Abstract
Several lattice collaborations performing simulations with 2+1 light dynamical quarks have experienced difficulties in fitting their data with standard N f = 3 chiral expansions at next-to-leading order, yielding low values of the quark condensate and/ or the decay constant in the N f = 3 chiral limit. A reordering of these expansions seems required to analyse these data in a consistent way. We discuss such a reordering, known as Resummed Chiral Perturbation Theory, in the case of pseudoscalar masses and decay constants, pion and kaon electromagnetic form factors and K ℓ3 form factors. We show that it provides a good fit of the recent results of two lattice collaborations (PACS-CS and RBC/UKQCD). We describe the emerging picture for the pattern of chiral symmetry breaking, marked by a strong dependence of the observables on the strange quark mass and thus a significant difference between chiral symmetry breaking in the N f = 2 and N f =3 chiral limits. We discuss the consequences for the ratio of decay constants F K /F π and the K ℓ3 form factor at vanishing momentum transfer.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. Gasser and H. Leutwyler, Chiral Perturbation Theory to One Loop, Ann. Phys. 158 (1984) 142 [SPIRES].
J. Gasser and H. Leutwyler, Chiral Perturbation Theory: Expansions in the Mass of the Strange Quark, Nucl. Phys. B 250 (1985) 465 [SPIRES].
PACS-CS collaboration, S. Aoki et al., 2+1 Flavor Lattice QCD toward the Physical Point, Phys. Rev. D 79 (2009) 034503 [arXiv:0807.1661] [SPIRES].
RBC -UKQCD collaboration, C. Allton et al., Physical Results from 2+1 Flavor Domain Wall QCD and SU(2) Chiral Perturbation Theory, Phys. Rev. D 78 (2008) 114509 [arXiv:0804.0473] [SPIRES].
P.A. Boyle et al., K l3 semileptonic form factor from 2+1 flavour lattice QCD, Phys. Rev. Lett. 100 (2008) 141601 [arXiv:0710.5136] [SPIRES].
P.A. Boyle et al., K→π form factors with reduced model dependence, arXiv:1004.0886 [SPIRES].
RBC collaboration, J.M. Flynn and C.T. Sachrajda, SU(2) chiral prturbation theory for K l3 decay amplitudes, Nucl. Phys. B 812 (2009) 64 [arXiv:0809.1229] [SPIRES].
C. Bernard et al., Status of the MILC light pseudoscalar meson project, PoS(LATTICE 2007)090 [arXiv:0710.1118] [SPIRES].
The MILC collaboration, A. Bazavov et al., Results from the MILC collaboration’s SU(3) chiral perturbation theory analysis, PoS(LAT2009)079 [arXiv:0910.3618] [SPIRES].
J. Bijnens, Chiral Perturbation Theory Beyond One Loop, Prog. Part. Nucl. Phys. 58 (2007) 521 [hep-ph/0604043] [SPIRES].
J. Bijnens and N. Danielsson, Electromagnetic Corrections in Partially Quenched Chiral Perturbation Theory, Phys. Rev. D 75 (2007) 014505 [hep-lat/0610127] [SPIRES].
J. Bijnens, N. Danielsson and T.A. Lahde, Three-flavor partially quenched chiral perturbation theory at NNLO for meson masses and decay constants, Phys. Rev. D 73 (2006) 074509 [hep-lat/0602003] [SPIRES].
J. Bijnens and N. Danielsson, The eta mass and NNLO three-flavor partially quenched chiral perturbation theory, Phys. Rev. D 74 (2006) 054503 [hep-lat/0606017] [SPIRES].
RBC collaboration, R. Mawhinney, NLO and NNLO chiral fits for 2+1 flavor DWF ensembles, PoS(LAT2009)081 [arXiv:0910.3194] [SPIRES].
M. Knecht, B. Moussallam, J. Stern and N.H. Fuchs, The Low-energy ππ amplitude to one and two loops, Nucl. Phys. B 457 (1995) 513 [hep-ph/9507319] [SPIRES].
B. Ananthanarayan, G. Colangelo, J. Gasser and H. Leutwyler, Roy equation analysis of ππ scattering, Phys. Rept. 353 (2001) 207 [hep-ph/0005297] [SPIRES].
G. Colangelo, J. Gasser and H. Leutwyler, The quark condensate from K e4 decays, Phys. Rev. Lett. 86 (2001) 5008 [hep-ph/0103063] [SPIRES].
S. Descotes-Genon, N.H. Fuchs, L. Girlanda and J. Stern, Analysis and interpretation of new low-energy ππ scattering data, Eur. Phys. J. C 24 (2002) 469 [hep-ph/0112088] [SPIRES].
J. Bijnens, P. Dhonte and P. Talavera, ππ scattering in three flavour ChPT, JHEP 01 (2004) 050 [hep-ph/0401039] [SPIRES].
NA48/2 collaboration, J.R. Batley et al., New high statistics measurement of K e4 decay form factors and ππ scattering phase shifts, Eur. Phys. J. C 54 (2008) 411 [SPIRES].
J.R. Batley et al., Determination of the S-wave ππ scattering lengths from a study of K ± → π±π0π0 decays, Eur. Phys. J. C 64 (2009) 589 [arXiv:0912.2165] [SPIRES].
G. Colangelo, J. Gasser and A. Rusetsky, Isospin breaking in Kl4 decays, Eur. Phys. J. C 59 (2009) 777 [arXiv:0811.0775] [SPIRES].
P. Büettiker, S. Descotes-Genon and B. Moussallam, Are-analysis of πK scattering a la Roy and Steiner, Eur. Phys. J. C 33 (2004) 409 [hep-ph/0310283] [SPIRES].
J. Bijnens, P. Dhonte and P. Talavera, πK scattering in three flavor ChPT, JHEP 05 (2004) 036 [hep-ph/0404150] [SPIRES].
S. Descotes-Genon, ππ and πK scatterings in three-flavour resummed chiral perturbation theory, J. Phys. Conf. Ser. 110 (2008) 052012 [arXiv:0710.1696] [SPIRES].
J. Bijnens and I. Jemos, Determination of Low Energy Constants and testing Chiral Perturbation Theory at order p 6 (NNLO), PoS(CD09)087 [arXiv:0909.4477] [SPIRES].
S. Descotes-Genon, L. Girlanda and J. Stern, Paramagnetic effect of light quark loops on chiral symmetry breaking, JHEP 01 (2000) 041 [hep-ph/9910537] [SPIRES].
S. Descotes-Genon and J. Stern, Vacuum fluctuations of anti-q q and values of low-energy constants, Phys. Lett. B 488 (2000) 274 [hep-ph/0007082] [SPIRES].
B. Moussallam, N f dependence of the quark condensate from a chiral sum rule, Eur. Phys. J. C 14 (2000) 111 [hep-ph/9909292] [SPIRES].
B. Moussallam, Flavor stability of the chiral vacuum and scalar meson dynamics, JHEP 08 (2000) 005 [hep-ph/0005245] [SPIRES].
S. Descotes-Genon, Zweig rule violation in the scalar sector and values of low-energy constants, JHEP 03 (2001) 002 [hep-ph/0012221] [SPIRES].
U.-G. Meißner, Chiral dynamics with strange quarks: Mysteries and opportunities, Phys. Scripta T 99 (2002) 68 [hep-ph/0201078] [SPIRES].
U.-G. Meißner, Chiral dynamics with strange quarks, AIP Conf. Proc. 717 (2004) 656 [hep-ph/0309248] [SPIRES].
V. Bernard, Chiral Perturbation Theory and Baryon Properties, Prog. Part. Nucl. Phys. 60 (2008) 82 [arXiv:0706.0312] [SPIRES].
S. Descotes-Genon, N.H. Fuchs, L. Girlanda and J. Stern, Resumming QCD vacuum fluctuations in three-flavour chiral perturbation theory, Eur. Phys. J. C 34 (2004) 201 [hep-ph/0311120] [SPIRES].
S. Dürr et al., The ratio F K /F π in QCD, Phys. Rev. D 81 (2010) 054507 [arXiv:1001.4692] [SPIRES].
S. Dürr et al., Ab-Initio Determination of Light Hadron Masses, Science 322 (2008) 1224 [arXiv:0906.3599] [SPIRES].
R. Baron et al., Light hadrons from lattice QCD with light (u,d), strange and charm dynamical quarks, JHEP 06 (2010) 111 [arXiv:1004.5284] [SPIRES].
TWQCD collaboration, J. Noaki et al., Chiral properties of light mesons with N f = 2+1 overlap fermions, PoS(LAT2009)096 [arXiv:0910.5532] [SPIRES].
S. Descotes-Genon, L. Girlanda and J. Stern, Chiral order and fluctuations in multi-flavour QCD, Eur. Phys. J. C 27 (2003) 115 [hep-ph/0207337] [SPIRES].
J. Gasser and H. Leutwyler, Low-Energy Expansion of Meson Form-Factors, Nucl. Phys. B 250 (1985) 517 [SPIRES].
J. Gasser and U.G. Meißner, Chiral expansion of pion form-factors beyond one loop, Nucl. Phys. B 357 (1991) 90 [SPIRES].
J. Bijnens and P. Talavera, Pion and kaon electromagnetic form factors, JHEP 03 (2002) 046 [hep-ph/0203049] [SPIRES].
V. Bernard and E. Passemar, Chiral Extrapolation of the Strangeness Changing K π Form Factor, JHEP 04 (2010) 001 [arXiv:0912.3792] [SPIRES].
Particle Data Group collaboration, C. Amsler et al., Review of particle physics, Phys. Lett. B 667 (2008) 1 @@@@@[SPIRES] update online at http://pdg.lbl.gov.
Flavia Net Working Group on Kaon Decays collaboration, M. Antonelli et al., Precision tests of the Standard Model with leptonic and semileptonic kaon decays, arXiv:0801.1817 [SPIRES].
M. Antonelli et al., An evaluation of |Vus| and precise tests of the Standard Model from world data on leptonic and semileptonic kaon decays, Eur. Phys. J. C 69 (2010) 399 [arXiv:1005.2323] [SPIRES].
W.J. Marciano and A. Sirlin, Improved calculation of electroweak radiative corrections and the value of V ud, Phys. Rev. Lett. 96 (2006) 032002 [hep-ph/0510099] [SPIRES].
I.S. Towner and J.C. Hardy, An improved calculation of the isospin-symmetry-breaking corrections to superallowed Fermi β decay, Phys. Rev. C 77 (2008) 025501 [arXiv:0710.3181] [SPIRES].
J.C. Hardy and I.S. Towner, Superallowed 0+ → 0+ nuclear beta decays: A new survey with precision tests of the conserved vector current hypothesis and the standard model, Phys. Rev. C 79 (2009) 055502 [arXiv:0812.1202] [SPIRES].
C.G. Callan and S.B. Treiman, Equal Time Commutators and K Meson Decays, Phys. Rev. Lett. 16 (1966) 153 [SPIRES].
J. Gasser and H. Leutwyler, Low-Energy Expansion of Meson Form-Factors, Nucl. Phys. B 250 (1985) 517 [SPIRES].
V. Bernard, M. Oertel, E. Passemar and J. Stern, K Lμ3 decay: A stringent test of right-handed quark currents, Phys. Lett. B 638 (2006) 480 [hep-ph/0603202] [SPIRES].
V. Bernard, M. Oertel, E. Passemar and J. Stern, Dispersive representation and shape of the K l3 form factors: robustness, Phys. Rev. D 80 (2009) 034034 [arXiv:0903.1654] [SPIRES].
NA48 collaboration, A. Lai et al., Measurement of K0μ3 form factors, Phys. Lett. B 647 (2007) 341 [hep-ex/0703002] [SPIRES].
KLOE collaboration, F. Ambrosino et al., Measurement of the K L→πμν form factor parameters with the KLOE detector, JHEP 12 (2007) 105 [arXiv:0710.4470] [SPIRES].
KTeV collaboration, E. Abouzaid et al., Dispersive analysis of K Lμ3 and K Le3 scalar and vector form factors using KTeV data, Phys. Rev. D 81 (2010) 052001 [arXiv:0912.1291] [SPIRES].
G. Ecker, J. Gasser, A. Pich and E. de Rafael, The Role of Resonances in Chiral Perturbation Theory, Nucl. Phys. B 321 (1989) 311 [SPIRES].
PACS-CS collaboration, S. Aoki et al., Physical Point Simulation in 2+1 Flavor Lattice QCD, Phys. Rev. D 81 (2010) 074503 [arXiv:0911.2561] [SPIRES].
T.A. Lahde and U.-G. Meißner, Improved Analysis of J/ψ Decays into a Vector Meson and Two Pseudoscalars, Phys. Rev. D 74 (2006) 034021 [hep-ph/0606133] [SPIRES].
J. Gasser, C. Haefeli, M.A. Ivanov and M. Schmid, Integrating out strange quarks in ChPT: terms at order p 6, Phys. Lett. B 675 (2009) 49 [arXiv:0903.0801] [SPIRES].
E. Scholz, private communication.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint:1009.5066
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Bernard, V., Descotes-Genon, S. & Toucas, G. Chiral dynamics with strange quarks in the light of recent lattice simulations. J. High Energ. Phys. 2011, 107 (2011). https://doi.org/10.1007/JHEP01(2011)107
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2011)107