Four-loop corrections with two closed fermion loops to fermion self energies and the lepton anomalous magnetic moment

Journal of High Energy Physics

Volumn 2013, Issue 3, 2013, Pages

  Lee, Roman ^a   Marquard, Peter ^b   Smirnov, Alexander V ^c   Smirnov, Vladimir A ^c,d   Steinhauser, Matthias ^b  

^a NOVOSIBIRSK STATE UNIVERSITY   (Russian Federation)

^b KARLSRUHE INSTITUTE OF TECHNOLOGY   (Germany)

^c MOSCOW STATE UNIVERSITY   (Russian Federation)

^d HUMBOLDT UNIVERSITY   (Germany)

Author keywords

Electromagnetic Processes and Properties; QCD; Standard Model

Indexed keywords

EID: 84876231526     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP03(2013)162     Document Type: Article

References (62)

1. 4}, Higgs decay into b-quarks and bounds on the light quark masses, Phys. Rev. Lett. 96 (2006) 012003 [ hep-ph/0511063 ] [ INSPIRE ]. (Pubitemid 43248335)
2. 4 QCD corrections to Z and τ decays, Phys. Rev. Lett. 101 (2008) 012002 [ arXiv:0801.1821 ] [ INSPIRE ].
3. 4} QCD corrections to hadronic Z-decays, Phys. Rev. Lett. 108 (2012) 222003 [ arXiv:1201.5804 ] [ INSPIRE ].
4. K.G. Chetyrkin, J.H. Kuhn and C. Sturm, Four-loop moments of the heavy quark vacuum polarization function in perturbative QCD, Eur. Phys. J. C 48 (2006) 107 [ hep-ph/0604234 ] [ INSPIRE ]. (Pubitemid 44601861)
5. R. Boughezal, M. Czakon and T. Schutzmeier, Charm and bottom quark masses from perturbative QCD, Phys. Rev. D 74 (2006) 074006 [ hep-ph/0605023 ] [ INSPIRE ].
6. C. Sturm, Moments of heavy quark current correlators at four-loop order in perturbative QCD, JHEP 09 (2008) 075 [ arXiv:0805.3358 ] [ INSPIRE ].
7. 3}, Phys. Lett. B 669 (2008) 88 [ arXiv:0806.3405 ] [ INSPIRE ].
8. A. Maier, P. Maierhofer, P. Marquard and A.V. Smirnov, Low energy moments of heavy quark current correlators at four loops, Nucl. Phys. B 824 (2010) 1 [ arXiv:0907.2117 ] [ INSPIRE ].
9. K.G. Chetyrkin, J.H. Kühn, A. Maier, P. Maierhöfer, P. Marquard, M. Steinhauser and C. Sturm, Charm and bottom quark masses: An update, Phys. Rev. D 80 (2009) 074010 [ arXiv:0907.2110 ] [ INSPIRE ].
10. 6}ln(1/g), Phys. Rev. D 67 (2003) 105008 [ hep-ph/0211321 ] [ INSPIRE ].
11. N. Gray, D.J. Broadhurst, W. Grafe and K. Schilcher, Three loop relation of quark (modified) MS and pole masses, Z. Phys. C 48 (1990) 673 [ INSPIRE ].
12. 2 in QED, QCD and the effective field theory of a static quark, Z. Phys. C 52 (1991) 111 [ INSPIRE ].
13. 3 in QED, Phys. Lett. B 379 (1996) 283 [ hep-ph/9602417 ] [ INSPIRE ].
14. K. Melnikov and T.v. Ritbergen, The three loop relation between the MS-bar and the pole quark masses, Phys. Lett. B 482 (2000) 99 [ hep-ph/9912391 ] [ INSPIRE ].
15. P. Marquard, L. Mihaila, J.H. Piclum and M. Steinhauser, Relation between the pole and the minimally subtracted mass in dimensional regularization and dimensional reduction to three-loop order, Nucl. Phys. B 773 (2007) 1 [ hep-ph/0702185 ] [ INSPIRE ].
16. K. Melnikov and T. van Ritbergen, The three loop on-shell renormalization of QCD and QED, Nucl. Phys. B 591 (2000) 515 [ hep-ph/0005131 ] [ INSPIRE ].
17. 3), Phys. Rev. Lett. 83 (1999) 4001 [ hep-ph/9907509 ] [ INSPIRE ].
18. 3), Nucl. Phys. B 573 (2000) 617 [ hep-ph/9911434 ] [ INSPIRE ].
19. K. Melnikov and T. van Ritbergen, The three loop slope of the Dirac form-factor and the S Lamb shift in hydrogen, Phys. Rev. Lett. 84 (2000) 1673 [ hep-ph/9911277 ] [ INSPIRE ].
20. A.G. Grozin, P. Marquard, J.H. Piclum and M. Steinhauser, Three-loop chromomagnetic interaction in HQET, Nucl. Phys. B 789 (2008) 277 [ arXiv:0707.1388 ] [ INSPIRE ].
21. B.E. Lautrup and E. De Rafael, The anomalous magnetic moment of the muon and short-distance behaviour of quantum electrodynamics, Nucl. Phys. B 70 (1974) 317 [Erratum ibid. B 78 (1974) 576] [ INSPIRE ].
22. T. Kinoshita, H. Kawai and Y. Okamoto, Asymptotic photon propagator in massive QED and the muon anomalous magnetic moment, Phys. Lett. B 254 (1991) 235 [ INSPIRE ].
23. H. Kawai, T. Kinoshita and Y. Okamoto, Asymptotic photon propagator and higher order QED Callan-Symanzik β-function, Phys. Lett. B 260 (1991) 193 [ INSPIRE ].
24. R.N. Faustov, A.L. Kataev, S.A. Larin and V.V. Starshenko, The analytical contribution of the three loop diagrams with two fermion circles to the photon propagator and the muon anomalous magnetic moment, Phys. Lett. B 254 (1991) 241 [ INSPIRE ].
25. D.J. Broadhurst, A.L. Kataev and O.V. Tarasov, Analytical on-shell QED results: Three loop vacuum polarization, four loop β-function and the muon anomaly, Phys. Lett. B 298 (1993) 445 [ hep-ph/9210255 ] [ INSPIRE ].
26. P.A. Baikov and D.J. Broadhurst, Three loop QED vacuum polarization and the four loop muon anomalous magnetic moment, hep-ph/9504398 [ INSPIRE ].
27. P.A. Baikov et al., The relation between the QED charge renormalized in MSbar and on-shell schemes at four loops, the QED on-shell β-function at five loops and asymptotic contributions to the muon anomaly at five and six loops, Nucl. Phys. B 867 (2013) 182 [ arXiv:1207.2199 ] [ INSPIRE ].
28. S. Laporta, The Analytical contribution of some eighth order graphs containing vacuum polarization insertions to the muon (g-2) in QED, Phys. Lett. B 312 (1993) 495 [ hep-ph/9306324 ] [ INSPIRE ].
29. J.-P. Aguilar, D. Greynat and E. De Rafael, Muon anomaly from lepton vacuum polarization and the Mellin-Barnes representation, Phys. Rev. D 77 (2008) 093010 [ arXiv:0802.2618 ] [ INSPIRE ].
30. 4 term of the muon anomalous magnetic moment, Phys. Rev. D 70 (2004) 113001 [ hep-ph/0402206 ] [ INSPIRE ].
31. T. Aoyama, M. Hayakawa, T. Kinoshita and M. Nio, Revised value of the eighth-order QED contribution to the anomalous magnetic moment of the electron, Phys. Rev. D 77 (2008) 053012 [ arXiv:0712.2607 ] [ INSPIRE ].
32. T. Aoyama, M. Hayakawa, T. Kinoshita and M. Nio, Tenth-order QED contribution to the electron g-2 and an improved value of the fine structure constant, Phys. Rev. Lett. 109 (2012) 111807 [ arXiv:1205.5368 ] [ INSPIRE ].
33. T. Aoyama, M. Hayakawa, T. Kinoshita and M. Nio, Complete tenth-order QED contribution to the muon g-2, Phys. Rev. Lett. 109 (2012) 111808 [ arXiv:1205.5370 ] [ INSPIRE ].
34. F. Jegerlehner, The anomalous magnetic moment of the muon, Springer Tracts Mod. Phys. 226 (2008) 1 [ INSPIRE ].
35. F. Jegerlehner and A. Nyffeler, The muon g-2, Phys. Rept. 477 (2009) 1 [ arXiv:0902.3360 ] [ INSPIRE ].
36. P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys. 105 (1993) 279 [ INSPIRE ].
37. s to the decay of the Z boson into bottom quarks, Phys. Lett. B 426 (1998) 125 [ hep-ph/9712228 ] [ INSPIRE ].
38. T. Seidensticker, Automatic application of successive asymptotic expansions of Feynman diagrams, hep-ph/9905298 [ INSPIRE ].
39. J. Vermaseren, New features of FORM, math-ph/0010025 [ INSPIRE ].
40. P. Marquard and D. Seidel, unpublished.
41. A. Smirnov, Algorithm FIRE - Feynman Integral REduction, JHEP 10 (2008) 107 [ arXiv:0807.3243 ] [ INSPIRE ].
42. S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15 (2000) 5087 [ hep-ph/0102033 ] [ INSPIRE ].
43. K. Chetyrkin and F. Tkachov, Integration by parts: the algorithm to calculate β-functions in 4 loops, Nucl. Phys. B 192 (1981) 159 [ INSPIRE ].
44. R. Lee, Space-time dimensionality D as complex variable: calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D, Nucl. Phys. B 830 (2010) 474 [ arXiv:0911.0252 ] [ INSPIRE ].
45. A.V. Smirnov and M.N. Tentyukov, Feynman integral evaluation by a sector decomposition approach (FIESTA), Comput. Phys. Commun. 180 (2009) 735 [ arXiv:0807.4129 ] [ INSPIRE ].
46. A.V. Smirnov, V.A. Smirnov and M.N. Tentyukov, FIESTA 2: parallelizeable multiloop numerical calculations, Comput. Phys. Commun. 182 (2011) 790 [ arXiv:0912.0158 ] [ INSPIRE ].
47. V.A. Smirnov, Analytical result for dimensionally regularized massless on shell double box, Phys. Lett. B 460 (1999) 397 [ hep-ph/9905323 ] [ INSPIRE ].
48. J.B. Tausk, Nonplanar massless two loop Feynman diagrams with four on-shell legs, Phys. Lett. B 469 (1999) 225 [ hep-ph/9909506 ] [ INSPIRE ].
49. V.A. Smirnov, Analytic tools for Feynman integrals, Springer Tracts Mod. Phys. 250 (2013) 1 [ INSPIRE ].
50. M. Czakon, Automatized analytic continuation of Mellin-Barnes integrals, Comput. Phys. Commun. 175 (2006) 559 [ hep-ph/0511200 ] [ INSPIRE ]. (Pubitemid 44415767)
51. A.V. Smirnov and V.A. Smirnov, On the resolution of singularities of multiple Mellin-Barnes integrals, Eur. Phys. J. C 62 (2009) 445 [ arXiv:0901.0386 ] [ INSPIRE ].
52. H.R.P. Ferguson and D.H. Bailey, A polynomial time, numerically stable integer relation algorithm, RNR Techn. Rept. RNR-91-032 (1992).
53. S. Laporta, High precision Ïμ-expansions of three loop master integrals contributing to the electron g-2 in QED, Phys. Lett. B 523 (2001) 95 [ hep-ph/0111123 ] [ INSPIRE ].
54. 4), Phys. Lett. B 404 (1997) 161 [ hep-ph/9703278 ] [ INSPIRE ].
55. J.A.M. Vermaseren, S.A. Larin and T. van Ritbergen, The four loop quark mass anomalous dimension and the invariant quark mass, Phys. Lett. B 405 (1997) 327 [ hep-ph/9703284 ] [ INSPIRE ].
56. K.G. Chetyrkin, Four-loop renormalization of QCD: full set of renormalization constants and anomalous dimensions, Nucl. Phys. B 710 (2005) 499 [ hep-ph/0405193 ] [ INSPIRE ]. (Pubitemid 40280324)
57. M. Beneke and V.M. Braun, Naive non-abelianization and resummation of fermion bubble chains, Phys. Lett. B 348 (1995) 513 [ hep-ph/9411229 ] [ INSPIRE ].
58. B. Krause, Zwei- und Dreischleifen-Berechnungen zu elektrischen und magnetischen Dipolmomenten von Elementarteilchen, Ph.D. thesis, University of Karlsruhe, Germany (1997).
59. D.J. Broadhurst, Three loop on-shell charge renormalization without integration: Λ-MS (QED) to four loops, Z. Phys. C 54 (1992) 599 [ INSPIRE ].
60. P.J. Mohr, B.N. Taylor and D.B. Newell, CODATA recommended values of the fundamental physical constants: 2010, Rev. Mod. Phys. 84 (2012) 1527 [ arXiv:1203.5425 ] [ INSPIRE ].
61. J.A.M. Vermaseren, Axodraw, Comput. Phys. Commun. 83 (1994) 45 [ INSPIRE ].
62. D. Binosi, J. Collins, C. Kaufhold and L. Theussl, JaxoDraw: a graphical user interface for drawing Feynman diagrams. Version 2.0 release notes, Comput. Phys. Commun. 180 (2009) 1709 [ arXiv:0811.4113 ] [ INSPIRE ].