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→π transition at zero momentum transfer as well as the ratio f K /f π 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) L ×SU(2) R and SU(3) L ×SU(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 Sect. 1.2, but we stress the importance of the detailed discussion that underlies these results and constitutes the bulk of the present review.
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References
Flavianet Lattice Averaging Group (FLAG), Review of lattice results concerning low energy particle physics. http://itpwiki.unibe.ch/flag
J. Laiho, E. Lunghi, R. Van de Water, 2+1 flavor lattice QCD averages. http://krone.physik.unizh.ch/~lunghi/webpage/LatAves
J. Laiho, E. Lunghi, R.S. Van de Water, Lattice QCD inputs to the CKM unitarity triangle analysis. Phys. Rev. D 81, 034503 (2010). arXiv:0910.2928 [hep-ph]
K. Jansen, Lattice QCD: a critical status report. PoS LAT2008, 010 (2008). arXiv:0810.5634 [hep-lat]
C. Jung, Status of dynamical ensemble generation. PoS LAT2009, 002 (2009). arXiv:1001.0941 [hep-lat]
A. Bazavov et al. (MILC 09), Full nonperturbative QCD simulations with 2+1 flavors of improved staggered quarks. Rev. Mod. Phys. 82, 1349–1417 (2010). arXiv:0903.3598 [math.PR]
M. Hasenbusch, Speeding up the hybrid Monte Carlo algorithm for dynamical fermions. Phys. Lett. B 519, 177–182 (2001). hep-lat/0107019
M. Lüscher, Schwarz-preconditioned HMC algorithm for two-flavour lattice QCD. Comput. Phys. Commun. 165, 199–220 (2005). hep-lat/0409106
C. Urbach, K. Jansen, A. Shindler, U. Wenger, HMC algorithm with multiple time scale integration and mass preconditioning. Comput. Phys. Commun. 174, 87–98 (2006). hep-lat/0506011
M.A. Clark, A.D. Kennedy, Accelerating dynamical fermion computations using the rational hybrid Monte Carlo (RHMC) algorithm with multiple pseudofermion fields. Phys. Rev. Lett. 98, 051601 (2007). hep-lat/0608015
K.-I. Ishikawa, Recent algorithm and machine developments for lattice QCD. PoS LAT2008, 013 (2008). arXiv:0811.1661 [hep-lat]
D.J. Antonio et al. (RBC 07A), Localization and chiral symmetry in 3 flavor domain wall QCD. Phys. Rev. D 77, 014509 (2008). arXiv:0705.2340 [hep-lat]
A. Bazavov et al. (MILC 10), Topological susceptibility with the asqtad action. Phys. Rev. D 81, 114501 (2010). arXiv:1003.5695 [hep-lat]
S. Schaefer, R. Sommer, F. Virotta, Critical slowing down and error analysis in lattice QCD simulations. arXiv:1009.5228 [hep-lat]
M. Lüscher, Topology, the Wilson flow and the HMC algorithm. arXiv:1009.5877 [hep-lat]
S. Schaefer, Algorithms for lattice QCD: progress and challenges. arXiv:1011.5641 [hep-ph]
S. Dürr et al. (BMW 08), Ab-initio determination of light hadron masses. Science 322, 1224–1227 (2008). arXiv:0906.3599 [hep-lat]
K. Symanzik, Continuum limit and improved action in lattice theories. 1. Principles and φ 4 theory. Nucl. Phys. B 226, 187 (1983)
K. Symanzik, Continuum limit and improved action in lattice theories. 2. O(N) nonlinear sigma model in perturbation theory. Nucl. Phys. B 226, 205 (1983)
C.W. Bernard, M.F.L. Golterman, Partially quenched gauge theories and an application to staggered fermions. Phys. Rev. D 49, 486–494 (1994). hep-lat/9306005
S.R. Sharpe, Enhanced chiral logarithms in partially quenched QCD. Phys. Rev. D 56, 7052–7058 (1997). hep-lat/9707018. Erratum: Phys. Rev. D 62, 099901 (2000)
M.F.L. Golterman, K.-C. Leung, Applications of partially quenched chiral perturbation theory. Phys. Rev. D 57, 5703–5710 (1998). hep-lat/9711033
S.R. Sharpe, R.L. Singleton Jr., Spontaneous flavor and parity breaking with Wilson fermions. Phys. Rev. D 58, 074501 (1998). hep-lat/9804028
W.-J. Lee, S.R. Sharpe, Partial flavor symmetry restoration for chiral staggered fermions. Phys. Rev. D 60, 114503 (1999). hep-lat/9905023
S.R. Sharpe, N. Shoresh, Physical results from unphysical simulations. Phys. Rev. D 62, 094503 (2000). hep-lat/0006017
G. Rupak, N. Shoresh, Chiral perturbation theory for the Wilson lattice action. Phys. Rev. D 66, 054503 (2002). hep-lat/0201019
O. Bär, G. Rupak, N. Shoresh, Simulations with different lattice Dirac operators for valence and sea quarks. Phys. Rev. D 67, 114505 (2003). hep-lat/0210050
C. Aubin, C. Bernard, Pion and kaon masses in staggered chiral perturbation theory. Phys. Rev. D 68, 034014 (2003). hep-lat/0304014
O. Bär, G. Rupak, N. Shoresh, Chiral perturbation theory at O(a ∗∗2) for lattice QCD. Phys. Rev. D 70, 034508 (2004). hep-lat/0306021
C. Aubin, C. Bernard, Pseudoscalar decay constants in staggered chiral perturbation theory. Phys. Rev. D 68, 074011 (2003). hep-lat/0306026
S. Aoki, Chiral perturbation theory with Wilson-type fermions including a ∗∗2 effects: N(f)=2 degenerate case. Phys. Rev. D 68, 054508 (2003). hep-lat/0306027
S. Aoki, O. Bär, Twisted-mass QCD, O(a) improvement and Wilson chiral perturbation theory. Phys. Rev. D 70, 116011 (2004). hep-lat/0409006
S.R. Sharpe, R.S. Van de Water, Staggered chiral perturbation theory at next-to-leading order. Phys. Rev. D 71, 114505 (2005). hep-lat/0409018
S.R. Sharpe, J.M.S. Wu, Twisted mass chiral perturbation theory at next-to-leading order. Phys. Rev. D 71, 074501 (2005). hep-lat/0411021
O. Bär, C. Bernard, G. Rupak, N. Shoresh, Chiral perturbation theory for staggered sea quarks and Ginsparg–Wilson valence quarks. Phys. Rev. D 72, 054502 (2005). hep-lat/0503009
M. Golterman, T. Izubuchi, Y. Shamir, The role of the double pole in lattice QCD with mixed actions. Phys. Rev. D 71, 114508 (2005). hep-lat/0504013
J.-W. Chen, D. O’Connell, A. Walker-Loud, Two meson systems with Ginsparg–Wilson valence quarks. Phys. Rev. D 75, 054501 (2007). hep-lat/0611003
J.-W. Chen, D. O’Connell, A. Walker-Loud, Universality of mixed action extrapolation formulae. J. High Energy Phys. 04, 090 (2009). arXiv:0706.0035 [hep-lat]
J.-W. Chen, M. Golterman, D. O’Connell, A. Walker-Loud, Mixed action effective field theory: an addendum. Phys. Rev. D 79, 117502 (2009). arXiv:0905.2566 [hep-lat]
O. Bär, Chiral logs in twisted mass lattice QCD with large isospin breaking. arXiv:1008.0784 [hep-lat]
S. Dürr et al. (BMW 10), The ratio F K /F π in QCD. Phys. Rev. D 81, 054507 (2010). arXiv:1001.4692 [hep-lat]
S. Aoki et al. (PACS-CS 09), Physical point simulation in 2+1 flavor lattice QCD. Phys. Rev. D 81, 074503 (2010). arXiv:0911.2561 [hep-lat]
J. Bijnens, G. Colangelo, G. Ecker, Double chiral logs. Phys. Lett. B 441, 437–446 (1998). hep-ph/9808421
G. Ecker, P. Masjuan, H. Neufeld, Chiral extrapolation of lattice data. Phys. Lett. B 692, 184–188 (2010). arXiv:1004.3422 [hep-ph]
G. Ecker, Chiral extrapolation of SU(3) amplitudes. arXiv:1012.1522 [hep-ph]
W. Bietenholz et al. (QCDSF/UKQCD 10), Tuning the strange quark mass in lattice simulations. Phys. Lett. B 690, 436–441 (2010). arXiv:1003.1114 [hep-lat]
W. Bietenholz et al. (QCDSF/UKQCD 10A), Flavour symmetry breaking and tuning the strange quark mass for 2+1 quark flavours. PoS LAT2010, 122 (2010). arXiv:1012.4371 [hep-lat]
A. Manohar, C.T. Sachrajda, Quark masses. J. Phys. G 37, 075021 (2010). Review of Particle Physics, p. 583
B. Blossier et al. (ETM 07), Light quark masses and pseudoscalar decay constants from N f =2 Lattice QCD with twisted mass fermions. J. High Energy Phys. 04, 020 (2008). arXiv:0709.4574 [hep-lat]
J.C. Hardy, I.S. Towner, Superallowed 0+→0+ nuclear β decays: A new survey with precision tests of the conserved vector current hypothesis and the Standard Model. Phys. Rev. C 79, 055502 (2009). arXiv:0812.1202 [nucl-ex]
C. Pena, Twisted mass QCD for weak matrix elements. PoS LAT2006, 019 (2006). hep-lat/0610109. This is, to the best of our knowledge, the first time colour coding was used. It does not appear in the proceedings but in the slides, see http://www.physics.utah.edu/lat06/abstracts/sessions/plenary.html
R. Frezzotti, P.A. Grassi, S. Sint, P. Weisz (ALPHA 01), Lattice QCD with a chirally twisted mass term. J. High Energy Phys. 08, 058 (2001). hep-lat/0101001
R. Frezzotti, G.C. Rossi, Chirally improving Wilson fermions. I: O(a) improvement. J. High Energy Phys. 08, 007 (2004). hep-lat/0306014
P. Boucaud et al. (ETM 07A), Dynamical twisted mass fermions with light quarks. Phys. Lett. B 650, 304–311 (2007). hep-lat/0701012
S. Dürr, Theoretical issues with staggered fermion simulations. PoS LAT2005, 021 (2006). hep-lat/0509026
S.R. Sharpe, Rooted staggered fermions: good, bad or ugly? PoS LAT2006, 022 (2006). hep-lat/0610094
A.S. Kronfeld, Lattice gauge theory with staggered fermions: how, where, and why (not). PoS LAT2007, 016 (2007). arXiv:0711.0699 [hep-lat]
M. Golterman, QCD with rooted staggered fermions. PoS CONFINEMENT8, 014 (2008). arXiv:0812.3110 [hep-ph]
A. Bazavov et al. (MILC 09A), MILC results for light pseudoscalars. PoS CD09, 007 (2009). arXiv:0910.2966 [hep-ph]
R. Baron, P. Boucaud, J. Carbonell, A. Deuzeman, V. Drach et al. (ETM 10), Light hadrons from lattice QCD with light (u,d), strange and charm dynamical quarks. J. High Energy Phys. 1006, 111 (2010). arXiv:1004.5284 [hep-lat]
L. Lellouch, Kaon physics: a lattice perspective. PoS LAT2008, 015 (2009). arXiv:0902.4545 [hep-lat]
M. Gell-Mann, R.J. Oakes, B. Renner, Behavior of current divergences under SU(3)×SU(3). Phys. Rev. 175, 2195–2199 (1968)
S. Aoki et al. (PACS-CS 08), 2+1 Flavor lattice QCD toward the physical point. Phys. Rev. D 79, 034503 (2009). arXiv:0807.1661 [hep-lat]
S. Aoki et al. (PACS-CS 10), Non-perturbative renormalization of quark mass in N f =2+1 QCD with the Schroedinger functional scheme. J. High Energy Phys. 08, 101 (2010). arXiv:1006.1164 [hep-lat]
S. Dürr et al. (BMW 10A), Lattice QCD at the physical point: light quark masses. arXiv:1011.2403 [hep-lat]
B. Bloch-Devaux, Results from NA48/2 on ππ scattering lengths measurements in K ±→π + π − e ± ν and K ±→π 0 π 0 π ± decays. PoS CONFINEMENT8, 029 (2008)
J. Gasser, A. Rusetsky, I. Scimemi, Electromagnetic corrections in hadronic processes. Eur. Phys. J. C 32, 97–114 (2003). hep-ph/0305260
A. Rusetsky, Isospin symmetry breaking. PoS CD09, 071 (2009). arXiv:0910.5151 [hep-ph]
J. Gasser, Theoretical progress on cusp effect and K ℓ4 decays. PoS KAON, 033 (2008). arXiv:0710.3048 [hep-ph]
H. Leutwyler, Light quark masses. PoS CD09, 005 (2009). arXiv:0911.1416 [hep-ph]
R.F. Dashen, Chiral SU(3)×SU(3) as a symmetry of the strong interactions. Phys. Rev. 183, 1245–1260 (1969)
A. Duncan, E. Eichten, H. Thacker, Electromagnetic splittings and light quark masses in lattice QCD. Phys. Rev. Lett. 76, 3894–3897 (1996). hep-lat/9602005
T. Blum, T. Doi, M. Hayakawa, T. Izubuchi, N. Yamada (RBC 07), Determination of light quark masses from the electromagnetic splitting of pseudoscalar meson masses computed with two flavors of domain wall fermions. Phys. Rev. D 76, 114508 (2007). arXiv:0708.0484 [hep-lat]
T. Blum et al. (Blum 10), Electromagnetic mass splittings of the low lying hadrons and quark masses from 2+1 flavor lattice QCD+QED. Phys. Rev. D 82, 094508 (2010). arXiv:1006.1311 [hep-lat]
A. Portelli et al. (BMW 10C), Electromagnetic corrections to light hadron masses. PoS LAT2010, 121 (2010). arXiv:1011.4189 [hep-lat]
C. Aubin et al. (MILC 04A), Results for light pseudoscalars from three-flavor simulations. Nucl. Phys. Proc. Suppl. 140, 231–233 (2005). hep-lat/0409041
C. Aubin et al. (MILC 04), Light pseudoscalar decay constants, quark masses, and low energy constants from three-flavor lattice QCD. Phys. Rev. D 70, 114501 (2004). hep-lat/0407028
J. Bijnens, J. Prades, Electromagnetic corrections for pions and kaons: masses and polarizabilities. Nucl. Phys. B 490, 239–271 (1997). hep-ph/9610360
J.F. Donoghue, A.F. Perez, The electromagnetic mass differences of pions and kaons. Phys. Rev. D 55, 7075–7092 (1997). hep-ph/9611331
S. Basak et al. (MILC 08), Electromagnetic splittings of hadrons from improved staggered quarks in full QCD. PoS LAT2008, 127 (2008). arXiv:0812.4486 [hep-lat]
C. Bernard, E.D. Freeland, Electromagnetic corrections in staggered chiral perturbation theory. PoS LAT2010, 084 (2010). arXiv:1011.3994 [hep-lat]
R. Urech, Virtual photons in chiral perturbation theory. Nucl. Phys. B 433, 234–254 (1995). hep-ph/9405341
R. Baur, R. Urech, On the corrections to Dashen’s theorem. Phys. Rev. D 53, 6552–6557 (1996). hep-ph/9508393
R. Baur, R. Urech, Resonance contributions to the electromagnetic low energy constants of chiral perturbation theory. Nucl. Phys. B 499, 319–348 (1997). hep-ph/9612328
B. Moussallam, A sum rule approach to the violation of Dashen’s theorem. Nucl. Phys. B 504, 381–414 (1997). hep-ph/9701400
W. Cottingham, The neutron proton mass difference and electron scattering experiments. Ann. Phys. 25, 424 (1963)
R.H. Socolow, Departures from the Eightfold Way. 3. Pseudoscalar-meson electromagnetic masses. Phys. Rev. B 137, 1221–1228 (1965)
D.J. Gross, S.B. Treiman, F. Wilczek, Light quark masses and isospin violation. Phys. Rev. D 19, 2188 (1979)
J. Gasser, H. Leutwyler, Quark masses. Phys. Rep. 87, 77–169 (1982)
T. Das, G.S. Guralnik, V.S. Mathur, F.E. Low, J.E. Young, Electromagnetic mass difference of pions. Phys. Rev. Lett. 18, 759–761 (1967)
J. Gasser, H. Leutwyler (GL 85), Chiral perturbation theory: expansions in the mass of the strange quark. Nucl. Phys. B 250, 465 (1985)
G. Amoros, J. Bijnens, P. Talavera, QCD isospin breaking in meson masses, decay constants and quark mass ratios. Nucl. Phys. B 602, 87–108 (2001). hep-ph/0101127
J. Gasser, H. Leutwyler (GL 84), Chiral perturbation theory to one loop. Ann. Phys. 158, 142 (1984)
B. Blossier et al. (ETM 10B), Average up/down, strange and charm quark masses with N f =2 twisted mass lattice QCD. Phys. Rev. D 82, 114513 (2010). arXiv:1010.3659 [hep-lat]
J. Noaki et al. (JLQCD/TWQCD 08A), Convergence of the chiral expansion in two-flavor lattice QCD. Phys. Rev. Lett. 101, 202004 (2008). arXiv:0806.0894 [hep-lat]
M. Göckeler et al. (QCDSF/UKQCD 06), Estimating the unquenched strange quark mass from the lattice axial Ward identity. Phys. Rev. D 73, 054508 (2006). hep-lat/0601004
D. Becirevic et al. (SPQcdR 05), Non-perturbatively renormalised light quark masses from a lattice simulation with N f =2. Nucl. Phys. B 734, 138–155 (2006). hep-lat/0510014
M. Della Morte et al. (ALPHA 05), Non-perturbative quark mass renormalization in two-flavor QCD. Nucl. Phys. B 729, 117–134 (2005). hep-lat/0507035
M. Göckeler et al. (QCDSF/UKQCD 04), Determination of light and strange quark masses from full lattice QCD. Phys. Lett. B 639, 307–311 (2006). hep-ph/0409312
S. Aoki et al. (JLQCD 02), Light hadron spectroscopy with two flavors of O(a)-improved dynamical quarks. Phys. Rev. D 68, 054502 (2003). hep-lat/0212039
A. Ali Khan et al. (CP-PACS 01), Light hadron spectroscopy with two flavors of dynamical quarks on the lattice. Phys. Rev. D 65, 054505 (2002). hep-lat/0105015. Erratum: Phys. Rev. D 66, 059901 (2003)
M. Constantinou et al. (ETM 10C), Non-perturbative renormalization of quark bilinear operators with N f =2 (tmQCD) Wilson fermions and the tree-level improved gauge action. J. High Energy Phys. 08, 068 (2010). arXiv:1004.1115 [hep-lat]
A. Bazavov et al. (MILC 10A), Staggered chiral perturbation theory in the two-flavor case and SU(2) analysis of the MILC data. PoS LAT2010, 083 (2010). arXiv:1011.1792 [hep-lat]
C. McNeile, C.T.H. Davies, E. Follana, K. Hornbostel, G.P. Lepage (HPQCD 10), High-precision c and b masses, and QCD coupling from current-current correlators in lattice and continuum QCD. Phys. Rev. D 82, 034512 (2010). arXiv:1004.4285 [hep-lat]
S. Dürr et al. (BMW 10B), Lattice QCD at the physical point: Simulation and analysis details. arXiv:1011.2711 [hep-lat]
Y. Aoki et al. (RBC/UKQCD 10A), Continuum limit physics from 2+1 flavor domain wall QCD. arXiv:1011.0892 [hep-lat]
C.T.H. Davies et al. (HPQCD 09), Precise charm to strange mass ratio and light quark masses from full lattice QCD. Phys. Rev. Lett. 104, 132003 (2010). arXiv:0910.3102 [hep-ph]
C. Allton et al. (RBC/UKQCD 08), Physical results from 2+1 flavor domain wall QCD and SU(2) chiral perturbation theory. Phys. Rev. D 78, 114509 (2008). arXiv:0804.0473 [hep-lat]
T. Ishikawa et al. (CP-PACS/JLQCD 07), Light quark masses from unquenched lattice QCD. Phys. Rev. D 78, 011502 (2008). arXiv:0704.1937 [hep-lat]
Q. Mason, H.D. Trottier, R. Horgan, C.T.H. Davies, G.P. Lepage (HPQCD 05), High-precision determination of the light-quark masses from realistic lattice QCD. Phys. Rev. D 73, 114501 (2006). hep-ph/0511160
C. Aubin et al. (HPQCD/MILC/UKQCD 04), First determination of the strange and light quark masses from full lattice QCD. Phys. Rev. D 70, 031504 (2004). hep-lat/0405022
J. Garden, J. Heitger, R. Sommer, H. Wittig (ALPHA 99), Precision computation of the strange quark’s mass in quenched QCD. Nucl. Phys. B 571, 237–256 (2000). hep-lat/9906013
A.T. Lytle, Non-perturbative calculation of Z m using Asqtad fermions. PoS LAT2009, 202 (2009). arXiv:0910.3721 [hep-lat]
M. Lüscher, R. Narayanan, P. Weisz, U. Wolff, The Schrödinger functional: a renormalizable probe for non-Abelian gauge theories. Nucl. Phys. B 384, 168–228 (1992). hep-lat/9207009
G. Martinelli, C. Pittori, C.T. Sachrajda, M. Testa, A. Vladikas, A general method for nonperturbative renormalization of lattice operators. Nucl. Phys. B 445, 81–108 (1995). hep-lat/9411010
I. Allison et al. (HPQCD 08), High-precision charm-quark mass from current-current correlators in lattice and continuum QCD. Phys. Rev. D 78, 054513 (2008). arXiv:0805.2999 [hep-lat]
A.I. Vainshtein et al., Sum rules for light quarks in quantum chromodynamics. Sov. J. Nucl. Phys. 27, 274 (1978)
S. Narison, Strange quark mass from e + e − revisited and present status of light quark masses. Phys. Rev. D 74, 034013 (2006). hep-ph/0510108
M. Jamin, J.A. Oller, A. Pich, Scalar Kπ form factor and light quark masses. Phys. Rev. D 74, 074009 (2006). hep-ph/0605095
K.G. Chetyrkin, A. Khodjamirian, Strange quark mass from pseudoscalar sum rule with \(O(\alpha _{s}^{4})\) accuracy. Eur. Phys. J. C 46, 721–728 (2006). hep-ph/0512295
C.A. Dominguez, N.F. Nasrallah, R. Röntsch, K. Schilcher, Light quark masses from QCD sum rules with minimal hadronic bias. Nucl. Phys. Proc. Suppl. 186, 133–136 (2009). arXiv:0808.3909 [hep-ph]
K. Nakamura et al. (PDG 10), Review of particle physics. J. Phys. G 37, 075021 (2010)
K. Maltman, J. Kambor, m u +m d from isovector pseudoscalar sum rules. Phys. Lett. B 517, 332–338 (2001). hep-ph/0107060
T. van Ritbergen, J.A.M. Vermaseren, S.A. Larin, The four-loop β-function in quantum chromodynamics. Phys. Lett. B 400, 379–384 (1997). hep-ph/9701390
K.G. Chetyrkin, B.A. Kniehl, M. Steinhauser, Strong coupling constant with flavour thresholds at four loops in the \(\overline{\mathrm{MS}}\) scheme. Phys. Rev. Lett. 79, 2184–2187 (1997). hep-ph/9706430
K.G. Chetyrkin, A. Retey, Renormalization and running of quark mass and field in the regularization invariant and \(\overline{\mathrm{MS}}\) schemes at three and four loops. Nucl. Phys. B 583, 3–34 (2000). hep-ph/9910332
S. Bethke, The 2009 World Average of α s (M Z ). Eur. Phys. J. C 64, 689–703 (2009). arXiv:0908.1135 [hep-ph]
S. Weinberg, The problem of mass. Trans. New York Acad. Sci. 38, 185–201 (1977)
H. Leutwyler, The ratios of the light quark masses. Phys. Lett. B 378, 313–318 (1996). hep-ph/9602366
R. Kaiser, The η and the η′ at large N c . Diploma work, University of Bern, 1997
H. Leutwyler, On the 1/N-expansion in chiral perturbation theory. Nucl. Phys. Proc. Suppl. 64, 223–231 (1998). hep-ph/9709408
J.A. Oller, L. Roca, Non-perturbative study of the light pseudoscalar masses in chiral dynamics. Eur. Phys. J. A 34, 371–386 (2007). hep-ph/0608290
J. Gasser, H. Leutwyler, η→3π to one loop. Nucl. Phys. B 250, 539 (1985)
J. Kambor, C. Wiesendanger, D. Wyler, Final state interactions and Khuri-Treiman equations in η→3π decays. Nucl. Phys. B 465, 215–266 (1996). hep-ph/9509374
A.V. Anisovich, H. Leutwyler, Dispersive analysis of the decay η→3π. Phys. Lett. B 375, 335–342 (1996). hep-ph/9601237
C. Ditsche, B. Kubis, U.-G. Meissner, Electromagnetic corrections in η→3π decays. Eur. Phys. J. C 60, 83–105 (2009). arXiv:0812.0344 [hep-ph]
G. Colangelo, S. Lanz, E. Passemar, A new dispersive analysis of η→3π. PoS CD09, 047 (2009). arXiv:0910.0765 [hep-ph]
J. Bijnens, K. Ghorbani, η→3π at two loops in chiral perturbation theory. J. High Energy Phys. 11, 030 (2007). arXiv:0709.0230 [hep-ph]
M. Antonelli et al., An evaluation of |V us | and precise tests of the Standard Model from world data on leptonic and semileptonic kaon decays. Eur. Phys. J. C 69, 399–424 (2010). arXiv:1005.2323 [hep-ph]
J. Gasser, G.R.S. Zarnauskas, On the pion decay constant. Phys. Lett. B 693, 122–128 (2010). arXiv:1008.3479 [hep-ph]
J.L. Rosner, S. Stone, Decay constants of charged pseudoscalar mesons. J. Phys. G 37, 075021 (2010). Review of Particle Physics, p. 861
V. Cirigliano, H. Neufeld, A note on isospin violation in P l2(γ) decays. arXiv:1102.0563 [hep-ph]
I.S. Towner, J.C. Hardy, An improved calculation of the isospin-symmetry-breaking corrections to superallowed Fermi beta decay. Phys. Rev. C 77, 025501 (2008). arXiv:0710.3181 [nucl-th]
G.A. Miller, A. Schwenk, Isospin-symmetry-breaking corrections to superallowed Fermi beta decay: formalism and schematic models. Phys. Rev. C 78, 035501 (2008). arXiv:0805.0603 [nucl-th]
N. Auerbach, Coulomb corrections to superallowed beta decay in nuclei. Phys. Rev. C 79, 035502 (2009). arXiv:0811.4742 [nucl-th]
H. Liang, N. Van Giai, J. Meng, Isospin corrections for superallowed Fermi beta decay in self-consistent relativistic random-phase approximation approaches. Phys. Rev. C 79, 064316 (2009). arXiv:0904.3673 [nucl-th]
G.A. Miller, A. Schwenk, Isospin-symmetry-breaking corrections to superallowed Fermi beta decay: radial excitations. Phys. Rev. C 80, 064319 (2009). arXiv:0910.2790 [nucl-th]
I.S. Towner, J.C. Hardy, Comparative tests of isospin-symmetry-breaking corrections to superallowed 0+→0+ nuclear beta decay. arXiv:1007.5343 [nucl-th]
E. Gamiz, M. Jamin, A. Pich, J. Prades, F. Schwab, Determination of m s and |V us | from hadronic tau decays. J. High Energy Phys. 01, 060 (2003). hep-ph/0212230
E. Gamiz, M. Jamin, A. Pich, J. Prades, F. Schwab, V us and m s from hadronic τ decays. Phys. Rev. Lett. 94, 011803 (2005). hep-ph/0408044
K. Maltman, A mixed τ-electroproduction sum rule for V us . Phys. Lett. B 672, 257–263 (2009). arXiv:0811.1590 [hep-ph]
A. Pich, R. Kass, talks given at CKM 08, Rome, Italy, 2008. http://ckm2008.roma1.infn.it
E. Gamiz, M. Jamin, A. Pich, J. Prades, F. Schwab, Theoretical progress on the V us determination from τ decays. PoS KAON, 008 (2008). arXiv:0709.0282 [hep-ph]
K. Maltman, C.E. Wolfe, S. Banerjee, J.M. Roney, I. Nugent, Status of the hadronic τ determination of V us . Int. J. Mod. Phys. A 23, 3191–3195 (2008). arXiv:0807.3195 [hep-ph]
K. Maltman, C.E. Wolfe, S. Banerjee, I.M. Nugent, J.M. Roney, Status of the hadronic τ decay determination of |V us |. Nucl. Phys. Proc. Suppl. 189, 175–180 (2009). arXiv:0906.1386 [hep-ph]
M. Beneke, M. Jamin, α s and the τ hadronic width: fixed-order, contour-improved and higher-order perturbation theory. J. High Energy Phys. 09, 044 (2008). arXiv:0806.3156 [hep-ph]
I. Caprini, J. Fischer, α s from τ decays: contour-improved versus fixed-order summation in a new QCD perturbation expansion. Eur. Phys. J. C 64, 35–45 (2009). arXiv:0906.5211 [hep-ph]
S. Menke, On the determination of α s from hadronic τ decays with contour-improved, fixed order and renormalon-chain perturbation theory. arXiv:0904.1796 [hep-ph]
P.A. Boyle et al. (RBC/UKQCD 10), K→π form factors with reduced model dependence. Eur. Phys. J. C 69, 159–167 (2010). arXiv:1004.0886 [hep-lat]
P.A. Boyle et al. (RBC/UKQCD 07), K l3 semileptonic form factor from 2+1 flavour lattice QCD. Phys. Rev. Lett. 100, 141601 (2008). arXiv:0710.5136 [hep-lat]
V. Lubicz, F. Mescia, L. Orifici, S. Simula, C. Tarantino (ETM 10D), Improved analysis of the scalar and vector form factors of kaon semileptonic decays with N f =2 twisted-mass fermions. PoS LAT2010, 316 (2010). arXiv:1012.3573 [hep-lat]
V. Lubicz, F. Mescia, S. Simula, C. Tarantino (ETM 09A), K→πℓν semileptonic form factors from two-flavor lattice QCD. Phys. Rev. D 80, 111502 (2009). arXiv:0906.4728 [hep-lat]
D. Brömmel et al. (QCDSF 07), Kaon semileptonic decay form factors from N f =2 non-perturbatively O(a)-improved Wilson fermions. PoS LAT2007, 364 (2007). arXiv:0710.2100 [hep-lat]
C. Dawson, T. Izubuchi, T. Kaneko, S. Sasaki, A. Soni (RBC 06), Vector form factor in K l3 semileptonic decay with two flavors of dynamical domain-wall quarks. Phys. Rev. D 74, 114502 (2006). hep-ph/0607162
N. Tsutsui et al. (JLQCD 05), Kaon semileptonic decay form factors in two-flavor QCD. PoS LAT2005, 357 (2006). hep-lat/0510068
M. Ademollo, R. Gatto, Nonrenormalization theorem for the strangeness violating vector currents. Phys. Rev. Lett. 13, 264–265 (1964)
G. Furlan, F. Lannoy, C. Rossetti, G. Segré, Symmetry-breaking corrections to weak vector currents. Nuovo Cimento 38, 1747 (1965)
J. Gasser, H. Leutwyler, Low-energy expansion of meson form factors. Nucl. Phys. B 250, 517–538 (1985)
D. Becirevic, G. Martinelli, G. Villadoro, The Ademollo-Gatto theorem for lattice semileptonic decays. Phys. Lett. B 633, 84–88 (2006). hep-lat/0508013
J.M. Flynn, C.T. Sachrajda (RBC 08), SU(2) chiral perturbation theory for Kl3 decay amplitudes. Nucl. Phys. B 812, 64–80 (2009). arXiv:0809.1229 [hep-ph]
F. Farchioni, G. Herdoiza, K. Jansen, M. Petschlies, C. Urbach et al. (ETM 10E), Pseudoscalar decay constants from N f =2+1+1 twisted mass lattice QCD. PoS LAT2010, 128 (2010). arXiv:1012.0200 [hep-lat]
A. Bazavov et al. (MILC 10), Results for light pseudoscalar mesons. PoS LAT2010, 074 (2010). arXiv:1012.0868 [hep-lat]
J. Noaki et al. (JLQCD/TWQCD 09A), Chiral properties of light mesons with N f =2+1 overlap fermions. PoS LAT2009, 096 (2009). arXiv:0910.5532 [hep-lat]
C. Aubin, J. Laiho, R.S. Van de Water (Aubin 08), Light pseudoscalar meson masses and decay constants from mixed action lattice QCD. PoS LAT2008, 105 (2008). arXiv:0810.4328 [hep-lat]
Y. Kuramashi (PACS-CS 08A), PACS-CS results for 2+1 flavor lattice QCD simulation on and off the physical point. PoS LAT2008, 018 (2008). arXiv:0811.2630 [hep-lat]
E. Follana, C.T.H. Davies, G.P. Lepage, J. Shigemitsu (HPQCD/UKQCD 07), High precision determination of the π, K, D and D s decay constants from lattice QCD. Phys. Rev. Lett. 100, 062002 (2008). arXiv:0706.1726 [hep-lat]
S.R. Beane, P.F. Bedaque, K. Orginos, M.J. Savage (NPLQCD 06), f K /f π in full QCD with domain wall valence quarks. Phys. Rev. D 75, 094501 (2007). hep-lat/0606023
B. Blossier et al. (ETM 09), Pseudoscalar decay constants of kaon and D-mesons from N f =2 twisted mass Lattice QCD. J. High Energy Phys. 07, 043 (2009). arXiv:0904.0954 [hep-lat]
G. Schierholz et al. (QCDSF/UKQCD 07), Probing the chiral limit with clover fermions I: The meson sector, talk given at Lattice 2007, Regensburg, Germany, PoS LAT2007, 133. http://www.physik.uni-regensburg.de/lat07/hevea/schierholz.pdf
H. Leutwyler, M. Roos (LR 84), Determination of the elements V us and V ud of the Kobayashi-Maskawa matrix. Z. Phys. C 25, 91 (1984)
P. Post, K. Schilcher, K l3 form factors at order p 6 in chiral perturbation theory. Eur. Phys. J. C 25, 427–443 (2002). hep-ph/0112352
J. Bijnens, P. Talavera, K l3 decays in chiral perturbation theory. Nucl. Phys. B 669, 341–362 (2003). hep-ph/0303103
M. Jamin, J.A. Oller, A. Pich, Order p 6 chiral couplings from the scalar Kπ form factor. J. High Energy Phys. 02, 047 (2004). hep-ph/0401080
V. Cirigliano et al., The Green function and SU(3) breaking in K l3 decays. J. High Energy Phys. 04, 006 (2005). hep-ph/0503108
A. Kastner, H. Neufeld, The K l3 scalar form factors in the Standard Model. Eur. Phys. J. C 57, 541–556 (2008). arXiv:0805.2222 [hep-ph]
V. Bernard, M. Oertel, E. Passemar, J. Stern, Dispersive representation and shape of the K ℓ3 form factors: robustness. Phys. Rev. D 80, 034034 (2009). arXiv:0903.1654 [hep-ph]
V. Bernard, E. Passemar, Chiral extrapolation of the strangeness changing Kπ form factor. J. High Energy Phys. 04, 001 (2010). arXiv:0912.3792 [hep-ph]
E. Passemar, Dispersive approach to K ℓ3 form factors, in NA62 Physics Handbook Workshop (CERN 2009) (2009)
E. Passemar, Precision SM calculations and theoretical interests beyond the SM in K ℓ2 and K ℓ3 decays. PoS KAON09, 024 (2009). arXiv:1003.4696 [hep-ph]
S. Di Vita et al., Vector and scalar form factors for K- and D-meson semileptonic decays from twisted mass fermions with N f =2. PoS LAT2009, 257 (2009). arXiv:0910.4845 [hep-ph]
D. Becirevic et al. (SPQcdR 04), The K→π vector form factor at zero momentum transfer on the lattice. Nucl. Phys. B 705, 339–362 (2005). hep-ph/0403217
R. Kowalewski, T. Mannel, Determination of V cb and V ub . J. Phys. G 37, 075021 (2010). Review of Particle Physics, p. 1014
M.E. Fisher, V. Privman, First-order transitions breaking O(n) symmetry: Finite-size scaling. Phys. Rev. B 32, 447–464 (1985)
E. Brezin, J. Zinn-Justin, Finite size effects in phase transitions. Nucl. Phys. B 257, 867 (1985)
J. Gasser, H. Leutwyler, Light quarks at low temperatures. Phys. Lett. B 184, 83 (1987)
J. Gasser, H. Leutwyler, Thermodynamics of chiral symmetry. Phys. Lett. B 188, 477 (1987)
J. Gasser, H. Leutwyler, Spontaneously broken symmetries: effective Lagrangians at finite volume. Nucl. Phys. B 307, 763 (1988)
P. Hasenfratz, H. Leutwyler, Goldstone boson related finite size effects in field theory and critical phenomena with O(N) symmetry. Nucl. Phys. B 343, 241–284 (1990)
G. Colangelo, J. Gasser, H. Leutwyler (CGL 01), ππ scattering. Nucl. Phys. B 603, 125–179 (2001). hep-ph/0103088
F.C. Hansen, Finite size effects in spontaneously broken SU(N)×SU(N) theories. Nucl. Phys. B 345, 685–708 (1990)
F.C. Hansen, H. Leutwyler, Charge correlations and topological susceptibility in QCD. Nucl. Phys. B 350, 201–227 (1991)
H. Leutwyler, A.V. Smilga, Spectrum of Dirac operator and role of winding number in QCD. Phys. Rev. D 46, 5607–5632 (1992)
P.H. Damgaard, M.C. Diamantini, P. Hernandez, K. Jansen, Finite-size scaling of meson propagators. Nucl. Phys. B 629, 445–478 (2002). hep-lat/0112016
P.H. Damgaard, P. Hernandez, K. Jansen, M. Laine, L. Lellouch, Finite-size scaling of vector and axial current correlators. Nucl. Phys. B 656, 226–238 (2003). hep-lat/0211020
S. Aoki, H. Fukaya, Chiral perturbation theory in a theta vacuum. Phys. Rev. D 81, 034022 (2010). arXiv:0906.4852 [hep-lat]
F. Bernardoni, P.H. Damgaard, H. Fukaya, P. Hernandez, Finite volume scaling of Pseudo Nambu–Goldstone Bosons in QCD. J. High Energy Phys. 10, 008 (2008). arXiv:0808.1986 [hep-lat]
P.H. Damgaard, H. Fukaya, The chiral condensate in a finite volume. J. High Energy Phys. 01, 052 (2009). arXiv:0812.2797 [pdf]
H. Leutwyler, Energy levels of light quarks confined to a box. Phys. Lett. B 189, 197 (1987)
P. Hasenfratz, The QCD rotator in the chiral limit. Nucl. Phys. B 828, 201–214 (2010). arXiv:0909.3419 [hep-th]
F. Niedermayer, C. Weiermann, The rotator spectrum in the δ-regime of the O(n) effective field theory in 3 and 4 dimensions. Nucl. Phys. B 842, 248–263 (2011). arXiv:1006.5855 [hep-lat]
M. Weingart, The QCD rotator with a light quark mass. arXiv:1006.5076 [hep-lat]
A. Hasenfratz, P. Hasenfratz, F. Niedermayer, D. Hierl, A. Schafer, First results in QCD with 2+1 light flavors using the fixed-point action. PoS LAT2006, 178 (2006). hep-lat/0610096
W. Bietenholz et al. (QCDSF 10), Pion in a box. Phys. Lett. B 687, 410–414 (2010). arXiv:1002.1696 [hep-lat]
P. Di Vecchia, G. Veneziano, Chiral dynamics in the large N limit. Nucl. Phys. B 171, 253 (1980)
Y.-Y. Mao, T.-W. Chiu (TWQCD 09), Topological susceptibility to the one-loop order in chiral perturbation theory. Phys. Rev. D 80, 034502 (2009). arXiv:0903.2146 [hep-lat]
L. Giusti, M. Lüscher (CERN 08), Chiral symmetry breaking and the Banks–Casher relation in lattice QCD with Wilson quarks. J. High Energy Phys. 03, 013 (2009). arXiv:0812.3638 [hep-lat]
T. Banks, A. Casher, Chiral symmetry breaking in confining theories. Nucl. Phys. B 169, 103 (1980)
E.V. Shuryak, J.J.M. Verbaarschot, Random matrix theory and spectral sum rules for the Dirac operator in QCD. Nucl. Phys. A 560, 306–320 (1993). hep-th/9212088
J.J.M. Verbaarschot, I. Zahed, Spectral density of the QCD Dirac operator near zero virtuality. Phys. Rev. Lett. 70, 3852–3855 (1993). hep-th/9303012
J.J.M. Verbaarschot, The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way. Phys. Rev. Lett. 72, 2531–2533 (1994). hep-th/9401059
J.J.M. Verbaarschot, T. Wettig, Random matrix theory and chiral symmetry in QCD. Annu. Rev. Nucl. Part. Sci. 50, 343–410 (2000). hep-ph/0003017
S.M. Nishigaki, P.H. Damgaard, T. Wettig, Smallest Dirac eigenvalue distribution from random matrix theory. Phys. Rev. D 58, 087704 (1998). hep-th/9803007
P.H. Damgaard, S.M. Nishigaki, Distribution of the k-th smallest Dirac operator eigenvalue. Phys. Rev. D 63, 045012 (2001). hep-th/0006111
F. Basile, G. Akemann, Equivalence of QCD in the epsilon-regime and chiral random matrix theory with or without chemical potential. J. High Energy Phys. 12, 043 (2007). arXiv:0710.0376 [hep-th]
G. Akemann, P.H. Damgaard, J.C. Osborn, K. Splittorff, A new chiral two-matrix theory for Dirac spectra with imaginary chemical potential. Nucl. Phys. B 766, 34–67 (2007). hep-th/0609059
C. Lehner, S. Hashimoto, T. Wettig, The epsilon expansion at next-to-next-to-leading order with small imaginary chemical potential. J. High Energy Phys. 06, 028 (2010). arXiv:1004.5584 [hep-lat]
C. Lehner, J. Bloch, S. Hashimoto, T. Wettig, Geometry dependence of RMT-based methods to extract the low-energy constants Sigma and F. arXiv:1101.5576 [hep-lat]
L. Del Debbio, L. Giusti, M. Lüscher, R. Petronzio, N. Tantalo (CERN-TOV 05), Stability of lattice QCD simulations and the thermodynamic limit. J. High Energy Phys. 02, 011 (2006). hep-lat/0512021
H. Fukaya et al., Two-flavor lattice QCD in the epsilon-regime and chiral random matrix theory. Phys. Rev. D 76, 054503 (2007). arXiv:0705.3322 [hep-lat]
C.B. Lang, P. Majumdar, W. Ortner, The condensate for two dynamical chirally improved quarks in QCD. Phys. Lett. B 649, 225–229 (2007). hep-lat/0611010
T. DeGrand, Z. Liu, S. Schaefer, Quark condensate in two-flavor QCD. Phys. Rev. D 74, 094504 (2006). hep-lat/0608019
P. Hasenfratz et al., 2+1 Flavor QCD simulated in the epsilon-regime in different topological sectors. J. High Energy Phys. 11, 100 (2009). arXiv:0707.0071 [hep-lat]
T. DeGrand, S. Schaefer, Parameters of the lowest order chiral Lagrangian from fermion eigenvalues. Phys. Rev. D 76, 094509 (2007). arXiv:0708.1731 [hep-lat]
J.F. Donoghue, J. Gasser, H. Leutwyler, The decay of a light Higgs boson. Nucl. Phys. B 343, 341–368 (1990)
J. Bijnens, G. Colangelo, P. Talavera (BCT 98), The vector and scalar form factors of the pion to two loops. J. High Energy Phys. 05, 014 (1998). hep-ph/9805389
R. Frezzotti, V. Lubicz, S. Simula (ETM 08), Electromagnetic form factor of the pion from twisted-mass lattice QCD at N f =2. Phys. Rev. D 79, 074506 (2009). arXiv:0812.4042 [hep-lat]
T. Kaneko et al. (JLQCD/TWQCD 08), Pion vector and scalar form factors with dynamical overlap quarks. PoS LAT2008, 158 (2008). arXiv:0810.2590 [hep-lat]
R. Baron et al. (ETM 09C), Light meson physics from maximally twisted mass lattice QCD. J. High Energy Phys. 08, 097 (2010). arXiv:0911.5061 [hep-lat]
J. Gasser, C. Haefeli, M.A. Ivanov, M. Schmid, Integrating out strange quarks in ChPT. Phys. Lett. B 652, 21–26 (2007). arXiv:0706.0955 [hep-ph]
J. Gasser, C. Haefeli, M.A. Ivanov, M. Schmid, Integrating out strange quarks in ChPT: terms at order p 6. Phys. Lett. B 675, 49–53 (2009). arXiv:0903.0801 [hep-ph]
H. Fukaya et al. (JLQCD/TWQCD 10), Determination of the chiral condensate from QCD Dirac spectrum on the lattice. Phys. Rev. D 83, 074501 (2011). arXiv:1012.4052 [hep-lat]
H. Fukaya et al. (JLQCD 09), Determination of the chiral condensate from 2+1-flavor lattice QCD. Phys. Rev. Lett. 104, 122002 (2010). arXiv:0911.5555 [hep-lat]
T.-W. Chiu, T.-H. Hsieh, P.-K. Tseng (TWQCD 08), Topological susceptibility in 2+1 flavors lattice QCD with domain-wall fermions. Phys. Lett. B 671, 135–138 (2009). arXiv:0810.3406 [hep-lat]
T.W. Chiu et al. (JLQCD/TWQCD 08B), Topological susceptibility in (2+1)-flavor lattice QCD with overlap fermion. PoS LAT2008, 072 (2008). arXiv:0810.0085 [hep-lat]
F. Bernardoni, P. Hernandez, N. Garron, S. Necco, C. Pena (Bernardoni 10), Probing the chiral regime of N f =2 QCD with mixed actions. Phys. Rev. D 83, 054503 (2011). arXiv:1008.1870 [hep-lat]
S. Aoki et al. (JLQCD/TWQCD 07A), Topological susceptibility in two-flavor lattice QCD with exact chiral symmetry. Phys. Lett. B 665, 294–297 (2008). arXiv:0710.1130 [hep-lat]
K. Jansen, A. Shindler (ETM 09B), The epsilon regime of chiral perturbation theory with Wilson-type fermions. PoS LAT2009, 070 (2009). arXiv:0911.1931 [hep-lat]
A. Hasenfratz, R. Hoffmann, S. Schaefer (HHS 08), Low energy chiral constants from epsilon-regime simulations with improved Wilson fermions. Phys. Rev. D 78, 054511 (2008). arXiv:0806.4586 [hep-lat]
H. Fukaya et al. (JLQCD/TWQCD 07), Lattice study of meson correlators in the epsilon-regime of two-flavor QCD. Phys. Rev. D 77, 074503 (2008). arXiv:0711.4965 [hep-lat]
R. Baron et al. (ETM 11), Light hadrons from N f =2+1+1 dynamical twisted mass fermions. PoS LAT2010, 123 (2010). arXiv:1101.0518 [hep-lat]
P.A. Boyle et al. (RBC/UKQCD 08A), The pion’s electromagnetic form factor at small momentum transfer in full lattice QCD. J. High Energy Phys. 07, 112 (2008). arXiv:0804.3971 [hep-lat]
G. Colangelo, S. Dürr (CD 03), The pion mass in finite volume. Eur. Phys. J. C 33, 543–553 (2004). hep-lat/0311023
S. Aoki et al. (JLQCD/TWQCD 09), Pion form factors from two-flavor lattice QCD with exact chiral symmetry. Phys. Rev. D 80, 034508 (2009). arXiv:0905.2465 [hep-lat]
S. Dürr, \(M_{\pi}^{2}\) versus m q : Comparing CP-PACS and UKQCD data to chiral perturbation theory. Eur. Phys. J. C 29, 383–395 (2003). hep-lat/0208051
L. Del Debbio, L. Giusti, M. Lüscher, R. Petronzio, N. Tantalo (CERN-TOV 06), QCD with light Wilson quarks on fine lattices (I): first experiences and physics results. J. High Energy Phys. 02, 056 (2007). hep-lat/0610059
N.H. Fuchs, H. Sazdjian, J. Stern, How to probe the scale of (anti-q q) in chiral perturbation theory. Phys. Lett. B 269, 183–188 (1991)
J. Stern, H. Sazdjian, N.H. Fuchs, What pi–pi scattering tells us about chiral perturbation theory. Phys. Rev. D 47, 3814–3838 (1993). hep-ph/9301244
S. Descotes-Genon, L. Girlanda, J. Stern, Paramagnetic effect of light quark loops on chiral symmetry breaking. J. High Energy Phys. 01, 041 (2000). hep-ph/9910537
V. Bernard, S. Descotes-Genon, G. Toucas, Chiral dynamics with strange quarks in the light of recent lattice simulations. arXiv:1009.5066 [hep-ph]
F.D.R. Bonnet, R.G. Edwards, G.T. Fleming, R. Lewis, D.G. Richards (LHP 04), Lattice computations of the pion form factor. Phys. Rev. D 72, 054506 (2005). hep-lat/0411028
D. Brommel et al. (QCDSF/UKQCD 06A), The pion form factor from lattice QCD with two dynamical flavours. Eur. Phys. J. C 51, 335–345 (2007). hep-lat/0608021
S.R. Amendolia et al., A measurement of the space-like pion electromagnetic form factor. Nucl. Phys. B 277, 168 (1986)
J. Bijnens, N. Danielsson, T.A. Lähde, Three-flavor partially quenched chiral perturbation theory at NNLO for meson masses and decay constants. Phys. Rev. D 73, 074509 (2006). hep-lat/0602003
J. Bijnens, Status of strong ChPT. PoS EFT09, 022 (2009). arXiv:0904.3713 [hep-ph]
E. Shintani et al. (JLQCD 08A), S-parameter and pseudo-Nambu–Goldstone boson mass from lattice QCD. Phys. Rev. Lett. 101, 242001 (2008). arXiv:0806.4222 [hep-lat]
G.C. Branco, L. Lavoura, J.P. Silva, CP Violation, Int. Ser. Monogr. Phys., vol. 103 (Springer, Berlin, 1999), p. 536
G. Buchalla, A.J. Buras, M.E. Lautenbacher, Weak decays beyond leading logarithms. Rev. Mod. Phys. 68, 1125–1144 (1996). hep-ph/9512380
A.J. Buras, Weak Hamiltonian, CP violation and rare decays, in Les Houches 1997, Probing the Standard Model of Particle Interactions, pt. 1 (1997), pp. 281–539. hep-ph/9806471
T. Inami, C.S. Lim, Effects of superheavy quarks and leptons in low-energy weak processes \(K_{L}\to\mu\bar{\mu}\), \(K^{+}\to\pi^{+}\nu\bar{\nu}\) and \(K^{0}\leftrightarrow\bar{K}^{0}\). Prog. Theor. Phys. 65, 297 (1981)
C. Aubin, J. Laiho, R.S. Van de Water (Aubin 09), The neutral kaon mixing parameter B K from unquenched mixed-action lattice QCD. Phys. Rev. D 81, 014507 (2010). arXiv:0905.3947 [hep-lat]
J. Brod, M. Gorbahn, ε K at next-to-next-to-leading order: The charm-top-quark contribution. Phys. Rev. D 82, 094026 (2010). arXiv:1007.0684 [hep-ph]
U. Nierste, private communication, 2010
K. Anikeev et al., B physics at the Tevatron: Run II and beyond. hep-ph/0201071
U. Nierste, Three lectures on meson mixing and CKM phenomenology, in Dubna 2008, Heavy Quark Physics HQP08 (2008), pp. 1–39. arXiv:0904.1869 [hep-ph]
A.J. Buras, D. Guadagnoli, Correlations among new CP violating effects in ΔF=2 observables. Phys. Rev. D 78, 033005 (2008). arXiv:0805.3887 [hep-ph]
A.J. Buras, D. Guadagnoli, G. Isidori, On ε K beyond lowest order in the operator product expansion. Phys. Lett. B 688, 309–313 (2010). arXiv:1002.3612 [hep-ph]
D. Becirevic et al., \(K^{0} \bar{K}^{0}\) mixing with Wilson fermions without subtractions. Phys. Lett. B 487, 74–80 (2000). hep-lat/0005013
P. Dimopoulos et al. (ALPHA 06), A precise determination of B K in quenched QCD. Nucl. Phys. B 749, 69–108 (2006). hep-ph/0601002
P.H. Ginsparg, K.G. Wilson, A remnant of chiral symmetry on the lattice. Phys. Rev. D 25, 2649 (1982)
M. Della Morte et al. (ALPHA 04), Computation of the strong coupling in QCD with two dynamical flavours. Nucl. Phys. B 713, 378–406 (2005). hep-lat/0411025
S. Aoki et al. (JLQCD 08), B K with two flavors of dynamical overlap fermions. Phys. Rev. D 77, 094503 (2008). arXiv:0801.4186 [hep-lat]
J. Kim, C. Jung, H.-J. Kim, W. Lee, S.R. Sharpe (SWME 11), Finite volume effects in B K with improved staggered fermions. arXiv:1101.2685 [hep-lat]
Y. Aoki et al. (RBC/UKQCD 10B), Continuum limit of B K from 2+1 flavor domain wall QCD. arXiv:1012.4178 [hep-lat]
T. Bae et al. (SWME 10), B K using HYP-smeared staggered fermions in N f =2+1 unquenched QCD. Phys. Rev. D 82, 114509 (2010). arXiv:1008.5179 [hep-lat]
D.J. Antonio et al. (RBC/UKQCD 07A), Neutral kaon mixing from 2+1 flavor domain wall QCD. Phys. Rev. Lett. 100, 032001 (2008). hep-ph/0702042
E. Gamiz et al. (HPQCD/UKQCD 06), Unquenched determination of the kaon parameter B K from improved staggered fermions. Phys. Rev. D 73, 114502 (2006). hep-lat/0603023
M. Constantinou et al. (ETM 10A), BK-parameter from N f =2 twisted mass lattice QCD. Phys. Rev. D 83, 014505 (2011). arXiv:1009.5606 [hep-lat]
Y. Aoki et al. (RBC 04), Lattice QCD with two dynamical flavors of domain wall fermions. Phys. Rev. D 72, 114505 (2005). hep-lat/0411006
J.M. Flynn, F. Mescia, A.S.B. Tariq (UKQCD 04), Sea quark effects in B K from N f =2 clover-improved Wilson fermions. J. High Energy Phys. 11, 049 (2004). hep-lat/0406013
A. Hasenfratz, F. Knechtli, Flavor symmetry and the static potential with hypercubic blocking. Phys. Rev. D 64, 034504 (2001). hep-lat/0103029
Y. Aoki et al., Non-perturbative renormalization of quark bilinear operators and B K using domain wall fermions. Phys. Rev. D 78, 054510 (2008). arXiv:0712.1061 [hep-lat]
V. Bertone et al. (ETM 09D), Kaon oscillations in the Standard Model and beyond using N f =2 dynamical quarks. PoS LAT2009, 258 (2009). arXiv:0910.4838 [hep-lat]
P. Dimopoulos, H. Simma, A. Vladikas (ALPHA 09), Quenched B K -parameter from Osterwalder-Seiler tmQCD quarks and mass-splitting discretization effects. J. High Energy Phys. 07, 007 (2009). arXiv:0902.1074 [hep-lat]
Y. Nakamura, S. Aoki, Y. Taniguchi, T. Yoshie (CP-PACS 08), Precise determination of B K and light quark masses in quenched domain-wall QCD. Phys. Rev. D 78, 034502 (2008). arXiv:0803.2569 [hep-lat]
P. Dimopoulos et al. (ALPHA 07), Flavour symmetry restoration and kaon weak matrix elements in quenched twisted mass QCD. Nucl. Phys. B 776, 258–285 (2007). hep-lat/0702017
S. Aoki et al. (JLQCD 97), Kaon B parameter from quenched lattice QCD. Phys. Rev. Lett. 80, 5271–5274 (1998). hep-lat/9710073
K.G. Wilson, Confinement of quarks. Phys. Rev. D 10, 2445–2459 (1974)
M. Lüscher, P. Weisz, On-shell improved lattice gauge theories. Commun. Math. Phys. 97, 59 (1985)
Y. Iwasaki, Renormalization group analysis of lattice theories and improved lattice action: two-dimensional nonlinear O(N) sigma model. Nucl. Phys. B 258, 141–156 (1985)
T. Takaishi, Heavy quark potential and effective actions on blocked configurations. Phys. Rev. D 54, 1050–1053 (1996)
P. de Forcrand et al., Renormalization group flow of SU(3) lattice gauge theory: numerical studies in a two coupling space. Nucl. Phys. B 577, 263–278 (2000). hep-lat/9911033
G.P. Lepage, P.B. Mackenzie, On the viability of lattice perturbation theory. Phys. Rev. D 48, 2250–2264 (1993). hep-lat/9209022
M. Lüscher, S. Sint, R. Sommer, P. Weisz, U. Wolff, Non-perturbative O(a) improvement of lattice QCD. Nucl. Phys. B 491, 323–343 (1997). hep-lat/9609035
L. Susskind, Lattice fermions. Phys. Rev. D 16, 3031–3039 (1977)
K. Orginos, D. Toussaint, R.L. Sugar (MILC 99), Variants of fattening and flavor symmetry restoration. Phys. Rev. D 60, 054503 (1999). hep-lat/9903032
E. Follana et al. (HPQCD 06), Highly improved staggered quarks on the lattice, with applications to charm physics. Phys. Rev. D 75, 054502 (2007). hep-lat/0610092
M. Creutz, Why rooting fails. PoS LAT2007, 007 (2007). arXiv:0708.1295 [hep-lat]
P. Hasenfratz, V. Laliena, F. Niedermayer, The index theorem in QCD with a finite cut-off. Phys. Lett. B 427, 125–131 (1998). hep-lat/9801021
M. Lüscher, Exact chiral symmetry on the lattice and the Ginsparg–Wilson relation. Phys. Lett. B 428, 342–345 (1998). hep-lat/9802011
D.B. Kaplan, A Method for simulating chiral fermions on the lattice. Phys. Lett. B 288, 342–347 (1992). hep-lat/9206013
V. Furman, Y. Shamir, Axial symmetries in lattice QCD with Kaplan fermions. Nucl. Phys. B 439, 54–78 (1995). hep-lat/9405004
H. Neuberger, Exactly massless quarks on the lattice. Phys. Lett. B 417, 141–144 (1998). hep-lat/9707022
P. Hasenfratz et al., The construction of generalized Dirac operators on the lattice. Int. J. Mod. Phys. C 12, 691–708 (2001). hep-lat/0003013
P. Hasenfratz, S. Hauswirth, T. Jorg, F. Niedermayer, K. Holland, Testing the fixed-point QCD action and the construction of chiral currents. Nucl. Phys. B 643, 280–320 (2002). hep-lat/0205010
C. Gattringer, A new approach to Ginsparg–Wilson fermions. Phys. Rev. D 63, 114501 (2001). hep-lat/0003005
A. Hasenfratz, R. Hoffmann, S. Schaefer, Hypercubic smeared links for dynamical fermions. J. High Energy Phys. 05, 029 (2007). hep-lat/0702028
C. Morningstar, M.J. Peardon, Analytic smearing of SU(3) link variables in lattice QCD. Phys. Rev. D 69, 054501 (2004). hep-lat/0311018
S. Dürr et al. (BMW 08A), Scaling study of dynamical smeared-link clover fermions. Phys. Rev. D 79, 014501 (2009). arXiv:0802.2706 [hep-lat]
S. Capitani, S. Dürr, C. Hoelbling, Rationale for UV-filtered clover fermions. J. High Energy Phys. 11, 028 (2006). hep-lat/0607006
R. Sommer, A new way to set the energy scale in lattice gauge theories and its applications to the static force and α s in SU(2) Yang-Mills theory. Nucl. Phys. B 411, 839–854 (1994). hep-lat/9310022
C.W. Bernard et al., The static quark potential in three flavor QCD. Phys. Rev. D 62, 034503 (2000). hep-lat/0002028
R. Arthur, P.A. Boyle (RBC Collaboration), Step scaling with off-shell renormalisation. arXiv:1006.0422 [hep-lat]
C. Bernard et al. (MILC 07), Status of the MILC light pseudoscalar meson project. PoS LAT2007, 090 (2007). arXiv:0710.1118 [hep-lat]
G. Colangelo, S. Dürr, C. Haefeli (CDH 05), Finite volume effects for meson masses and decay constants. Nucl. Phys. B 721, 136–174 (2005). hep-lat/0503014
G. Herdoiza, private communication, 2011
R. Brower, S. Chandrasekharan, J.W. Negele, U. Wiese, QCD at fixed topology. Phys. Lett. B 560, 64–74 (2003). hep-lat/0302005
O. Bär, S. Necco, S. Schaefer, The epsilon regime with Wilson fermions. J. High Energy Phys. 03, 006 (2009). arXiv:0812.2403 [hep-lat]
T. Bunton, F.-J. Jiang, B. Tiburzi, Extrapolations of lattice meson form factors. Phys. Rev. D 74, 034514 (2006). hep-lat/0607001
B. Borasoy, R. Lewis, Volume dependences from lattice chiral perturbation theory. Phys. Rev. D 71, 014033 (2005). hep-lat/0410042
S. Aoki, H. Fukaya, S. Hashimoto, T. Onogi, Finite volume QCD at fixed topological charge. Phys. Rev. D 76, 054508 (2007). arXiv:0707.0396 [hep-lat]
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FLAG working group of FLAVIANET., Colangelo, G., Dürr, S. et al. Review of lattice results concerning low-energy particle physics. Eur. Phys. J. C 71, 1695 (2011). https://doi.org/10.1140/epjc/s10052-011-1695-1
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DOI: https://doi.org/10.1140/epjc/s10052-011-1695-1