991
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M. Lüscher, R. Narayanan, P. Weisz, and U. Wolff, The Schrödinger functional: a renormalizable probe for non-Abelian gauge theories
1992
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H. Leutwyler and A. V. Smilga, Spectrum of Dirac operator and role of winding number in QCD
1992
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D. B. Kaplan, A Method for simulating chiral fermions on the lattice
1992
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E. V. Shuryak and J. J. M. Verbaarschot, Random matrix theory and spectral sum rules for the Dirac operator in QCD
1993
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J. J. M. Verbaarschot and I. Zahed, Spectral density of the QCD Dirac operator near zero virtuality
1993
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J. Stern, H. Sazdjian, and N. H. Fuchs, What pi - pi scattering tells us about chiral perturbation theory
1993
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G. P. Lepage and P. B. Mackenzie, On the viability of lattice perturbation theory
1993
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C. W. Bernard and M. F. L. Golterman, Partially quenched gauge theories and an application to staggered fermions
1994
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J. J. M. Verbaarschot, The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way
1994
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R. Sommer, A new way to set the energy scale in lattice gauge theories and its applications to the static force and α s \alpha_{s} in SU(2) Yang-Mills theory
1994
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R. Urech, Virtual photons in chiral perturbation theory
1995
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G. Martinelli, C. Pittori, C. T. Sachrajda, M. Testa, and A. Vladikas, A general method for nonperturbative renormalization of lattice operators
1995
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V. Furman and Y. Shamir, Axial symmetries in lattice QCD with Kaplan fermions
1995
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A. Duncan, E. Eichten, and H. Thacker, Electromagnetic splittings and light quark masses in lattice QCD
1996
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R. Baur and R. Urech, On the corrections to Dashen’s theorem
1996
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H. Leutwyler, The ratios of the light quark masses
1996
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J. Kambor, C. Wiesendanger, and D. Wyler, Final state interactions and Khuri-Treiman equations in η → 3 π \eta\to 3\pi decays
1996
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A. V. Anisovich and H. Leutwyler, Dispersive analysis of the decay η → 3 π \eta\to 3\pi
1996
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G. Buchalla, A. J. Buras, and M. E. Lautenbacher, Weak decays beyond leading logarithms
1996
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T. Takaishi, Heavy quark potential and effective actions on blocked configurations
1996
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J. Bijnens and J. Prades, Electromagnetic corrections for pions and kaons: masses and polarizabilities
1997
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J. F. Donoghue and A. F. Perez, The electromagnetic mass differences of pions and kaons
1997
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R. Baur and R. Urech, Resonance contributions to the electromagnetic low energy constants of chiral perturbation theory
1997
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B. Moussallam, A sum rule approach to the violation of Dashen’s theorem
1997
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T. van Ritbergen, J. A. M. Vermaseren, and S. A. Larin, The four-loop β \beta -function in Quantum Chromodynamics
1997
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K. G. Chetyrkin, B. A. Kniehl, and M. Steinhauser, Strong coupling constant with flavour thresholds at four loops in the MS ¯ {\overline{\mathrm{MS}}} scheme
1997
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A. J. Buras, Weak Hamiltonian, CP violation and rare decays
1997
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M. Lüscher, S. Sint, R. Sommer, P. Weisz, and U. Wolff, Non-perturbative O(a) improvement of lattice QCD
1997
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M. F. L. Golterman and K.-C. Leung, Applications of Partially Quenched Chiral Perturbation Theory
1998
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S. R. Sharpe and R. L. Singleton, Jr, Spontaneous flavor and parity breaking with Wilson fermions
1998
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J. Bijnens, G. Colangelo, and G. Ecker, Double chiral logs
1998
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R. Kaiser, The η \eta and the η ′ \eta^{\prime} at large N c N_{c} , diploma work, University of Bern
1998
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S. M. Nishigaki, P. H. Damgaard, and T. Wettig, Smallest Dirac eigenvalue distribution from random matrix theory
1998
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[BCT 98], J. Bijnens, G. Colangelo, and P. Talavera, The vector and scalar form factors of the pion to two loops
1998
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[JLQCD 97], S. Aoki, et. al
1998
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P. Hasenfratz, V. Laliena, and F. Niedermayer, The index theorem in QCD with a finite cut-off
1998
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M. Lüscher, Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation
1998
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H. Neuberger, Exactly massless quarks on the lattice
1998
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W.-J. Lee and S. R. Sharpe, Partial Flavor Symmetry Restoration for Chiral Staggered Fermions
1999
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G. C. Branco, L. Lavoura, and J. P. Silva, CP violation
1999
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[MILC 99], K. Orginos, D. Toussaint, and R. L. Sugar, Variants of fattening and flavor symmetry restoration
1999
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S. R. Sharpe, Enhanced chiral logarithms in partially quenched QCD
2000
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S. R. Sharpe and N. Shoresh, Physical results from unphysical simulations
2000
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[ALPHA 99], J. Garden, J. Heitger, R. Sommer, and H. Wittig, Precision computation of the strange quark’s mass in quenched QCD
2000
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K. G. Chetyrkin and A. Retey, Renormalization and running of quark mass and field in the regularization invariant and MS ¯ {\overline{\mathrm{MS}}} schemes at three and four loops
2000
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J. J. M. Verbaarschot and T. Wettig, Random matrix theory and chiral symmetry in QCD
2000
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S. Descotes-Genon, L. Girlanda, and J. Stern, Paramagnetic effect of light quark loops on chiral symmetry breaking
2000
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D. Becirevic et. al
2000
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P. de Forcrand et. al
2000
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C. W. Bernard et. al
2000
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M. Hasenbusch, Speeding up the hybrid Monte Carlo algorithm for dynamical fermions
2001
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[ALPHA 01], R. Frezzotti, P. A. Grassi, S. Sint, and P. Weisz, Lattice QCD with a chirally twisted mass term
2001
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G. Amoros, J. Bijnens, and P. Talavera, QCD isospin breaking in meson masses, decay constants and quark mass ratios
2001
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K. Maltman and J. Kambor, m u + m d m_{u}+m_{d} from isovector pseudoscalar sum rules
2001
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[CGL 01], G. Colangelo, J. Gasser, and H. Leutwyler, π π \pi\pi scattering
2001
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P. H. Damgaard and S. M. Nishigaki, Distribution of the k-th smallest Dirac operator eigenvalue
2001
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A. Hasenfratz and F. Knechtli, Flavor symmetry and the static potential with hypercubic blocking
2001
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P. Hasenfratz et. al
2001
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C. Gattringer, A new approach to Ginsparg-Wilson fermions
2001
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G. Rupak and N. Shoresh, Chiral perturbation theory for the Wilson lattice action
2002
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P. Post and K. Schilcher, K l 3 K_{l3} form factors at order p 6 p^{6} in chiral perturbation theory
2002
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P. H. Damgaard, M. C. Diamantini, P. Hernandez, and K. Jansen, Finite-size scaling of meson propagators
2002
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P. Hasenfratz, S. Hauswirth, T. Jorg, F. Niedermayer, and K. Holland, Testing the fixed-point QCD action and the construction of chiral currents
2002
Cited alongside, same era.
O. Bär, G. Rupak, and N. Shoresh, Simulations with different lattice Dirac operators for valence and sea quarks
2003
Cited alongside, same era.
C. Aubin and C. Bernard, Pion and kaon masses in staggered chiral perturbation theory
2003
Cited alongside, same era.
C. Aubin and C. Bernard, Pseudoscalar decay constants in staggered chiral perturbation theory
2003
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S. Aoki, Chiral perturbation theory with Wilson-type fermions including a**2 effects: N(f) = 2 degenerate case
2003
Cited alongside, same era.
2008
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A. Kastner and H. Neufeld, The K l 3 K_{l3} scalar form factors in the Standard Model
2008
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[JLQCD/TWQCD 08], T. Kaneko, et. al
2008
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[JLQCD/TWQCD 08B], T. W. Chiu, et. al
2008
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[JLQCD/TWQCD 07A], S. Aoki, et. al
2008
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2003
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[JLQCD 02], S. Aoki, et. al
2003
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[CP-PACS 01], A. Ali Khan, et. al
2003
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E. Gamiz, M. Jamin, A. Pich, J. Prades, and F. Schwab, Determination of m s m_{s} and | V u s | |V_{us}| from hadronic tau decays
2003
Cited alongside, same era.
J. Bijnens and P. Talavera, K l 3 K_{l3} decays in chiral perturbation theory
2003
Cited alongside, same era.
P. H. Damgaard, P. Hernandez, K. Jansen, M. Laine, and L. Lellouch, Finite-size scaling of vector and axial current correlators
2003
Cited alongside, same era.
S. Dürr, M π 2 M_{\pi}^{2} versus m q m_{q} : Comparing CP-PACS and UKQCD data to chiral perturbation theory
2003
Cited alongside, same era.
2008
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[JLQCD/TWQCD 07], H. Fukaya, et. al
2008
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[RBC/UKQCD 08A], P. A. Boyle, et. al
2008
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[JLQCD 08A], E. Shintani, et. al
2008
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2008
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2008
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2008
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[RBC/UKQCD 07A], D. J. Antonio, et. al
2008
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2008
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2008
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C. Jung, Status of dynamical ensemble generation
2009
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J.-W. Chen, D. O’Connell, and A. Walker-Loud, Universality of Mixed Action Extrapolation Formulae
2009
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2009
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2009
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[MILC 09A], A. Bazavov, et. al
2009
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L. Lellouch, Kaon physics: a lattice perspective
2009
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2009
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A. Rusetsky, Isospin symmetry breaking
2009
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H. Leutwyler, Light quark masses
2009
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A. T. Lytle, Non-perturbative calculation of Z m Z_{m} using Asqtad fermions
2009
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2009
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S. Bethke, The 2009 World Average of α s ( M Z ) \alpha_{s}(M_{Z})
2009
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2009
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G. Colangelo, S. Lanz, and E. Passemar, A new dispersive analysis of η → 3 π \eta\to 3\pi
2009
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N. Auerbach, Coulomb corrections to superallowed beta decay in nuclei
2009
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2009
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2009
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K. Maltman, A mixed τ \tau -electroproduction sum rule for V u s V_{us}
2009
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2009
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2009
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2009
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2009
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[JLQCD/TWQCD 09A], J. Noaki, et. al
2009
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2009
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2009
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E. Passemar, Dispersive approach to K ℓ 3 K_{\ell 3} form factors
2009
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2009
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2009
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P. H. Damgaard and H. Fukaya, The chiral condensate in a finite volume
2009
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2009
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2009
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2009
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2009
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[JLQCD/TWQCD 09], S. Aoki, et. al
2009
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J. Bijnens, Status of strong ChPT
2009
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2009
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2009
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2009
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O. Bär, S. Necco, and S. Schaefer, The epsilon regime with Wilson fermions
2009
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G. Ecker, P. Masjuan, and H. Neufeld, Chiral extrapolation of lattice data
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J. Gasser and G. R. S. Zarnauskas, On the pion decay constant
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V. Bernard and E. Passemar, Chiral extrapolation of the strangeness changing K π K\pi form factor
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S. Aoki and H. Fukaya, Chiral perturbation theory in a theta vacuum
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