1
|
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.
Collapse
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
| |
Collapse
|
2
|
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.
Collapse
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
| |
Collapse
|
3
|
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.
Collapse
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
| |
Collapse
|
4
|
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).
Collapse
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
| |
Collapse
|
5
|
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]
|
6
|
Borsanyi S, Fodor Z, Katz SD, Krieg S, Ratti C, Szabo KK. Freeze-out parameters from electric charge and baryon number fluctuations: is there consistency? Phys Rev Lett 2014; 113:052301. [PMID: 25126910 DOI: 10.1103/physrevlett.113.052301] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2014] [Indexed: 06/03/2023]
Abstract
Recent results for moments of multiplicity distributions of net protons and net-electric charge from the STAR Collaboration are compared to lattice QCD results for higher order fluctuations of baryon number and electric charge by the Wuppertal-Budapest Collaboration, with the purpose of extracting the freeze-out temperature and chemical potential. All lattice simulations are performed for a system of 2+1 dynamical quark flavors, at the physical mass for light and strange quarks; all results are continuum extrapolated. We show that it is possible to extract an upper value for the freeze-out temperature, as well as precise baryochemical potential values corresponding to the four highest collision energies of the experimental beam energy scan. Consistency between the freeze-out parameters obtained from baryon number and electric charge fluctuations is found. The freeze-out chemical potentials are now in agreement with the statistical hadronization model.
Collapse
Affiliation(s)
- S Borsanyi
- Department of Physics, Wuppertal University, Gauss Strasse 20, D-42119 Wuppertal, Germany
| | - Z Fodor
- Department of Physics, Wuppertal University, Gauss Strasse 20, D-42119 Wuppertal, Germany and Institute for Theoretical Physics, Eötvös University, Pázmány P. sétány 1/A, H-1117 Budapest, Hungary and Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - S D Katz
- Institute for Theoretical Physics, Eötvös University, Pázmány P. sétány 1/A, H-1117 Budapest, Hungary and MTA-ELTE "Lendület" Lattice Gauge Theory Research Group, Pázmány P. sétány 1/A, H-1117 Budapest, Hungary
| | - S Krieg
- Department of Physics, Wuppertal University, Gauss Strasse 20, D-42119 Wuppertal, Germany and Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - C Ratti
- Dipartimento di Fisica, Università di Torino and INFN, Sezione di Torino via Giuria 1, I-10125 Torino, Italy
| | - K K Szabo
- Department of Physics, Wuppertal University, Gauss Strasse 20, D-42119 Wuppertal, Germany and Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52425 Jülich, Germany
| |
Collapse
|
7
|
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
| |
Collapse
|