Quantum electrodynamics calculation of lepton anomalous magnetic moments: Numerical approach to the perturbation theory of QED
In this review, we summarize the results of our numerical work carried out over nearly ten years on the complete determination of the 10th-order contribution to the anomalous magnetic moments of leptons in the perturbation theory of quantum electrodynamics. Our approach is based on a reorganized ren...
Saved in:
| Published in | Progress of theoretical and experimental physics Vol. 2012; no. 1 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Oxford
Oxford University Press
01.01.2012
|
| Online Access | Get full text |
| ISSN | 2050-3911 2050-3911 |
| DOI | 10.1093/ptep/pts030 |
Cover
| Abstract | In this review, we summarize the results of our numerical work carried out over nearly ten years on the complete determination of the 10th-order contribution to the anomalous magnetic moments of leptons in the perturbation theory of quantum electrodynamics. Our approach is based on a reorganized renormalization method in which no divergent quantities appear explicitly in any part of the calculation, which is crucial for the feasibility of numerical integration. The enormous number of 10th-order diagrams and the complexity of the renormalization procedure are such that we could not have handled this problem without the development of an automated code-generating algorithm. The systematic approach to these problems is described in some detail. |
|---|---|
| AbstractList | In this review, we summarize the results of our numerical work carried out over nearly ten years on the complete determination of the 10th-order contribution to the anomalous magnetic moments of leptons in the perturbation theory of quantum electrodynamics. Our approach is based on a reorganized renormalization method in which no divergent quantities appear explicitly in any part of the calculation, which is crucial for the feasibility of numerical integration. The enormous number of 10th-order diagrams and the complexity of the renormalization procedure are such that we could not have handled this problem without the development of an automated code-generating algorithm. The systematic approach to these problems is described in some detail. |
| Author | Kinoshita, Toichiro Aoyama, Tatsumi Hayakawa, Masashi Nio, Makiko |
| Author_xml | – sequence: 1 givenname: Tatsumi surname: Aoyama fullname: Aoyama, Tatsumi email: nio@riken.jp organization: 1Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI), Nagoya University, Nagoya 464-8602, Japan – sequence: 2 givenname: Masashi surname: Hayakawa fullname: Hayakawa, Masashi email: nio@riken.jp organization: 2Nishina Center, RIKEN, Wako, Saitama 351-0198, Japan – sequence: 3 givenname: Toichiro surname: Kinoshita fullname: Kinoshita, Toichiro email: nio@riken.jp organization: 2Nishina Center, RIKEN, Wako, Saitama 351-0198, Japan – sequence: 4 givenname: Makiko surname: Nio fullname: Nio, Makiko email: nio@riken.jp organization: 2Nishina Center, RIKEN, Wako, Saitama 351-0198, Japan |
| BookMark | eNqFkM1qGzEUhUVJoUnqVV9AEMgmdSqNZMvTXUmcHzANhnQ9XGvu1BM0kqIfgjd99sidLEKgzUa6iO98ks4RObDOIiFfODvnrBbffEJflsgE-0AOKzZjU1FzfvBq_kQmMT4wxjhTikl-SP6sM9iUB4oGdQqu3VkYeh2pBqOzgdQ7S11HDfpUJrBuAONypAP8tph6TQc3oE3xO_2ZBwx9yVHwPjjQW5ocTVukHkPKYTPKyoELu71zvbz8TD52YCJOXvZj8utqeX9xM13dXd9e_FhNtVzING1n1Qa0UIhttWDzbq6khJlUqBjUqlPtRtcbhbrtpORQMa4UVrXoeItSaABxTL6O3mw97J7AmMaHfoCwazhr9vU1-_qasb6Cn4x4-cdjxpiaB5eDLS9sBFdclqvnolBnI6WDizFg946Tv6F1n_5WkgL05h-Z0zHjsv-v_Bn-hKPa |
| CitedBy_id | crossref_primary_10_1103_PhysRevD_106_056009 crossref_primary_10_1038_nature13059 crossref_primary_10_1051_epjconf_201817901008 crossref_primary_10_1103_PhysRevD_104_094506 crossref_primary_10_1103_PhysRevD_90_057301 crossref_primary_10_3390_atoms7010028 crossref_primary_10_1119_1_4944357 crossref_primary_10_1146_annurev_nucl_031312_120340 crossref_primary_10_1103_PhysRevD_105_025019 crossref_primary_10_7498_aps_73_20240683 crossref_primary_10_1007_s11467_013_0294_z crossref_primary_10_1134_S1063772923140196 |
| Cites_doi | 10.1016/0370-2693(93)91176-N 10.1103/PhysRevD.82.113004 10.1016/0370-2693(93)90988-T 10.1103/PhysRev.72.241 10.1103/PhysRevD.70.113006 10.1016/j.physletb.2008.07.018 10.1103/PhysRevLett.106.080801 10.1103/RevModPhys.72.351 10.1016/S0370-2693(99)00076-3 10.1088/1674-1137/34/6/021 10.1103/PhysRevD.83.053002 10.1103/PhysRevD.73.053007 10.1103/PhysRevD.44.3935 10.1103/PhysRevLett.109.111808 10.1103/PhysRevD.10.3991 10.1016/0370-2693(91)90427-R 10.1103/PhysRevD.73.013003 10.1103/PhysRevD.85.033007 10.1103/PhysRev.74.250 10.1103/PhysRev.74.1439 10.1103/PhysRevLett.75.4728 10.1103/PhysRevD.6.2923 10.1142/9789814271844_0009 10.1016/0370-2693(91)90990-8 10.1016/S0370-2693(96)01346-9 10.1088/1126-6708/2002/11/003 10.1103/PhysRevD.10.3978 10.1103/PhysRevLett.92.161802 10.1103/PhysRevA.83.052122 10.1103/PhysRevD.78.053005 10.1103/PhysRevD.75.013002 10.1103/PhysRev.73.416 10.1016/0550-3213(78)90512-6 10.1103/PhysRevD.67.073006 10.1103/PhysRevD.85.093013 10.1103/PhysRevLett.76.3267 10.1103/PhysRevD.52.402 10.1103/RevModPhys.80.633 10.1016/j.nuclphysb.2007.12.013 10.1103/PhysRevLett.109.111807 10.1103/PhysRevD.83.053003 10.1103/PhysRevD.84.053003 10.1088/0954-3899/38/8/085003 10.1103/PhysRevLett.90.021803 10.1103/PhysRevD.3.356 10.1007/BF01645676 10.1103/PhysRevD.79.073012 10.1103/PhysRev.107.328 10.1140/epjc/s10052-011-1632-3 10.1103/PhysRevD.81.053009 10.1103/PhysRevD.74.073011 10.1016/0031-9163(66)91171-1 10.1103/PhysRevD.47.1723 10.1103/PhysRevLett.99.110406 10.1016/j.physrep.2009.04.003 10.1103/PhysRev.74.224 10.1016/0021-9991(78)90004-9 10.1103/PhysRevD.78.113006 10.1103/PhysRev.72.1256.2 10.1143/PTP.1.27 10.1140/epjc/s10052-010-1515-z 10.1103/PhysRevD.77.053012 10.1103/PhysRevD.10.4007 10.1016/0370-2693(96)00439-X 10.1016/j.nuclphysb.2006.01.040 10.1007/BF02787236 10.1103/PhysRevD.1.2378 10.1103/PhysRev.77.536 10.1142/9789814503273_0007 10.1016/0370-2693(94)91513-X 10.1103/PhysRevLett.97.030801 10.1103/PhysRevD.73.072003 10.1103/PhysRevD.77.093010 10.1016/j.nuclphysbps.2011.06.039 10.1103/PhysRevLett.23.441 10.1103/PhysRevLett.100.120801 10.1103/PhysRevLett.59.26 10.1142/S0217732307022992 |
| ContentType | Journal Article |
| Copyright | The Author(s) 2012. Published by Oxford University Press on behalf of the Physical Society of Japan. 2012 The Author(s) 2012. Published by Oxford University Press on behalf of the Physical Society of Japan. This work is published under http://creativecommons.org/licenses/by/3.0 (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| Copyright_xml | – notice: The Author(s) 2012. Published by Oxford University Press on behalf of the Physical Society of Japan. 2012 – notice: The Author(s) 2012. Published by Oxford University Press on behalf of the Physical Society of Japan. This work is published under http://creativecommons.org/licenses/by/3.0 (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| DBID | TOX AAYXX CITATION 3V. 7XB 88I 8FK ABUWG AFKRA AZQEC BENPR CCPQU DWQXO GNUQQ HCIFZ M2P PHGZM PHGZT PIMPY PKEHL PQEST PQQKQ PQUKI PRINS Q9U ADTOC UNPAY |
| DOI | 10.1093/ptep/pts030 |
| DatabaseName | Oxford Journals Open Access Collection CrossRef ProQuest Central (Corporate) ProQuest Central (purchase pre-March 2016) Science Database (Alumni Edition) ProQuest Central (Alumni) (purchase pre-March 2016) ProQuest Central (Alumni) ProQuest Central UK/Ireland ProQuest Central Essentials ProQuest Central ProQuest One ProQuest Central Korea ProQuest Central Student SciTech Premium Collection Science Database ProQuest Central Premium ProQuest One Academic Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Academic ProQuest One Academic UKI Edition ProQuest Central China ProQuest Central Basic Unpaywall for CDI: Periodical Content Unpaywall |
| DatabaseTitle | CrossRef Publicly Available Content Database ProQuest Science Journals (Alumni Edition) ProQuest Central Student ProQuest One Academic Middle East (New) ProQuest Central Basic ProQuest Central Essentials ProQuest Science Journals ProQuest One Academic Eastern Edition ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central China ProQuest Central ProQuest One Academic UKI Edition ProQuest Central Korea ProQuest Central (New) ProQuest One Academic ProQuest One Academic (New) ProQuest Central (Alumni) |
| DatabaseTitleList | Publicly Available Content Database |
| Database_xml | – sequence: 1 dbid: TOX name: Oxford Journals Open Access Collection url: https://academic.oup.com/journals/ sourceTypes: Publisher – sequence: 2 dbid: UNPAY name: Unpaywall url: https://proxy.k.utb.cz/login?url=https://unpaywall.org/ sourceTypes: Open Access Repository – sequence: 3 dbid: BENPR name: ProQuest Central url: http://www.proquest.com/pqcentral?accountid=15518 sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences |
| EISSN | 2050-3911 |
| ExternalDocumentID | 10.1093/ptep/pts030 10_1093_ptep_pts030 |
| GroupedDBID | .I3 0R~ 5VS AAFWJ AAMVS AAPPN AAPXW AAVAP ABEJV ABGNP ABPTD ABXVV ACGFS ADHZD AENEX AENZO AFPKN AFULF AIBLX ALMA_UNASSIGNED_HOLDINGS ALUQC AMNDL BAYMD BTTYL CIDKT D~K EBS EJD ER. GROUPED_DOAJ H13 IAO ISR ITC KQ8 KSI M~E O9- OAWHX OJQWA OK1 PEELM RHF ROL ROX RXO TOX ~D7 88I AAYXX ABUWG AFKRA AZQEC BENPR CCPQU CITATION DWQXO GNUQQ HCIFZ M2P PHGZM PHGZT PIMPY PUEGO 3V. 7XB 8FK PKEHL PQEST PQQKQ PQUKI PRINS Q9U 4.4 ADTOC UNPAY |
| ID | FETCH-LOGICAL-c484t-d52bac37eed2806f6744a547e70a97f7dbc9b7ecdf441a20177e293f1de43caa3 |
| IEDL.DBID | UNPAY |
| ISSN | 2050-3911 |
| IngestDate | Tue Aug 19 21:37:09 EDT 2025 Sat Sep 20 14:20:57 EDT 2025 Wed Oct 01 02:50:20 EDT 2025 Thu Apr 24 23:12:30 EDT 2025 Fri Jan 31 08:06:29 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Language | English |
| License | This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c484t-d52bac37eed2806f6744a547e70a97f7dbc9b7ecdf441a20177e293f1de43caa3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| OpenAccessLink | https://proxy.k.utb.cz/login?url=https://academic.oup.com/ptep/article-pdf/2012/1/01A107/11590859/pts030.pdf |
| PQID | 3171454763 |
| PQPubID | 7121340 |
| ParticipantIDs | unpaywall_primary_10_1093_ptep_pts030 proquest_journals_3171454763 crossref_primary_10_1093_ptep_pts030 crossref_citationtrail_10_1093_ptep_pts030 oup_primary_10_1093_ptep_pts030 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2012-01-01 |
| PublicationDateYYYYMMDD | 2012-01-01 |
| PublicationDate_xml | – month: 01 year: 2012 text: 2012-01-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | Oxford |
| PublicationPlace_xml | – name: Oxford |
| PublicationTitle | Progress of theoretical and experimental physics |
| PublicationYear | 2012 |
| Publisher | Oxford University Press |
| Publisher_xml | – name: Oxford University Press |
| References | Nomura ( key 20170727055708_PTS030C52) Hanneke ( key 20170727055708_PTS030C12) 2011; 83 Lee Roberts ( key 20170727055708_PTS030C9) 2010 Laporta ( key 20170727055708_PTS030C78) 1993; 312 Samuel ( key 20170727055708_PTS030C73) 1991; 44 Aoyama ( key 20170727055708_PTS030C36) 2008; 796 Odom ( key 20170727055708_PTS030C10) 2006; 97 Schwinger ( key 20170727055708_PTS030C8) 1949; 73 Kusch ( key 20170727055708_PTS030C2) 1948; 73 Laporta ( key 20170727055708_PTS030C29) 1993; 106 Aldins ( key 20170727055708_PTS030C70) 1970; 1 Laporta ( key 20170727055708_PTS030C30) 1993; 301 Aoyama ( key 20170727055708_PTS030C77) 2012; 109 Aoyama ( key 20170727055708_PTS030C41) 2010; 81 Brodsky ( key 20170727055708_PTS030C62) 1971; 3 Aoyama ( key 20170727055708_PTS030C44) 2011; 83 Aoyama ( key 20170727055708_PTS030C47) 2012; 85 Bouchendira ( key 20170727055708_PTS030C61) 2011; 106 Lepage ( key 20170727055708_PTS030C93) 1978; 27 Czarnecki ( key 20170727055708_PTS030C75) 1999; 449 Kusch ( key 20170727055708_PTS030C1) 1947; 72 Mohr ( key 20170727055708_PTS030C16) 2008; 80 Bijnens ( key 20170727055708_PTS030C83) 2007; 22 Karshenboim ( key 20170727055708_PTS030C72) 1993; 56 Kinoshita ( key 20170727055708_PTS030C33) 2006; 73 Kinoshita ( key 20170727055708_PTS030C32) 2003; 90 Cvitanovic ( key 20170727055708_PTS030C86) 1974; 10 Aoyama ( key 20170727055708_PTS030C35) 2006; 740 Krause ( key 20170727055708_PTS030C80) 1997; 390 Passera ( key 20170727055708_PTS030C74) 2007; 75 Hanneke ( key 20170727055708_PTS030C11) 2008; 100 Aoyama ( key 20170727055708_PTS030C45) 2011; 84 Mohr ( key 20170727055708_PTS030C51) 2000; 72 Aoyama ( key 20170727055708_PTS030C39) 2008; 78 Kataev ( key 20170727055708_PTS030C65) 1992; 284 Tomonaga ( key 20170727055708_PTS030C5) 1946; 1 Cvitanovic ( key 20170727055708_PTS030C89) 1974; 10 Mibe ( key 20170727055708_PTS030C20) 2011; 218 Aoyama ( key 20170727055708_PTS030C42) 2010; 82 Lamb ( key 20170727055708_PTS030C4) 1947; 72 Tomonaga ( key 20170727055708_PTS030C6) 1948; 74 Czarnecki ( key 20170727055708_PTS030C60) 2006; 67 Karplus ( key 20170727055708_PTS030C88) 1950; 77 Nakanishi ( key 20170727055708_PTS030C91) 1971 Aldins ( key 20170727055708_PTS030C69) 1969; 23 Lee Roberts ( key 20170727055708_PTS030C19) 2011; 218 Van Dyck ( key 20170727055708_PTS030C13) 1987; 59 Aoyama ( key 20170727055708_PTS030C37) 2007; 99 Davier ( key 20170727055708_PTS030C55) 2011; 71 Prades ( key 20170727055708_PTS030C56) 2009 Sommerfield ( key 20170727055708_PTS030C24) 1957; 107 Kinoshita ( key 20170727055708_PTS030C34) 2006; 73 Kinoshita ( key 20170727055708_PTS030C87) 1990 Bennett ( key 20170727055708_PTS030C15) 2006; 73 Jegerlehner ( key 20170727055708_PTS030C81) 2009; 477 Kawai ( key 20170727055708_PTS030C64) 1991; 260 Nyffeler ( key 20170727055708_PTS030C85) 2009; 79 Kataev ( key 20170727055708_PTS030C67) 1995; 52 Fujikawa ( key 20170727055708_PTS030C57) 1972; 6 Aoyama ( key 20170727055708_PTS030C48) 2012; 109 Bennett ( key 20170727055708_PTS030C14) 2004; 92 Aoyama ( key 20170727055708_PTS030C38) 2008; 77 Melnikov ( key 20170727055708_PTS030C82) 2004; 70 Li ( key 20170727055708_PTS030C28) 1993; 47 Aoyama ( key 20170727055708_PTS030C40) 2008; 78 Aoyama ( key 20170727055708_PTS030C46) 2012; 85 Schwinger ( key 20170727055708_PTS030C7) 1948; 74 Laporta ( key 20170727055708_PTS030C50) 1994; 328 Broadhurst ( key 20170727055708_PTS030C66) 1993; 298 Elikhovskii ( key 20170727055708_PTS030C71) 1989; 49 Amsler ( key 20170727055708_PTS030C18) 2008; 667 Lee Roberts ( key 20170727055708_PTS030C17) 2010; 34 Zimmermann ( key 20170727055708_PTS030C92) 1969; 15 Iinuma ( key 20170727055708_PTS030C21) 2011; 295 Caffo ( key 20170727055708_PTS030C49) 1978; 141 Samuel ( key 20170727055708_PTS030C27) 1991; 44 Czarnecki ( key 20170727055708_PTS030C58) 1996; 76 Kinoshita ( key 20170727055708_PTS030C76) 2006; 73 Kusch ( key 20170727055708_PTS030C3) 1948; 74 Hagiwara ( key 20170727055708_PTS030C53) 2011; 38 Kinoshita ( key 20170727055708_PTS030C31) 1995; 75 Mohr ( key 20170727055708_PTS030C22) Kinoshita ( key 20170727055708_PTS030C63) 1991; 254 Elend ( key 20170727055708_PTS030C26) 1966; 20 Aoyama ( key 20170727055708_PTS030C43) 2011; 83 Cvitanovic ( key 20170727055708_PTS030C90) 1974; 10 Petermann ( key 20170727055708_PTS030C23) 1957; 30 Kataev ( key 20170727055708_PTS030C68) 2006; 74 Laporta ( key 20170727055708_PTS030C25) 1996; 379 Jegerlehner ( key 20170727055708_PTS030C54) 2011; 71 Knecht ( key 20170727055708_PTS030C59) 2002; 11 Aguilar ( key 20170727055708_PTS030C79) 2008; 77 Prades ( key 20170727055708_PTS030C84) 2009 |
| References_xml | – volume: 301 start-page: 440 year: 1993 ident: key 20170727055708_PTS030C30 publication-title: Phys. Lett. B doi: 10.1016/0370-2693(93)91176-N – volume: 82 start-page: 113004 year: 2010 ident: key 20170727055708_PTS030C42 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.82.113004 – volume: 312 start-page: 495 year: 1993 ident: key 20170727055708_PTS030C78 publication-title: Phys. Lett. B doi: 10.1016/0370-2693(93)90988-T – volume: 72 start-page: 241 year: 1947 ident: key 20170727055708_PTS030C4 publication-title: Phys. Rev. doi: 10.1103/PhysRev.72.241 – volume: 49 start-page: 1056 year: 1989 ident: key 20170727055708_PTS030C71 publication-title: Yad. Fiz. – volume: 70 start-page: 113006 year: 2004 ident: key 20170727055708_PTS030C82 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.70.113006 – volume-title: Graph Theory and Feynman Integrals year: 1971 ident: key 20170727055708_PTS030C91 – volume: 667 start-page: 1 year: 2008 ident: key 20170727055708_PTS030C18 article-title: [Particle Data Group] publication-title: Phys. Lett. B doi: 10.1016/j.physletb.2008.07.018 – volume: 106 start-page: 080801 year: 2011 ident: key 20170727055708_PTS030C61 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.106.080801 – volume: 72 start-page: 351 year: 2000 ident: key 20170727055708_PTS030C51 publication-title: Rev. Mod. Phys. doi: 10.1103/RevModPhys.72.351 – volume: 449 start-page: 354 year: 1999 ident: key 20170727055708_PTS030C75 publication-title: Phys. Lett. B doi: 10.1016/S0370-2693(99)00076-3 – volume: 34 start-page: 741 year: 2010 ident: key 20170727055708_PTS030C17 publication-title: Chinese Phys. C doi: 10.1088/1674-1137/34/6/021 – volume: 83 start-page: 053002 year: 2011 ident: key 20170727055708_PTS030C43 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.83.053002 – volume: 73 start-page: 053007 year: 2006 ident: key 20170727055708_PTS030C34 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.73.053007 – volume: 44 start-page: 3935 year: 1991 ident: key 20170727055708_PTS030C73 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.44.3935 – volume: 73 start-page: 053007 year: 2006 ident: key 20170727055708_PTS030C76 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.73.053007 – volume: 109 start-page: 111808 year: 2012 ident: key 20170727055708_PTS030C77 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.109.111808 – volume: 10 start-page: 3991 year: 1974 ident: key 20170727055708_PTS030C90 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.10.3991 – volume: 73 start-page: 412 year: 1948 ident: key 20170727055708_PTS030C2 publication-title: Phys. Rev. – volume: 254 start-page: 235 year: 1991 ident: key 20170727055708_PTS030C63 publication-title: Phys. Lett. B doi: 10.1016/0370-2693(91)90427-R – volume: 73 start-page: 013003 year: 2006 ident: key 20170727055708_PTS030C33 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.73.013003 – volume: 85 start-page: 033007 year: 2012 ident: key 20170727055708_PTS030C46 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.85.033007 – volume: 74 start-page: 250 year: 1948 ident: key 20170727055708_PTS030C3 publication-title: Phys. Rev. doi: 10.1103/PhysRev.74.250 – volume: 74 start-page: 1439 year: 1948 ident: key 20170727055708_PTS030C7 publication-title: Phys. Rev. doi: 10.1103/PhysRev.74.1439 – volume: 75 start-page: 4728 year: 1995 ident: key 20170727055708_PTS030C31 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.75.4728 – volume: 6 start-page: 2923 year: 1972 ident: key 20170727055708_PTS030C57 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.6.2923 – start-page: 303 volume-title: Lepton Dipole Moments year: 2009 ident: key 20170727055708_PTS030C84 doi: 10.1142/9789814271844_0009 – volume: 260 start-page: 193 year: 1991 ident: key 20170727055708_PTS030C64 publication-title: Phys. Lett. B doi: 10.1016/0370-2693(91)90990-8 – volume: 30 start-page: 407 year: 1957 ident: key 20170727055708_PTS030C23 publication-title: Helv. Phys. Acta – volume: 390 start-page: 392 year: 1997 ident: key 20170727055708_PTS030C80 publication-title: Phys. Lett. B doi: 10.1016/S0370-2693(96)01346-9 – volume-title: Lepton Dipole Moments year: 2010 ident: key 20170727055708_PTS030C9 – volume: 11 start-page: 003 year: 2002 ident: key 20170727055708_PTS030C59 publication-title: J. High Energy Phys. doi: 10.1088/1126-6708/2002/11/003 – ident: key 20170727055708_PTS030C22 article-title: arXiv:1203.5425 – volume: 10 start-page: 3978 year: 1974 ident: key 20170727055708_PTS030C86 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.10.3978 – volume: 92 start-page: 161802 year: 2004 ident: key 20170727055708_PTS030C14 article-title: [Muon g-2 Collaboration] publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.92.161802 – volume: 83 start-page: 052122 year: 2011 ident: key 20170727055708_PTS030C12 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.83.052122 – volume: 78 start-page: 053005 year: 2008 ident: key 20170727055708_PTS030C39 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.78.053005 – volume: 284 start-page: 401 year: 1992 ident: key 20170727055708_PTS030C65 publication-title: Phys. Rev. B – ident: key 20170727055708_PTS030C52 publication-title: arXiv:1208.4194(hep-ph) – volume: 75 start-page: 013002 year: 2007 ident: key 20170727055708_PTS030C74 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.75.013002 – volume: 73 start-page: 416L year: 1949 ident: key 20170727055708_PTS030C8 publication-title: Phys. Rev. doi: 10.1103/PhysRev.73.416 – volume: 141 start-page: 302 year: 1978 ident: key 20170727055708_PTS030C49 publication-title: Nucl. Phys. B doi: 10.1016/0550-3213(78)90512-6 – volume: 67 start-page: 073006 year: 2006 ident: key 20170727055708_PTS030C60 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.67.073006 – volume: 218 start-page: 237 year: 2011 ident: key 20170727055708_PTS030C19 article-title: [Fermilab P989 Collaboration] publication-title: Nucl. Phys. Proc. Suppl. – volume: 85 start-page: 093013 year: 2012 ident: key 20170727055708_PTS030C47 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.85.093013 – volume: 44 start-page: 3935 year: 1991 ident: key 20170727055708_PTS030C27 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.44.3935 – volume: 76 start-page: 3267 year: 1996 ident: key 20170727055708_PTS030C58 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.76.3267 – volume: 52 start-page: 402 year: 1995 ident: key 20170727055708_PTS030C67 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.52.402 – volume: 80 start-page: 633 year: 2008 ident: key 20170727055708_PTS030C16 publication-title: Rev. Mod. Phys. doi: 10.1103/RevModPhys.80.633 – volume: 796 start-page: 184 year: 2008 ident: key 20170727055708_PTS030C36 publication-title: Nucl. Phys. B doi: 10.1016/j.nuclphysb.2007.12.013 – volume: 109 start-page: 111807 year: 2012 ident: key 20170727055708_PTS030C48 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.109.111807 – volume: 298 start-page: 445 year: 1993 ident: key 20170727055708_PTS030C66 publication-title: Phys. Rev. B – volume: 83 start-page: 053003 year: 2011 ident: key 20170727055708_PTS030C44 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.83.053003 – volume: 84 start-page: 053003 year: 2011 ident: key 20170727055708_PTS030C45 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.84.053003 – volume: 38 start-page: 085003 year: 2011 ident: key 20170727055708_PTS030C53 publication-title: J. Phys. G: Nucl. Part. Phys. doi: 10.1088/0954-3899/38/8/085003 – volume: 90 start-page: 021803 year: 2003 ident: key 20170727055708_PTS030C32 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.90.021803 – volume: 3 start-page: 356 year: 1971 ident: key 20170727055708_PTS030C62 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.3.356 – volume: 15 start-page: 208 year: 1969 ident: key 20170727055708_PTS030C92 publication-title: Commun. Math. Phys. doi: 10.1007/BF01645676 – volume: 295 start-page: 012032 year: 2011 ident: key 20170727055708_PTS030C21 article-title: [J-PARC g-2/EDM Collaboration] publication-title: J. Phys.: Conf. Ser. – volume: 79 start-page: 073012 year: 2009 ident: key 20170727055708_PTS030C85 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.79.073012 – volume: 107 start-page: 328 year: 1957 ident: key 20170727055708_PTS030C24 publication-title: Phys. Rev. doi: 10.1103/PhysRev.107.328 – volume: 71 start-page: 1632 year: 2011 ident: key 20170727055708_PTS030C54 publication-title: Eur. Phys. J. C doi: 10.1140/epjc/s10052-011-1632-3 – volume: 81 start-page: 053009 year: 2010 ident: key 20170727055708_PTS030C41 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.81.053009 – volume: 74 start-page: 073011 year: 2006 ident: key 20170727055708_PTS030C68 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.74.073011 – volume: 56 start-page: 252 year: 1993 ident: key 20170727055708_PTS030C72 publication-title: Yad. Fiz. – volume: 20 start-page: 682 year: 1966 ident: key 20170727055708_PTS030C26 publication-title: Phys. Lett. doi: 10.1016/0031-9163(66)91171-1 – volume: 47 start-page: 1723 year: 1993 ident: key 20170727055708_PTS030C28 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.47.1723 – volume: 99 start-page: 110406 year: 2007 ident: key 20170727055708_PTS030C37 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.99.110406 – volume: 477 start-page: 1 year: 2009 ident: key 20170727055708_PTS030C81 publication-title: Phys. Rep. doi: 10.1016/j.physrep.2009.04.003 – volume: 74 start-page: 224 year: 1948 ident: key 20170727055708_PTS030C6 publication-title: Phys. Rev. doi: 10.1103/PhysRev.74.224 – volume: 27 start-page: 192 year: 1978 ident: key 20170727055708_PTS030C93 publication-title: J. Comput. Phys. doi: 10.1016/0021-9991(78)90004-9 – volume: 78 start-page: 113006 year: 2008 ident: key 20170727055708_PTS030C40 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.78.113006 – volume: 72 start-page: 1256 year: 1947 ident: key 20170727055708_PTS030C1 publication-title: Phys. Rev. doi: 10.1103/PhysRev.72.1256.2 – volume: 1 start-page: 27 year: 1946 ident: key 20170727055708_PTS030C5 publication-title: Prog. Theor. Phys. doi: 10.1143/PTP.1.27 – volume: 71 start-page: 1515 year: 2011 ident: key 20170727055708_PTS030C55 publication-title: Eur. Phys. J. C doi: 10.1140/epjc/s10052-010-1515-z – volume: 77 start-page: 053012 year: 2008 ident: key 20170727055708_PTS030C38 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.77.053012 – volume: 10 start-page: 4007 year: 1974 ident: key 20170727055708_PTS030C89 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.10.4007 – volume: 379 start-page: 283 year: 1996 ident: key 20170727055708_PTS030C25 publication-title: Phys. Lett. B doi: 10.1016/0370-2693(96)00439-X – volume: 740 start-page: 138 year: 2006 ident: key 20170727055708_PTS030C35 publication-title: Nucl. Phys. B doi: 10.1016/j.nuclphysb.2006.01.040 – volume: 106 start-page: 675 year: 1993 ident: key 20170727055708_PTS030C29 publication-title: Nuovo Cim. A doi: 10.1007/BF02787236 – volume: 1 start-page: 2378 year: 1970 ident: key 20170727055708_PTS030C70 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.1.2378 – volume: 77 start-page: 536 year: 1950 ident: key 20170727055708_PTS030C88 publication-title: Phys. Rev. doi: 10.1103/PhysRev.77.536 – start-page: 218 volume-title: Quantum Electrodynamics year: 1990 ident: key 20170727055708_PTS030C87 doi: 10.1142/9789814503273_0007 – volume: 328 start-page: 522 year: 1994 ident: key 20170727055708_PTS030C50 publication-title: Phys. Lett. B doi: 10.1016/0370-2693(94)91513-X – volume: 97 start-page: 030801 year: 2006 ident: key 20170727055708_PTS030C10 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.97.030801 – volume: 73 start-page: 072003 year: 2006 ident: key 20170727055708_PTS030C15 article-title: [Muon g-2 Collaboration] publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.73.072003 – volume: 77 start-page: 093010 year: 2008 ident: key 20170727055708_PTS030C79 publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.77.093010 – volume: 218 start-page: 242 year: 2011 ident: key 20170727055708_PTS030C20 article-title: [J-PARC g-2/EDM Collaboration] publication-title: Nucl. Phys. Proc. Suppl. doi: 10.1016/j.nuclphysbps.2011.06.039 – volume: 23 start-page: 441 year: 1969 ident: key 20170727055708_PTS030C69 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.23.441 – volume: 100 start-page: 120801 year: 2008 ident: key 20170727055708_PTS030C11 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.100.120801 – volume: 59 start-page: 26 year: 1987 ident: key 20170727055708_PTS030C13 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.59.26 – start-page: 303 year: 2009 ident: key 20170727055708_PTS030C56 article-title: Lepton Dipole Momnets – volume: 22 start-page: 767 year: 2007 ident: key 20170727055708_PTS030C83 publication-title: Mod. Phys. Lett. A doi: 10.1142/S0217732307022992 |
| SSID | ssj0001077041 |
| Score | 2.0254338 |
| Snippet | In this review, we summarize the results of our numerical work carried out over nearly ten years on the complete determination of the 10th-order contribution... |
| SourceID | unpaywall proquest crossref oup |
| SourceType | Open Access Repository Aggregation Database Enrichment Source Index Database Publisher |
| SummonAdditionalLinks | – databaseName: ProQuest Central dbid: BENPR link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV07b9swED6kztAuadIH6sZJODhLAcGyRIlSgCDIw4YRIEYTNIA3geKjiywpsYTCS357jxLlpEDhRRN1w30k7yOPdx_AMIq0lFEQOJLHoUNV7DmxcLUTxjTwolS4qlGJuJuHs0d6uwgWOzDvamHMs8puT2w2alkIc0c-8o1Sd0BxOVyUT45RjTLZ1U5Cg1tpBXnetBh7B7ue6YzVg92ryfznw-uti8uYS8e2UA9P86OyUiV-Vs076Deh6Z9yN8M639d5ydd_eJa9CUDTfdizzJFctlAfwI7KP8FHyyKJXaOrz_ByX6O36iWxCjey1ZxfEURDWLEuUmiSqRJ5H-F5seQZnv_Jkv_OTUkjWRZN3dsZmddtPicjXetxUhUEKSMp1TPGqrQ11hRDro3N-8nNF3icTn5dzxyrsuAIGtHKkYGXcuEzDJYmy6pDRilHRyvm8phpJlMRp0wJqZE5ceQLjCnkCHosEUbBuf8VenmRq29AdGgaHyttClpN_hX_02Oq_AjPkKkXsj786BycCNuC3ChhZEmbCvcTg0bSotGH4WZw2Xbe-P-wE0Rq-4hBh2JiF-gqeZ1OfTjdILvNzPftZg7hA_rGa29nBtCrnmt1hHylSo_tJPwLbHTxAQ priority: 102 providerName: ProQuest |
| Title | Quantum electrodynamics calculation of lepton anomalous magnetic moments: Numerical approach to the perturbation theory of QED |
| URI | https://www.proquest.com/docview/3171454763 https://academic.oup.com/ptep/article-pdf/2012/1/01A107/11590859/pts030.pdf |
| UnpaywallVersion | publishedVersion |
| Volume | 2012 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAFT databaseName: Open Access Digital Library customDbUrl: eissn: 2050-3911 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0001077041 issn: 2050-3911 databaseCode: KQ8 dateStart: 20120101 isFulltext: true titleUrlDefault: http://grweb.coalliance.org/oadl/oadl.html providerName: Colorado Alliance of Research Libraries – providerCode: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources customDbUrl: eissn: 2050-3911 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0001077041 issn: 2050-3911 databaseCode: M~E dateStart: 20120101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre – providerCode: PRVASL databaseName: Oxford Journals Open Access Collection customDbUrl: eissn: 2050-3911 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0001077041 issn: 2050-3911 databaseCode: TOX dateStart: 20120101 isFulltext: true titleUrlDefault: https://academic.oup.com/journals/ providerName: Oxford University Press – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: http://www.proquest.com/pqcentral?accountid=15518 eissn: 2050-3911 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0001077041 issn: 2050-3911 databaseCode: BENPR dateStart: 20120101 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1Lb9QwEB7R3QNcKE-xtCw-lAtSdvNw4oTbAltVSCwt6krLKXL86IFsEjWJqnLgtzNeOxVFqOLAfWzFnrHnm4xnPoCjNNVSpnHsSZ4lHlVZ6GXC116S0ThMC-GrHUvE51VysqafNvHG0QGZWhjuXoXPhpKGplPN3O2i10iN0XoQzoO5HywwcpkjoMlMjy6Ua9FeZyixB-MkRmA-gvF6dbr4Zujl_BhvGzzXrkIPw3g7sR11yyfdqnMzcPN-XzX8-oqX5W-e53gfyuGb7YOT77O-K2bixx_tHP_Toh7BQ4dQycKOewz3VPUE9h1aJe4uaJ_Cz7MetdJviWPSkZbbviWodeFIwUitSakaxJeEV_WWl3Xfki2_qEzpJNnWu_q6d2TV27xRSYYW56SrCUJT0qhL9ImFnWxXdHlt5jxbfnwG6-Pl-YcTz7E5eIKmtPNkHBZcRAydssnm6oRRymPKFPN5xjSThcgKpoTUiNA4bghjCrGIDiSai-A8eg6jqq7UCyA6MQ2WlTaFsybPi-N0QFWUYqxahAmbwNtBn7lwrc4N40aZ25R7lBsF5HZ3J3B0I9zYDh9_F3uN2rtb4nAwmtxdBG0eGYJ5XGUSTeDNjSHdNc3Lf5Q7gAfGauzvoEMYdZe9eoUAqSumMH6_XJ1-ncLe-ZfN1B2DX69OFm8 |
| linkProvider | Unpaywall |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1LT9wwEB7xOMCFPijqUlp8gEuliGzixEklhNqyaCmwggokbsHxo5dskpJEaC_8NH4b48QBKlV745KTM1H82Z6xx998ADtRpKWMgsCRPA4dqmLPiYWrnTCmgRelwlWtSsTZJBxf0V_XwfUCPPRcGHOtsl8T24VaFsKcke_5Rqk7oDgdDsq_jlGNMtnVXkKDW2kFud-WGLPEjhM1u8MtXLV_fIh473re0ejy59ixKgOOoBGtHRl4KRc-Q2dhsow6ZJRy_JBiLo-ZZjIVccqUkBojB47-kjGFPlIPJf6G4NxHu4uwTH0a4-Zv-cdocv77-ZTHZcylQ0sMdGN_r6xViY-qvXf9whX-Q68zUe5Kk5d8dsez7IXDO3oLazZSJd-7ofUOFlT-Ht7YqJXYNaFah_uLBtFppsQq6shO474iiL6w4mCk0CRTJcaZhOfFlGdFU5Ep_5MbCiWZFi3P7huZNF3-KCN9qXNSFwRDVFKqW_SNaWesJV_OjM2L0eEHuHqV_t6ApbzI1UcgOjSFlpU2BFqT78X39JAqP8I9a-qFbABf-w5OhC15bpQ3sqRLvfuJQSPp0BjAzlPjsqv08f9m24jU_BZbPYqJXRCq5Hn4DmD3Cdl5Zjbnm9mGlfHl2Wlyejw5-QSr2E9edzK0BUv1baM-Y6xUp1_sgCRw89pz4BFkYC9Y |
| linkToUnpaywall | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1Lb9swDCa29LBd2j3RbF2nQ3YZ4MQP2bJ7C_pAMWDBAixAdzJkPXaYYxuxjSE99LePiuRiHYqih90pwhZp8aMp8gOYpKmWMo1jT_Is8ajKQi8TvvaSjMZhWghf7Vgivi6SyxX9chVfOTog0wvD3a3w6dDS0HSqmbld9BqpMVsPwlkw84M5Zi4zBDSZmdGFci366xQlnsJeEiMwH8HeavFt_sPQy_kxnjb4XbsOPUzjrWK76k5MutPnZuDms75q-PY3L8u_Is_FAZTDM9sLJ7-mfVdMxfU_4xz_00u9gH2HUMncrnsJT1T1Cg4cWiXuLGhfw82yR6v0a-KYdKTltm8JWl04UjBSa1KqBvEl4VW95mXdt2TNf1amdZKs611_3QlZ9LZuVJJhxDnpaoLQlDRqgzGxsMp2TZdbo3N5fvYGVhfn308vPcfm4Ama0s6TcVhwETEMyqaaqxNGKY8pU8znGdNMFiIrmBJSI0LjuCGMKcQiOpDoLoLz6C2MqrpSh0B0YgYsK20aZ02dF9fpgKooxVy1CBM2hs-DPXPhRp0bxo0ytyX3KDcGyO3ujmFyK9zYCR_3i31E6z0scTQ4Te4OgjaPDME8vmUSjeHTrSM9pObdI-Xew3PjNfZ30BGMuk2vPiBA6opj5_h_AIt7E7k |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Quantum+electrodynamics+calculation+of+lepton+anomalous+magnetic+moments%3A+Numerical+approach+to+the+perturbation+theory+of+QED&rft.jtitle=Progress+of+theoretical+and+experimental+physics&rft.au=Aoyama%2C+Tatsumi&rft.au=Hayakawa%2C+Masashi&rft.au=Kinoshita%2C+Toichiro&rft.au=Nio%2C+Makiko&rft.date=2012-01-01&rft.issn=2050-3911&rft.eissn=2050-3911&rft.volume=2012&rft.issue=1&rft_id=info:doi/10.1093%2Fptep%2Fpts030&rft.externalDBID=n%2Fa&rft.externalDocID=10_1093_ptep_pts030 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2050-3911&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2050-3911&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2050-3911&client=summon |