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Borsanyi S, Fodor Z, Guenther JN, Hoelbling C, Katz SD, Lellouch L, Lippert T, Miura K, Parato L, Szabo KK, Stokes F, Toth BC, Torok C, Varnhorst L. Leading hadronic contribution to the muon magnetic moment from lattice QCD. Nature 2021; 593:51-55. [PMID: 33828303 DOI: 10.1038/s41586-021-03418-1] [Citation(s) in RCA: 57] [Impact Index Per Article: 19.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2020] [Accepted: 03/04/2021] [Indexed: 02/02/2023]
Abstract
The standard model of particle physics describes the vast majority of experiments and observations involving elementary particles. Any deviation from its predictions would be a sign of new, fundamental physics. One long-standing discrepancy concerns the anomalous magnetic moment of the muon, a measure of the magnetic field surrounding that particle. Standard-model predictions1 exhibit disagreement with measurements2 that is tightly scattered around 3.7 standard deviations. Today, theoretical and measurement errors are comparable; however, ongoing and planned experiments aim to reduce the measurement error by a factor of four. Theoretically, the dominant source of error is the leading-order hadronic vacuum polarization (LO-HVP) contribution. For the upcoming measurements, it is essential to evaluate the prediction for this contribution with independent methods and to reduce its uncertainties. The most precise, model-independent determinations so far rely on dispersive techniques, combined with measurements of the cross-section of electron-positron annihilation into hadrons3-6. To eliminate our reliance on these experiments, here we use ab initio quantum chromodynamics (QCD) and quantum electrodynamics simulations to compute the LO-HVP contribution. We reach sufficient precision to discriminate between the measurement of the anomalous magnetic moment of the muon and the predictions of dispersive methods. Our result favours the experimentally measured value over those obtained using the dispersion relation. Moreover, the methods used and developed in this work will enable further increased precision as more powerful computers become available.
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Affiliation(s)
- Sz Borsanyi
- Department of Physics, University of Wuppertal, Wuppertal, Germany
| | - Z Fodor
- Department of Physics, University of Wuppertal, Wuppertal, Germany. .,Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany. .,Department of Physics, Pennsylvania State University, University Park, PA, USA. .,Institute for Theoretical Physics, Eötvös University, Budapest, Hungary. .,Department of Physics, University of California, San Diego, La Jolla, CA, USA.
| | - J N Guenther
- Department of Physics, University of Regensburg, Regensburg, Germany.,Aix Marseille Université, Université de Toulon, CNRS, CPT, IPhU, Marseille, France
| | - C Hoelbling
- Department of Physics, University of Wuppertal, Wuppertal, Germany
| | - S D Katz
- Institute for Theoretical Physics, Eötvös University, Budapest, Hungary
| | - L Lellouch
- Aix Marseille Université, Université de Toulon, CNRS, CPT, IPhU, Marseille, France
| | - T Lippert
- Department of Physics, University of Wuppertal, Wuppertal, Germany.,Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany
| | - K Miura
- Aix Marseille Université, Université de Toulon, CNRS, CPT, IPhU, Marseille, France.,Helmholtz Institute Mainz, Mainz, Germany.,Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya, Japan
| | - L Parato
- Aix Marseille Université, Université de Toulon, CNRS, CPT, IPhU, Marseille, France
| | - K K Szabo
- Department of Physics, University of Wuppertal, Wuppertal, Germany.,Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany
| | - F Stokes
- Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany
| | - B C Toth
- Department of Physics, University of Wuppertal, Wuppertal, Germany
| | - Cs Torok
- Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany
| | - L Varnhorst
- Department of Physics, University of Wuppertal, Wuppertal, Germany.,Aix Marseille Université, Université de Toulon, CNRS, CPT, IPhU, Marseille, France
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2
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Borsanyi S, Fodor Z, Hoelbling C, Kawanai T, Krieg S, Lellouch L, Malak R, Miura K, Szabo KK, Torrero C, Toth BC. Hadronic Vacuum Polarization Contribution to the Anomalous Magnetic Moments of Leptons from First Principles. Phys Rev Lett 2018; 121:022002. [PMID: 30085700 DOI: 10.1103/physrevlett.121.022002] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2017] [Indexed: 06/08/2023]
Abstract
We compute the leading, strong-interaction contribution to the anomalous magnetic moment of the electron, muon, and tau using lattice quantum chromodynamics (QCD) simulations. Calculations include the effects of u, d, s, and c quarks and are performed directly at the physical values of the quark masses and in volumes of linear extent larger than 6 fm. All connected and disconnected Wick contractions are calculated. Continuum limits are carried out using six lattice spacings. We obtain a_{e}^{LO-HVP}=189.3(2.6)(5.6)×10^{-14}, a_{μ}^{LO-HVP}=711.1(7.5)(17.4)×10^{-10} and a_{τ}^{LO-HVP}=341.0(0.8)(3.2)×10^{-8}, where the first error is statistical and the second is systematic.
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Affiliation(s)
- Sz Borsanyi
- Department of Physics, Bergische Universität Wuppertal, Gaussstrasse 20, D-42119 Wuppertal, Germany
| | - Z Fodor
- Department of Physics, Bergische Universität Wuppertal, Gaussstrasse 20, D-42119 Wuppertal, Germany
- Institute for Theoretical Physics, Eötvös University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
- Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - C Hoelbling
- Department of Physics, Bergische Universität Wuppertal, Gaussstrasse 20, D-42119 Wuppertal, Germany
| | - T Kawanai
- Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - S Krieg
- Department of Physics, Bergische Universität Wuppertal, Gaussstrasse 20, D-42119 Wuppertal, Germany
- Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - L Lellouch
- CNRS, Aix-Marseille Université, Université de Toulon, CPT, UMR 7332, F-13288 Marseille, France
| | - R Malak
- CNRS, Aix-Marseille Université, Université de Toulon, CPT, UMR 7332, F-13288 Marseille, France
- CNRS, CEA, Maison de la Simulation, USR 3441, F-91191 Gif-sur-Yvette Cedex, France
| | - K Miura
- CNRS, Aix-Marseille Université, Université de Toulon, CPT, UMR 7332, F-13288 Marseille, France
- Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602, Japan
| | - K K Szabo
- Department of Physics, Bergische Universität Wuppertal, Gaussstrasse 20, D-42119 Wuppertal, Germany
- Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - C Torrero
- CNRS, Aix-Marseille Université, Université de Toulon, CPT, UMR 7332, F-13288 Marseille, France
| | - B C Toth
- Department of Physics, Bergische Universität Wuppertal, Gaussstrasse 20, D-42119 Wuppertal, Germany
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3
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Aoki S, Aoki Y, Bečirević D, Bernard C, Blum T, Colangelo G, Della Morte M, Dimopoulos P, Dürr S, Fukaya H, Golterman M, Gottlieb S, Hashimoto S, Heller UM, Horsley R, Jüttner A, Kaneko T, Lellouch L, Leutwyler H, Lin CJD, Lubicz V, Lunghi E, Mawhinney R, Onogi T, Pena C, Sachrajda CT, Sharpe SR, Simula S, Sommer R, Vladikas A, Wenger U, Wittig H. Review of lattice results concerning low-energy particle physics: Flavour Lattice Averaging Group (FLAG). Eur Phys J C Part Fields 2017; 77:112. [PMID: 29033670 PMCID: PMC5588406 DOI: 10.1140/epjc/s10052-016-4509-7] [Citation(s) in RCA: 82] [Impact Index Per Article: 11.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2016] [Accepted: 11/11/2016] [Indexed: 06/07/2023]
Abstract
We review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the determination of the light-quark masses, the form factor [Formula: see text], arising in the semileptonic [Formula: see text] transition at zero momentum transfer, as well as the decay constant ratio [Formula: see text] and its consequences for the CKM matrix elements [Formula: see text] and [Formula: see text]. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of [Formula: see text] and [Formula: see text] Chiral Perturbation Theory. We review the determination of the [Formula: see text] parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. The latter quantities are an addition compared to the previous review. For the heavy-quark sector, we provide results for [Formula: see text] and [Formula: see text] (also new compared to the previous review), as well as those for D- and B-meson-decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. Finally, we review the status of lattice determinations of the strong coupling constant [Formula: see text].
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Affiliation(s)
- S. Aoki
- Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto, 606-8502 Japan
| | - Y. Aoki
- Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI), Nagoya University, Nagoya, 464-8602 Japan
- Brookhaven National Laboratory, RIKEN BNL Research Center, Upton, NY 11973 USA
- High Energy Accelerator Research Organization (KEK), Tsukuba, 305-0801 Japan
| | - D. Bečirević
- Laboratoire de Physique Théorique (UMR8627), CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - C. Bernard
- Department of Physics, Washington University, Saint Louis, MO 63130 USA
| | - T. Blum
- Brookhaven National Laboratory, RIKEN BNL Research Center, Upton, NY 11973 USA
- Physics Department, University of Connecticut, Storrs, CT 06269-3046 USA
| | - G. Colangelo
- Albert Einstein Center for Fundamental Physics, Institut für Theoretische Physik, Universität Bern, Sidlerstr. 5, 3012 Bern, Switzerland
| | - M. Della Morte
- CP3-Origins and Danish IAS, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark
- IFIC (CSIC), c/ Catedrático José Beltrán, 2, 46980 Paterna, Spain
| | - P. Dimopoulos
- Centro Fermi-Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi Compendio del Viminale, Piazza del Viminiale 1, 00184 Rome, Italy
- c/o Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - S. Dürr
- University of Wuppertal, Gaußstraße 20, 42119 Wuppertal, Germany
- Jülich Supercomputing Center, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - H. Fukaya
- Department of Physics, Osaka University, Toyonaka, Osaka 560-0043 Japan
| | - M. Golterman
- Department of Physics and Astronomy, San Francisco State University, San Francisco, CA 94132 USA
| | - Steven Gottlieb
- Department of Physics, Indiana University, Bloomington, IN 47405 USA
| | - S. Hashimoto
- High Energy Accelerator Research Organization (KEK), Tsukuba, 305-0801 Japan
- School of High Energy Accelerator Science, The Graduate University for Advanced Studies (Sokendai), Tsukuba, 305-0801 Japan
| | - U. M. Heller
- American Physical Society (APS), One Research Road, Ridge, NY 11961 USA
| | - R. Horsley
- Higgs Centre for Theoretical Physics, School of Physics and Astronomy, University of Edinburgh, Edinburgh, EH9 3FD UK
| | - A. Jüttner
- School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ UK
| | - T. Kaneko
- High Energy Accelerator Research Organization (KEK), Tsukuba, 305-0801 Japan
- School of High Energy Accelerator Science, The Graduate University for Advanced Studies (Sokendai), Tsukuba, 305-0801 Japan
| | - L. Lellouch
- Centre de Physique Théorique, UMR 7332, CNRS, Aix-Marseille Université, Université de Toulon, 13288 Marseille, France
| | - H. Leutwyler
- Albert Einstein Center for Fundamental Physics, Institut für Theoretische Physik, Universität Bern, Sidlerstr. 5, 3012 Bern, Switzerland
| | - C.-J. D. Lin
- Centre de Physique Théorique, UMR 7332, CNRS, Aix-Marseille Université, Université de Toulon, 13288 Marseille, France
- Institute of Physics, National Chiao-Tung University, Hsinchu, 30010 Taiwan
| | - V. Lubicz
- Dipartimento di Matematica e Fisica, Università Roma Tre, Via della Vasca Navale 84, 00146 Rome, Italy
- Sezione di Roma Tre, INFN, Via della Vasca Navale 84, 00146 Rome, Italy
| | - E. Lunghi
- Department of Physics, Indiana University, Bloomington, IN 47405 USA
| | - R. Mawhinney
- Physics Department, Columbia University, New York, NY 10027 USA
| | - T. Onogi
- Department of Physics, Osaka University, Toyonaka, Osaka 560-0043 Japan
| | - C. Pena
- Departamento de Física Teórica, Instituto de Física Teórica UAM/CSIC, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain
| | - C. T. Sachrajda
- School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ UK
| | - S. R. Sharpe
- Physics Department, University of Washington, Seattle, WA 98195-1560 USA
| | - S. Simula
- Sezione di Roma Tre, INFN, Via della Vasca Navale 84, 00146 Rome, Italy
| | - R. Sommer
- John von Neumann Institute for Computing (NIC), DESY, Platanenallee 6, 15738 Zeuthen, Germany
| | - A. Vladikas
- Sezione di Tor Vergata, INFN, c/o Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - U. Wenger
- Albert Einstein Center for Fundamental Physics, Institut für Theoretische Physik, Universität Bern, Sidlerstr. 5, 3012 Bern, Switzerland
| | - H. Wittig
- PRISMA Cluster of Excellence, Institut für Kernphysik and Helmholtz Institute Mainz, University of Mainz, 55099 Mainz, Germany
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4
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Fodor Z, Hoelbling C, Krieg S, Lellouch L, Lippert T, Portelli A, Sastre A, Szabo KK, Varnhorst L. Up and Down Quark Masses and Corrections to Dashen's Theorem from Lattice QCD and Quenched QED. Phys Rev Lett 2016; 117:082001. [PMID: 27588847 DOI: 10.1103/physrevlett.117.082001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2016] [Indexed: 06/06/2023]
Abstract
In a previous Letter [Borsanyi et al., Phys. Rev. Lett. 111, 252001 (2013)] we determined the isospin mass splittings of the baryon octet from a lattice calculation based on N_{f}=2+1 QCD simulations to which QED effects have been added in a partially quenched setup. Using the same data we determine here the corrections to Dashen's theorem and the individual up and down quark masses. Our ensembles include 5 lattice spacings down to 0.054 fm, lattice sizes up to 6 fm, and average up-down quark masses all the way down to their physical value. For the parameter which quantifies violations to Dashen's theorem, we obtain ϵ=0.73(2)(5)(17), where the first error is statistical, the second is systematic, and the third is an estimate of the QED quenching error. For the light quark masses we obtain, m_{u}=2.27(6)(5)(4) and m_{d}=4.67(6)(5)(4) MeV in the modified minimal subtraction scheme at 2 GeV and the isospin breaking ratios m_{u}/m_{d}=0.485(11)(8)(14), R=38.2(1.1)(0.8)(1.4), and Q=23.4(0.4)(0.3)(0.4). Our results exclude the m_{u}=0 solution to the strong CP problem by more than 24 standard deviations.
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Affiliation(s)
- Z Fodor
- Department of Physics, Wuppertal University, Gaussstr. 20, D-42119 Wuppertal, Germany
- Institute for Theoretical Physics, Eötvös University, Pázmány P. sét. 1/A, H-1117 Budapest, Hungary
- IAS/JSC, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - C Hoelbling
- Department of Physics, Wuppertal University, Gaussstr. 20, D-42119 Wuppertal, Germany
| | - S Krieg
- Department of Physics, Wuppertal University, Gaussstr. 20, D-42119 Wuppertal, Germany
- IAS/JSC, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - L Lellouch
- CNRS, Aix-Marseille U., U. de Toulon, Centre de Physique Théorique, UMR 7332, F-13288 Marseille, France
| | - Th Lippert
- IAS/JSC, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - A Portelli
- CNRS, Aix-Marseille U., U. de Toulon, Centre de Physique Théorique, UMR 7332, F-13288 Marseille, France
- School of Physics & Astronomy, University of Southampton, SO17 1BJ Southampton, United Kingdom
- School of Physics & Astronomy, The University of Edinburgh, EH9 3FD Edinburgh, United Kingdom
| | - A Sastre
- Department of Physics, Wuppertal University, Gaussstr. 20, D-42119 Wuppertal, Germany
- CNRS, Aix-Marseille U., U. de Toulon, Centre de Physique Théorique, UMR 7332, F-13288 Marseille, France
| | - K K Szabo
- Department of Physics, Wuppertal University, Gaussstr. 20, D-42119 Wuppertal, Germany
- IAS/JSC, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - L Varnhorst
- Department of Physics, Wuppertal University, Gaussstr. 20, D-42119 Wuppertal, Germany
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5
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Durr S, Fodor Z, Hoelbling C, Katz SD, Krieg S, Lellouch L, Lippert T, Metivet T, Portelli A, Szabo KK, Torrero C, Toth BC, Varnhorst L. Lattice Computation of the Nucleon Scalar Quark Contents at the Physical Point. Phys Rev Lett 2016; 116:172001. [PMID: 27176514 DOI: 10.1103/physrevlett.116.172001] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2016] [Indexed: 06/05/2023]
Abstract
We present a QCD calculation of the u, d, and s scalar quark contents of nucleons based on 47 lattice ensembles with N_{f}=2+1 dynamical sea quarks, 5 lattice spacings down to 0.054 fm, lattice sizes up to 6 fm, and pion masses down to 120 MeV. Using the Feynman-Hellmann theorem, we obtain f_{ud}^{N}=0.0405(40)(35) and f_{s}^{N}=0.113(45)(40), which translates into σ_{πN}=38(3)(3) MeV, σ_{sN}=105(41)(37) MeV, and y_{N}=0.20(8)(8) for the sigma terms and the related ratio, where the first errors are statistical and the second errors are systematic. Using isospin relations, we also compute the individual up and down quark contents of the proton and neutron (results in the main text).
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Affiliation(s)
- S Durr
- Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany
- Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52428 Jülich, Germany
| | - Z Fodor
- Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany
- Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52428 Jülich, Germany
| | - C Hoelbling
- Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany
| | - S D Katz
- Institute for Theoretical Physics, Eötvös University, H-1117 Budapest, Hungary
- MTA-ELTE Lendület Lattice Gauge Theory Research Group, H-1117 Budapest, Hungary
| | - S Krieg
- Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany
- Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52428 Jülich, Germany
| | - L Lellouch
- CNRS, Aix-Marseille U., Université de Toulon, Centre de Physique Théorique, UMR 7332, F-13288 Marseille, France
| | - T Lippert
- Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany
- Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52428 Jülich, Germany
| | - T Metivet
- CNRS, Aix-Marseille U., Université de Toulon, Centre de Physique Théorique, UMR 7332, F-13288 Marseille, France
- CEA-Saclay, IRFU/SPhN, 91191 Gif-sur-Yvette, France
| | - A Portelli
- CNRS, Aix-Marseille U., Université de Toulon, Centre de Physique Théorique, UMR 7332, F-13288 Marseille, France
- Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - K K Szabo
- Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany
- Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52428 Jülich, Germany
| | - C Torrero
- CNRS, Aix-Marseille U., Université de Toulon, Centre de Physique Théorique, UMR 7332, F-13288 Marseille, France
| | - B C Toth
- Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany
| | - L Varnhorst
- Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany
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6
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Borsanyi S, Durr S, Fodor Z, Hoelbling C, Katz SD, Krieg S, Lellouch L, Lippert T, Portelli A, Szabo KK, Toth BC. Ab initio calculation of the neutron-proton mass difference. Science 2015; 347:1452-5. [DOI: 10.1126/science.1257050] [Citation(s) in RCA: 216] [Impact Index Per Article: 24.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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7
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Aoki S, Aoki Y, Bernard C, Blum T, Colangelo G, Della Morte M, Dürr S, El-Khadra AX, Fukaya H, Horsley R, Jüttner A, Kaneko T, Laiho J, Lellouch L, Leutwyler H, Lubicz V, Lunghi E, Necco S, Onogi T, Pena C, Sachrajda CT, Sharpe SR, Simula S, Sommer R, Van de Water RS, Vladikas A, Wenger U, Wittig H. Review of lattice results concerning low-energy particle physics. Eur Phys J C Part Fields 2014; 74:2890. [PMID: 25972762 PMCID: PMC4410391 DOI: 10.1140/epjc/s10052-014-2890-7] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2013] [Accepted: 05/05/2014] [Indexed: 05/28/2023]
Abstract
We review lattice results related to pion, kaon, [Formula: see text]- and [Formula: see text]-meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the determination of the light-quark masses, the form factor [Formula: see text], arising in semileptonic [Formula: see text] transition at zero momentum transfer, as well as the decay-constant ratio [Formula: see text] of decay constants and its consequences for the CKM matrix elements [Formula: see text] and [Formula: see text]. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of [Formula: see text] and [Formula: see text] Chiral Perturbation Theory and review the determination of the [Formula: see text] parameter of neutral kaon mixing. The inclusion of heavy-quark quantities significantly expands the FLAG scope with respect to the previous review. Therefore, we focus here on [Formula: see text]- and [Formula: see text]-meson decay constants, form factors, and mixing parameters, since these are most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. In addition we review the status of lattice determinations of the strong coupling constant [Formula: see text].
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Affiliation(s)
| | - S. Aoki
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto, 606-8502 Japan
| | - Y. Aoki
- Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI), Nagoya University, Nagoya, 464-8602 Japan
- RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973 USA
| | - C. Bernard
- Department of Physics, Washington University, Saint Louis, MO 63130 USA
| | - T. Blum
- RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973 USA
- Physics Department, University of Connecticut, Storrs, CT 06269-3046 USA
| | - G. Colangelo
- Albert Einstein Center for Fundamental Physics, Institut für theoretische Physik, Universität Bern, Sidlerstr. 5, 3012 Bern, Switzerland
| | - M. Della Morte
- CP3-Origins & Danish IAS, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark
- IFIC (CSIC), c/ Catedrático José Beltrán, 2, 46980 Paterna, Spain
| | - S. Dürr
- Bergische Universität Wuppertal, Gaußstraße 20, 42119 Wuppertal, Germany
- Jülich Supercomputing Center, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - A. X. El-Khadra
- Department of Physics, University of Illinois, Urbana, IL 61801 USA
| | - H. Fukaya
- Department of Physics, Osaka University, Toyonaka, Osaka, 560-0043 Japan
| | - R. Horsley
- School of Physics, University of Edinburgh, Edinburgh, EH9 3JZ UK
| | - A. Jüttner
- School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ UK
| | - T. Kaneko
- High Energy Accelerator Research Organization (KEK), Ibaraki, 305-0801 Japan
| | - J. Laiho
- SUPA, Department of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ UK
- Present Address: Department of Physics, Syracuse University, Syracuse, New York USA
| | - L. Lellouch
- Aix-Marseille Université, CNRS, CPT, UMR 7332, 13288 Marseille, France
- Université de Toulon, CNRS, CPT, UMR 7332, 83957 La Garde, France
| | - H. Leutwyler
- Albert Einstein Center for Fundamental Physics, Institut für theoretische Physik, Universität Bern, Sidlerstr. 5, 3012 Bern, Switzerland
| | - V. Lubicz
- Dipartimento di Matematica e Fisica, Università Roma Tre, Via della Vasca Navale 84, 00146 Rome, Italy
- INFN, Sezione di Roma Tre, Via della Vasca Navale 84, 00146 Rome, Italy
| | - E. Lunghi
- Physics Department, Indiana University, Bloomington, IN 47405 USA
| | - S. Necco
- Albert Einstein Center for Fundamental Physics, Institut für theoretische Physik, Universität Bern, Sidlerstr. 5, 3012 Bern, Switzerland
| | - T. Onogi
- Department of Physics, Osaka University, Toyonaka, Osaka, 560-0043 Japan
| | - C. Pena
- Instituto de Física Teórica UAM/CSIC and Departamento de Física Teórica, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain
| | - C. T. Sachrajda
- School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ UK
| | - S. R. Sharpe
- Physics Department, University of Washington, Seattle, WA 98195-1560 USA
| | - S. Simula
- INFN, Sezione di Roma Tre, Via della Vasca Navale 84, 00146 Rome, Italy
| | - R. Sommer
- NIC @ DESY, Platanenallee 6, 15738 Zeuthen, Germany
| | | | - A. Vladikas
- INFN, Sezione di Tor Vergata, c/o Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - U. Wenger
- Albert Einstein Center for Fundamental Physics, Institut für theoretische Physik, Universität Bern, Sidlerstr. 5, 3012 Bern, Switzerland
| | - H. Wittig
- PRISMA Cluster of Excellence, Institut für Kernphysik and Helmholtz Institute Mainz, University of Mainz, 55099 Mainz, Germany
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Borsanyi S, Dürr S, Fodor Z, Frison J, Hoelbling C, Katz SD, Krieg S, Kurth T, Lellouch L, Lippert T, Portelli A, Ramos A, Sastre A, Szabo K. Isospin splittings in the light-baryon octet from lattice QCD and QED. Phys Rev Lett 2013; 111:252001. [PMID: 24483739 DOI: 10.1103/physrevlett.111.252001] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2013] [Indexed: 06/03/2023]
Abstract
While electromagnetic and up-down quark mass difference effects on octet baryon masses are very small, they have important consequences. The stability of the hydrogen atom against beta decay is a prominent example. Here, we include these effects by adding them to valence quarks in a lattice QCD calculation based on Nf=2+1 simulations with five lattice spacings down to 0.054 fm, lattice sizes up to 6 fm, and average up-down quark masses all the way down to their physical value. This allows us to gain control over all systematic errors, except for the one associated with neglecting electromagnetism in the sea. We compute the octet baryon isomultiplet mass splittings, as well as the individual contributions from electromagnetism and the up-down quark mass difference. Our results for the total splittings are in good agreement with experiment.
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Affiliation(s)
- Sz Borsanyi
- Department of Physics, Wuppertal University, Gaussstrasse 20, D-42119 Wuppertal, Germany
| | - S Dürr
- Department of Physics, Wuppertal University, Gaussstrasse 20, D-42119 Wuppertal, Germany and IAS/JSC, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - Z Fodor
- Department of Physics, Wuppertal University, Gaussstrasse 20, D-42119 Wuppertal, Germany and IAS/JSC, Forschungszentrum Jülich, D-52425 Jülich, Germany and Institute for Theoretical Physics, Eötvös University, Pázmány Peter sétany 1/A, H-1117 Budapest, Hungary
| | - J Frison
- Aix-Marseille Université, CNRS, CPT, UMR 7332, 13288 Marseille, France and Université de Toulon, CNRS, CPT, UMR 7332, 83957 La Garde, France
| | - C Hoelbling
- Department of Physics, Wuppertal University, Gaussstrasse 20, D-42119 Wuppertal, Germany
| | - S D Katz
- Institute for Theoretical Physics, Eötvös University, Pázmány Peter sétany 1/A, H-1117 Budapest, Hungary and MTA-ELTE Lendület Lattice Gauge Theory Research Group, H-1117 Budapest, Hungary
| | - S Krieg
- Department of Physics, Wuppertal University, Gaussstrasse 20, D-42119 Wuppertal, Germany and IAS/JSC, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - Th Kurth
- Department of Physics, Wuppertal University, Gaussstrasse 20, D-42119 Wuppertal, Germany
| | - L Lellouch
- Aix-Marseille Université, CNRS, CPT, UMR 7332, 13288 Marseille, France and Université de Toulon, CNRS, CPT, UMR 7332, 83957 La Garde, France
| | - Th Lippert
- IAS/JSC, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - A Portelli
- Aix-Marseille Université, CNRS, CPT, UMR 7332, 13288 Marseille, France and Université de Toulon, CNRS, CPT, UMR 7332, 83957 La Garde, France and School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, United Kingdom
| | - A Ramos
- Aix-Marseille Université, CNRS, CPT, UMR 7332, 13288 Marseille, France and Université de Toulon, CNRS, CPT, UMR 7332, 83957 La Garde, France
| | - A Sastre
- Aix-Marseille Université, CNRS, CPT, UMR 7332, 13288 Marseille, France and Université de Toulon, CNRS, CPT, UMR 7332, 83957 La Garde, France
| | - K Szabo
- Department of Physics, Wuppertal University, Gaussstrasse 20, D-42119 Wuppertal, Germany
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9
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Dürr S, Fodor Z, Frison J, Hoelbling C, Hoffmann R, Katz SD, Krieg S, Kurth T, Lellouch L, Lippert T, Szabo KK, Vulvert G. Ab Initio Determination of Light Hadron Masses. Science 2008; 322:1224-7. [DOI: 10.1126/science.1163233] [Citation(s) in RCA: 403] [Impact Index Per Article: 25.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- S. Dürr
- John von Neumann–Institut für Computing, Deutsches Elektronen-Synchrotron Zeuthen, D-15738 Zeuthen and Forschungszentrum Jülich, D-52425 Jülich, Germany
- Bergische Universität Wuppertal, Gaussstrasse 20, D-42119 Wuppertal, Germany
- Institute for Theoretical Physics, Eötvös University, H-1117 Budapest, Hungary
- Centre de Physique Théorique (UMR 6207 du CNRS et des Universités d'Aix-Marseille I, d'Aix-Marseille II et du Sud Toulon-Var, affiliée à la FRUMAM), Case 907, Campus de Luminy, F-13288, Marseille Cedex 9, France
- Jülich Supercomputing Centre, FZ Jülich, D-52425 Jülich, Germany
| | - Z. Fodor
- John von Neumann–Institut für Computing, Deutsches Elektronen-Synchrotron Zeuthen, D-15738 Zeuthen and Forschungszentrum Jülich, D-52425 Jülich, Germany
- Bergische Universität Wuppertal, Gaussstrasse 20, D-42119 Wuppertal, Germany
- Institute for Theoretical Physics, Eötvös University, H-1117 Budapest, Hungary
- Centre de Physique Théorique (UMR 6207 du CNRS et des Universités d'Aix-Marseille I, d'Aix-Marseille II et du Sud Toulon-Var, affiliée à la FRUMAM), Case 907, Campus de Luminy, F-13288, Marseille Cedex 9, France
- Jülich Supercomputing Centre, FZ Jülich, D-52425 Jülich, Germany
| | - J. Frison
- John von Neumann–Institut für Computing, Deutsches Elektronen-Synchrotron Zeuthen, D-15738 Zeuthen and Forschungszentrum Jülich, D-52425 Jülich, Germany
- Bergische Universität Wuppertal, Gaussstrasse 20, D-42119 Wuppertal, Germany
- Institute for Theoretical Physics, Eötvös University, H-1117 Budapest, Hungary
- Centre de Physique Théorique (UMR 6207 du CNRS et des Universités d'Aix-Marseille I, d'Aix-Marseille II et du Sud Toulon-Var, affiliée à la FRUMAM), Case 907, Campus de Luminy, F-13288, Marseille Cedex 9, France
- Jülich Supercomputing Centre, FZ Jülich, D-52425 Jülich, Germany
| | - C. Hoelbling
- John von Neumann–Institut für Computing, Deutsches Elektronen-Synchrotron Zeuthen, D-15738 Zeuthen and Forschungszentrum Jülich, D-52425 Jülich, Germany
- Bergische Universität Wuppertal, Gaussstrasse 20, D-42119 Wuppertal, Germany
- Institute for Theoretical Physics, Eötvös University, H-1117 Budapest, Hungary
- Centre de Physique Théorique (UMR 6207 du CNRS et des Universités d'Aix-Marseille I, d'Aix-Marseille II et du Sud Toulon-Var, affiliée à la FRUMAM), Case 907, Campus de Luminy, F-13288, Marseille Cedex 9, France
- Jülich Supercomputing Centre, FZ Jülich, D-52425 Jülich, Germany
| | - R. Hoffmann
- John von Neumann–Institut für Computing, Deutsches Elektronen-Synchrotron Zeuthen, D-15738 Zeuthen and Forschungszentrum Jülich, D-52425 Jülich, Germany
- Bergische Universität Wuppertal, Gaussstrasse 20, D-42119 Wuppertal, Germany
- Institute for Theoretical Physics, Eötvös University, H-1117 Budapest, Hungary
- Centre de Physique Théorique (UMR 6207 du CNRS et des Universités d'Aix-Marseille I, d'Aix-Marseille II et du Sud Toulon-Var, affiliée à la FRUMAM), Case 907, Campus de Luminy, F-13288, Marseille Cedex 9, France
- Jülich Supercomputing Centre, FZ Jülich, D-52425 Jülich, Germany
| | - S. D. Katz
- John von Neumann–Institut für Computing, Deutsches Elektronen-Synchrotron Zeuthen, D-15738 Zeuthen and Forschungszentrum Jülich, D-52425 Jülich, Germany
- Bergische Universität Wuppertal, Gaussstrasse 20, D-42119 Wuppertal, Germany
- Institute for Theoretical Physics, Eötvös University, H-1117 Budapest, Hungary
- Centre de Physique Théorique (UMR 6207 du CNRS et des Universités d'Aix-Marseille I, d'Aix-Marseille II et du Sud Toulon-Var, affiliée à la FRUMAM), Case 907, Campus de Luminy, F-13288, Marseille Cedex 9, France
- Jülich Supercomputing Centre, FZ Jülich, D-52425 Jülich, Germany
| | - S. Krieg
- John von Neumann–Institut für Computing, Deutsches Elektronen-Synchrotron Zeuthen, D-15738 Zeuthen and Forschungszentrum Jülich, D-52425 Jülich, Germany
- Bergische Universität Wuppertal, Gaussstrasse 20, D-42119 Wuppertal, Germany
- Institute for Theoretical Physics, Eötvös University, H-1117 Budapest, Hungary
- Centre de Physique Théorique (UMR 6207 du CNRS et des Universités d'Aix-Marseille I, d'Aix-Marseille II et du Sud Toulon-Var, affiliée à la FRUMAM), Case 907, Campus de Luminy, F-13288, Marseille Cedex 9, France
- Jülich Supercomputing Centre, FZ Jülich, D-52425 Jülich, Germany
| | - T. Kurth
- John von Neumann–Institut für Computing, Deutsches Elektronen-Synchrotron Zeuthen, D-15738 Zeuthen and Forschungszentrum Jülich, D-52425 Jülich, Germany
- Bergische Universität Wuppertal, Gaussstrasse 20, D-42119 Wuppertal, Germany
- Institute for Theoretical Physics, Eötvös University, H-1117 Budapest, Hungary
- Centre de Physique Théorique (UMR 6207 du CNRS et des Universités d'Aix-Marseille I, d'Aix-Marseille II et du Sud Toulon-Var, affiliée à la FRUMAM), Case 907, Campus de Luminy, F-13288, Marseille Cedex 9, France
- Jülich Supercomputing Centre, FZ Jülich, D-52425 Jülich, Germany
| | - L. Lellouch
- John von Neumann–Institut für Computing, Deutsches Elektronen-Synchrotron Zeuthen, D-15738 Zeuthen and Forschungszentrum Jülich, D-52425 Jülich, Germany
- Bergische Universität Wuppertal, Gaussstrasse 20, D-42119 Wuppertal, Germany
- Institute for Theoretical Physics, Eötvös University, H-1117 Budapest, Hungary
- Centre de Physique Théorique (UMR 6207 du CNRS et des Universités d'Aix-Marseille I, d'Aix-Marseille II et du Sud Toulon-Var, affiliée à la FRUMAM), Case 907, Campus de Luminy, F-13288, Marseille Cedex 9, France
- Jülich Supercomputing Centre, FZ Jülich, D-52425 Jülich, Germany
| | - T. Lippert
- John von Neumann–Institut für Computing, Deutsches Elektronen-Synchrotron Zeuthen, D-15738 Zeuthen and Forschungszentrum Jülich, D-52425 Jülich, Germany
- Bergische Universität Wuppertal, Gaussstrasse 20, D-42119 Wuppertal, Germany
- Institute for Theoretical Physics, Eötvös University, H-1117 Budapest, Hungary
- Centre de Physique Théorique (UMR 6207 du CNRS et des Universités d'Aix-Marseille I, d'Aix-Marseille II et du Sud Toulon-Var, affiliée à la FRUMAM), Case 907, Campus de Luminy, F-13288, Marseille Cedex 9, France
- Jülich Supercomputing Centre, FZ Jülich, D-52425 Jülich, Germany
| | - K. K. Szabo
- John von Neumann–Institut für Computing, Deutsches Elektronen-Synchrotron Zeuthen, D-15738 Zeuthen and Forschungszentrum Jülich, D-52425 Jülich, Germany
- Bergische Universität Wuppertal, Gaussstrasse 20, D-42119 Wuppertal, Germany
- Institute for Theoretical Physics, Eötvös University, H-1117 Budapest, Hungary
- Centre de Physique Théorique (UMR 6207 du CNRS et des Universités d'Aix-Marseille I, d'Aix-Marseille II et du Sud Toulon-Var, affiliée à la FRUMAM), Case 907, Campus de Luminy, F-13288, Marseille Cedex 9, France
- Jülich Supercomputing Centre, FZ Jülich, D-52425 Jülich, Germany
| | - G. Vulvert
- John von Neumann–Institut für Computing, Deutsches Elektronen-Synchrotron Zeuthen, D-15738 Zeuthen and Forschungszentrum Jülich, D-52425 Jülich, Germany
- Bergische Universität Wuppertal, Gaussstrasse 20, D-42119 Wuppertal, Germany
- Institute for Theoretical Physics, Eötvös University, H-1117 Budapest, Hungary
- Centre de Physique Théorique (UMR 6207 du CNRS et des Universités d'Aix-Marseille I, d'Aix-Marseille II et du Sud Toulon-Var, affiliée à la FRUMAM), Case 907, Campus de Luminy, F-13288, Marseille Cedex 9, France
- Jülich Supercomputing Centre, FZ Jülich, D-52425 Jülich, Germany
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10
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Bowler KC, Kenway RD, Oliveira O, Richards DG, Ueberholz P, Lellouch L, Nieves J, Sachrajda CT, Stella N, Wittig H. Heavy baryon spectroscopy from the lattice. Phys Rev D Part Fields 1996; 54:3619-3633. [PMID: 10021035 DOI: 10.1103/physrevd.54.3619] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Bowler KC, Hazel NM, Henty DS, Hoeber H, Kenway RD, Richards DG, Shanahan HP, Simone JN, Lellouch L, Nieves J, Sachrajda CT, Wittig H. Lattice study of semileptonic B decays: B-bar-->Dl nu -bar decays. Phys Rev D Part Fields 1995; 52:5067-5094. [PMID: 10019731 DOI: 10.1103/physrevd.52.5067] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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12
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Bowler KC, Hazel NM, Hoeber H, Kenway RD, Richards DG, Lellouch L, Nieves J, Sachrajda CT, Wittig H. "Improved" lattice study of semileptonic decays of D mesons. Phys Rev D Part Fields 1995; 51:4905-4923. [PMID: 10018966 DOI: 10.1103/physrevd.51.4905] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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13
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Baxter RM, Booth SP, Bowler KC, Collins S, Henty DS, Kenway RD, Richards DG, Shanahan HP, Simone JN, Simpson AD, Wilkes BE, Ewing AK, Lellouch L, Sachrajda CT, Wittig H. Quenched heavy-light decay constants. Phys Rev D Part Fields 1994; 49:1594-1605. [PMID: 10017135 DOI: 10.1103/physrevd.49.1594] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Booth SP, Bowler KC, Hazel NM, Henty DS, Hoeber H, Kenway RD, Richards DG, Shanahan HP, Simone JN, Simpson AD, Lellouch L, Nieves J, Sachrajda CT, Wittig H. The Isgur-Wise function from the lattice. Phys Rev Lett 1994; 72:462-465. [PMID: 10056439 DOI: 10.1103/physrevlett.72.462] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Allton CR, Lellouch L, Sachrajda CT, Wittig H, Baxter RM, Booth SP, Bowler KC, Henty DS, Kenway RD, McNeile C, Pendleton BJ, Richards DG, Simone JN, Simpson AD. Light hadron spectrum and decay constants in quenched lattice QCD. Phys Rev D Part Fields 1994; 49:474-485. [PMID: 10016785 DOI: 10.1103/physrevd.49.474] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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