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The Anomalous Magnetic Moment of the Muon: A Theoretical Introduction

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Part of the book series: Lecture Notes in Physics ((LNP,volume 629))

Abstract

In February 2001, the Muon (g-2) Collaboration of the E821 experiment at the Brookhaven AGS released a new value of the anomalous magnetic moment of the muon a μ , measured with an unprecedented accuracy of 1.3 ppm [parts per million]. This annoucement has caused quite some excitement in the particle physics community. Indeed, this experimental value was claimed to show a deviation of 2.6 σ with one of the most accurate evaluations of the anomalous magnetic moment of the muon within the standard model. It was subsequently shown that a sign error in one of the theoretical contributions was responsible for a sizeable part of this discrepancy, which eventually only amounted to 1.6 σ. However, this event had the merit to draw the attention to the fact that low energy but high precision experiments represent real potentialities, complementary to the high energy accelerator programs, for evidencing possible new degrees of freedom, supersymmetry or whatever else, beyond those described by the standard model of electromagnetic, weak, and strong interactions.

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References

  • 1. T. Kinoshita Ed., Quantum Electrodynamics, World Scientific Publishing Co. Pte. Ltd., 1990.

    Google Scholar 

  • 2. B. E. Lautrup, A. Peterman and E. de Rafael, Phys. Rept. 3, 193 (1972).

    Google Scholar 

  • 3. J. Calmet, S. Narison, M. Perrottet and E. de Rafael, Rev. Mod. Phys. 49, 21 (1977).

    Google Scholar 

  • 4. A. Czarnecki and W. J. Marciano, Nucl. Phys. B (Proc. Suppl.) 76, 245 (1998).

    Google Scholar 

  • 5. V. W. Hughes and T. Kinoshita, Rev. Mod. Phys. 71, S133 (1999).

    Google Scholar 

  • 6. K. Melnikov, Int. J. Mod. Phys. A 16, 4591 (2001).

    Google Scholar 

  • 7. E. de Rafael, arXiv:hep-ph/0208251.

    Google Scholar 

  • 8. A. Nyffeler, to appear in the proceedings of the 38th Rencontres de Moriond on Electroweak Interactions and Unified Theories, Les Arcs, 15-22 March 2003, and arXiv:hep-ph/0305135.

    Google Scholar 

  • 9. A. Czarnecki and W. J. Marciano, Phys. Rev. D 64, 013014 (2001).

    Google Scholar 

  • 10. A list of recent papers on the subject can be found under the URL http://www.slac.stanford.edu/spires/find/hep/www?c=PRLTA,86,2227.

    Google Scholar 

  • 11. L. L. Foldy, Phys. Rev. 87, 688 (1952); Rev. Mod. Phys. 30, 471 (1958).

    Google Scholar 

  • 12. Ya. B. Zeldovich, Soviet Phys. JETP 6, 1184 (1958).

    Google Scholar 

  • 13. Ya. B. Zeldovich and A. M. Perelomov, Soviet Phys. JETP 12, 777 (1961).

    Google Scholar 

  • 14. R. E. Marshak, Riazuddin, and C. P. Ryan, Theory of Weak Interactions in Particle Physics, John Wiley and Sons Inc., 1969.

    Google Scholar 

  • 15. S. J. Brodsky and J. D. Sullivan, Phys. Rev. 156, 1644 (1967).

    Google Scholar 

  • 16. R. Barbieri, J. A. Mignaco and E. Remiddi, Nuovo Cimento 11A, 824 (1972).

    Google Scholar 

  • 17. H. Pietschmann, Zeit. f. Phys. 178, 409 (1964).

    Google Scholar 

  • 18. T. Appelquist and J. Carazzone, Phys. Rev. D 11, 2856 (1975).

    Google Scholar 

  • 19. C. Bouchiat, J. Iliopoulos and P. Meyer, Phys. Lett. B38, 519 (1972).

    Google Scholar 

  • 20. D. J. Gross and R. Jackiw, Phys. Rev. D 6, 477 (1972).

    Google Scholar 

  • 21. C. P. Korthals Altes and M. Perrottet, Phys. Lett. B 39, 546 (1972).

    Google Scholar 

  • 22. T. Sterling and M. J. Veltman, Nucl. Phys. B 189, 557 (1981).

    Google Scholar 

  • 23. E. d’Hoker and E. Farhi, Nucl. Phys. B248, 59, 77 (1984).

    Google Scholar 

  • 24. T. Kinoshita, Nuovo Cimento 51B, 140 (1967).

    Google Scholar 

  • 25. B. E. Lautrup and E. de Rafael, Nucl. Phys. B70, 317 (1974).

    Google Scholar 

  • 26. E. de Rafael and J. L. Rosner, Ann. Phys. (N. Y.) 82, 369 (1974).

    Google Scholar 

  • 27. T. Kinoshita and W. J. Marciano, Theory of the Muon Anomalous Magnetic Moment, in [1], p. 419.

    Google Scholar 

  • 28. B. Kayser, Phys. Rev. D 26, 1662 (1982).

    Google Scholar 

  • 29. R. N. Mohapatra and P. B. Pal, Massive Neutrinos in Physics and Astrophysics, World Scientific Publishing Co. Pte. Ltd., 1991.

    Google Scholar 

  • 30. J. E. Nafe, E. B. Nelson and I. I. Rabi, Phys. Rev. 71, 914 (1947).

    Google Scholar 

  • 31. H. G. Dehmelt, Phys. Rev. 109, 381 (1958).

    Google Scholar 

  • 32. R. S. Van Dyck, P. B. Schwinberg and H. G. Dehmelt, Phys. Rev. Lett. 59, 26 (1987).

    Google Scholar 

  • 33. P. J. Mohr and B. N. Taylor, Rev. Mod. Phys. 72, 351 (2000).

    Google Scholar 

  • 34. K. Hagiwara et al. [Particle Data Group Collaboration], Phys. Rev. D 66, 010001 (2002).

    Google Scholar 

  • 35. R. S. Van Dyck, Anomalous Magnetic Moment of Single Electrons and Positrons: Experiment, in [1], p. 322.

    Google Scholar 

  • 36. A. Rich and J. C. Wesley, Rev. Mod. Phys. 44, 250 (1972).

    Google Scholar 

  • 37. P. Kusch and H. M. Fowley, Phys. Rev. 72, 1256 (1947).

    Google Scholar 

  • 38. P. A. Franken and S. Liebes Jr., Phys. Rev. 104, 1197 (1956).

    Google Scholar 

  • 39. A. A. Schuppe, R. W. Pidd, and H. R. Crane, Phys. Rev. 121, 1 (1961).

    Google Scholar 

  • 40. D. T. Wilkinson and H. R. Crane, Phys. Rev. 130, 852 (1963).

    Google Scholar 

  • 41. G. Gräff, E. Klempt and G. Werth, Z. Phys. 222, 201 (1968).

    Google Scholar 

  • 42. J. C. Wesley and A. Rich, Phys. Rev. A 4, 1341 (1971).

    Google Scholar 

  • 43. R. S. Van Dyck, P. B. Schwinberg and H. G. Dehmelt, Phys. Rev. Lett. 38, 310 (1977).

    Google Scholar 

  • 44. F. J. M. Farley and E. Picasso, The Muon g - 2 Experiments, in [1], p. 479.

    Google Scholar 

  • 45. J. Bailey et al., Phys. Lett. B28, 287 (1968).

    Google Scholar 

  • 46. J. Bailey et al., Phys. Lett. B55, 420 (1975).

    Google Scholar 

  • 47. J. Bailey et al. [CERN-Mainz-Daresbury Collaboration], Nucl. Phys. B 150, 1 (1979).

    Google Scholar 

  • 48. R. M. Carey et al.,Phys. Rev. Lett. 82, 1632 (1999).

    Google Scholar 

  • 49. H. N. Brown et al.[Muon (g - 2) Collaboration], Phys. Rev. D 62, 091101(R) (2000).

    Google Scholar 

  • 50. H. N. Brown et al.[Muon (g - 2) Collaboration], Phys. Rev. Lett. 86, 2227 (2001).

    Google Scholar 

  • 51. G. W. Bennett et al.[Muon (g - 2) Collaboration], Phys. Rev. Lett. 89, 101804 (2002); Erratum-ibid. 89, 129903 (2002).

    Google Scholar 

  • 52. E. D. Commins, S. B. Ross, D. DeMille and B. C. Regan, Phys. Rev. A 50, 2960 (1994).

    Google Scholar 

  • 53. B. C. Regan, E. D. Commins, C. J. Schmidt and D. DeMille, Phys. Rev. Lett. 88, 071805 (2002).

    Google Scholar 

  • 54. J. L. Feng, K. T. Matchev and Y. Shadmi, Nucl. Phys. B 613, 366 (2001); Phys. Lett. B555, 89 (2003).

    Google Scholar 

  • 55. Y. K. Semertzidis et al., Int. J. Mod. Phys. A 16S1B, 690 (2001).

    Google Scholar 

  • 56. K. Ackerstaff et al. [OPAL Collaboration], Phys. Lett. B431, 188 (1998).

    Google Scholar 

  • 57. M. Acciarri et al. [L3 Collaboration], Phys. Lett. B434, 169 (1998).

    Google Scholar 

  • 58. S. Narison, Phys. Lett. B513, 53 (2001); Erratum-ibid. B526, 414 (2002).

    Google Scholar 

  • 59. J. Schwinger, Phys. Rev. 73, 413 (1948); 76, 790 (1949).

    Google Scholar 

  • 60. R. Karplus and N. M. Kroll, Phys. Rev. 77, 536 (1950).

    Google Scholar 

  • 61. A. Peterman, Helv. Phys. Acta 30, 407 (1957).

    Google Scholar 

  • 62. C. M. Sommerfield, Phys. Rev. 107, 328 (1957).

    Google Scholar 

  • 63. C. M. Sommerfield, Ann. Phys. (N.Y.) 5, 26 (1958).

    Google Scholar 

  • 64. G. S. Adkins, Phys. Rev. D 39, 3798 (1989).

    Google Scholar 

  • 65. J. Schwinger, Particles, Sources and Fields, VolumeIII, Addison-Wesley Publishing Company, Inc., 1989.

    Google Scholar 

  • 66. D. Kreimer, arXiv:hep-th/9412045; D. Kreimer, J. Knot Theor. Ramifications 6, 479 (1997); D. J. Broadhurst, J. A. Gracey and D. Kreimer, Z. Phys. C 75, 559 (1997); D. J. Broadhurst and D. Kreimer, Phys. Lett. B393, 403 (1997).

    Google Scholar 

  • 67. D. Kreimer, Adv. Theor. Math. Phys. 2, 303 (1998).

    Google Scholar 

  • 68. A. Connes and D. Kreimer, Commun. Math. Phys. 199, 203 (1998).

    Google Scholar 

  • 69. S. Laporta and E. Remiddi, Phys. Lett. B379, 283 (1996).

    Google Scholar 

  • 70. R. Barbieri and E. Remiddi, Nucl. Phys. B 90, 233 (1975).

    Google Scholar 

  • 71. M. A. Samuel and G. Li, Phys. Rev. D 44, 3935 (1991); ibid. D 46, 4782 (1992) and D 48, 1879 (1993), errata.

    Google Scholar 

  • 72. S. Laporta and E. Remiddi, Phys. Lett. B265, 181 (1991).

    Google Scholar 

  • 73. S. Laporta, Phys. Rev. D 47, 4793 (1993).

    Google Scholar 

  • 74. S. Laporta, Phys. Lett. B343, 421 (1995).

    Google Scholar 

  • 75. S. Laporta and E. Remiddi, Phys. Lett. B356, 390 (1995).

    Google Scholar 

  • 76. R. Z. Roskies, E. Remiddi and M. J. Levine, Analytic evaluation of sixth-order contributions to the electron’s g factor, in [1], p. 162.

    Google Scholar 

  • 77. T. Kinoshita, Theory of the anomalous magnetic moment of the electron – Numerical Approach, in [1], p. 218.

    Google Scholar 

  • 78. J. Aldins, S. J. Brodsky, A. Dufner, and T. Kinoshita, Phys. Rev. Lett. 23, 441 (1970); Phys. Rev. D 1, 2378 (1970).

    Google Scholar 

  • 79. S. J. Brodsky and T. Kinoshita, Phys. Rev. D 3, 356 (1971).

    Google Scholar 

  • 80. J. Calmet and M. Perrottet, Phys. Rev. D 3, 3101 (1971).

    Google Scholar 

  • 81. J. Calmet and A. Peterman, Phys. Lett. B47, 369 (1973).

    Google Scholar 

  • 82. M. J. Levine and J. Wright, Phys. Rev. Lett. 26, 1351 (1971); Phys. Rev. D 8, 3171 (1973).

    Google Scholar 

  • 83. R. Carroll and Y. P. Yao, Phys. Lett. B48, 125 (1974).

    Google Scholar 

  • 84. P. Cvitanovic and T. Kinoshita, Phys. Rev. D 10, 3978, 3991, 4007 (1974).

    Google Scholar 

  • 85. T. Kinoshita and W. B. Lindquist, Phys. Rev. D 27, 867, 877, 886 (1983); D 39, 2407 (1989); D 42, 636 (1990).

    Google Scholar 

  • 86. M. Caffo, S. Turrini, and E. Remiddi, Phys. Rev. D 30, 483 (1984).

    Google Scholar 

  • 87. E. Remiddi and S. P. Sorella, Lett. Nuovo Cim. 44, 231 (1985).

    Google Scholar 

  • 88. T. Kinoshita, IEEE Trans. Instrum. Meas. 44, 498 (1995).

    Google Scholar 

  • 89. T. Kinoshita and M. Nio, Phys. Rev. Lett. 90, 021803 (2003).

    Google Scholar 

  • 90. H. Suura and E. Wichmann, Phys. Rev. 105, 1930 (1957).

    Google Scholar 

  • 91. A. Peterman, Phys. Rev. 105, 1931 (1957).

    Google Scholar 

  • 92. H. H. Elend, Phys. Lett. 20, 682 (1966); Erratum-ibid. 21, 720 (1966).

    Google Scholar 

  • 93. B. E. Lautrup and E. de Rafael, Phys. Rev. 174, 1835 (1968).

    Google Scholar 

  • 94. W. Liu et al., Phys. Rev. Lett. 82, 711 (1999).

    Google Scholar 

  • 95. S. Laporta, Nuovo Cimento 106A, 675 (1993).

    Google Scholar 

  • 96. S. Laporta and E. Remiddi, Phys. Lett. B301, 440 (1993).

    Google Scholar 

  • 97. A. Czarnecki, B. Krause and W. J. Marciano, Phys. Rev. Lett. 76, 3267 (1996).

    Google Scholar 

  • 98. B. Krause, Phys. Lett. B390, 392 (1997).

    Google Scholar 

  • 99. B. E. Lautrup, Phys. Lett. B32, 627 (1970).

    Google Scholar 

  • 100. B. E. Lautrup and E. de Rafael, Nuovo Cim. 64A, 322 (1970).

    Google Scholar 

  • 101. B. E. Lautrup, A. Peterman and E. de Rafael, Nuovo Cim. 1A, 238 (1971).

    Google Scholar 

  • 102. T. Kinoshita, Phys. Rev. D 47, 5013 (1993).

    Google Scholar 

  • 103. T. Kinoshita, B. Nizic, Y. Okamoto, Phys. Rev. D 41, 593 (1990).

    Google Scholar 

  • 104. A. S. Yelkhovsky, Sov. J. Nucl. Phys. 49, 656 (1989).

    Google Scholar 

  • 105. A. I. Milstein and A. S. Yelkhovsky, Phys. Lett. B233, 11 (1989).

    Google Scholar 

  • 106. S. G. Karshenboim, Phys. Atom. Nucl. 56, 857 (1993).

    Google Scholar 

  • 107. C. Bouchiat and L. Michel, J. Phys. Radium 22, 121 (1961).

    Google Scholar 

  • 108. L. Durand III, Phys. Rev. 128, 441 (1962); Erratum-ibid. 129, 2835 (1963).

    Google Scholar 

  • 109. J. Z. Bai et al. [BES Collaboration], Phys. Rev. Lett. 84, 594 (2000); Phys. Rev. Lett. 88, 101802 (2000).

    Google Scholar 

  • 110. R. R. Akhmetshin et al. [CMD-2 Collaboration], Phys. Lett. B527, 161 (2002).

    Google Scholar 

  • 111. R. Barate et al. [ALEPH Collaboration], Z. Phys. C 2, 123 (1997).

    Google Scholar 

  • 112. K. Ackerstaff at al. [OPAL Collaboration], Eur. J. Phys. C 7, 571 (1999).

    Google Scholar 

  • 113. S. Anderson et al. [CLEO Collaboration], Phys. Rev. D 61, 112002 (2000).

    Google Scholar 

  • 114. K. W. Edwards et al. [CLEO Collaboration], Phys. Rev. D 61, 072003 (2000).

    Google Scholar 

  • 115. S. Eidelman and F.Jegerlehner, Z. Phys. C 67, 585 (1995).

    Google Scholar 

  • 116. D. H. Brown and W. A. Worstell, Phys. Rev. D 54, 3237 (1996).

    Google Scholar 

  • 117. R. Alemany, M. Davier and A. Höcker, Eur. Phys. J. C 2, 123 (1998).

    Google Scholar 

  • 118. M. Davier and A. Höcker, Phys. Lett. B419, 419 (1998).

    Google Scholar 

  • 119. M. Davier and A. Höcker, Phys. Lett. B435, 427 (1998).

    Google Scholar 

  • 120. J. F. De Trocóniz and F. J. Ynduráin, Phys. Rev. D 65, 093001 (2002).

    Google Scholar 

  • 121. F. Jegerlehner, J. Phys. G 29, 101 (2003).

    Google Scholar 

  • 122. M. Davier, S. Eidelman, A. Höcker and Z. Zhang, Eur. Phys. J. C 27, 497 (2003).

    Google Scholar 

  • 123. K. Hagiwara, A. D. Martin, D. Nomura and T. Teubner, Phys. Lett. B 557, 69 (2003).

    Google Scholar 

  • 124. A. G. Denig et al. [the KLOE Collaboration], arXiv:hep-ex/0211024.

    Google Scholar 

  • 125. E. P. Solodov [BABAR collaboration], in Proc. of the e+ e- Physics at Intermediate Energies Conference ed. Diego Bettoni, and arXiv:hep-ex/0107027.

    Google Scholar 

  • 126. M. Perrottet and E. de Rafael, unpublished.

    Google Scholar 

  • 127. S. Peris, M. Perrottet and E. de Rafael, JHEP 9805, 011 (1998).

    Google Scholar 

  • 128. G. ‘t Hooft, Nucl. Phys. B 72, 461 (1974).

    Google Scholar 

  • 129. E. Witten, Nucl. Phys. B 160, 157 (1979).

    Google Scholar 

  • 130. J. Calmet, S. Narison, M. Perrottet and E. de Rafael, Phys. Lett. B61, 283 (1976).

    Google Scholar 

  • 131. T. Kinoshita, B. Nizic, Y. Okamoto, Phys. Rev. D 31, 2108 (1985).

    Google Scholar 

  • 132. J. Bijnens, E. Pallante and J. Prades, Nucl. Phys. B 474, 379 (1996).

    Google Scholar 

  • 133. M. Hayakawa, T. Kinoshita and A. I. Sanda, Phys. Rev. Lett. 75, 790 (1995); Phys. Rev. D 54, 3137 (1996).

    Google Scholar 

  • 134. M. Hayakawa and T. Kinoshita, Phys. Rev. D 57, 465 (1998).

    Google Scholar 

  • 135. M. Knecht and A. Nyffeler, Phys. Rev. D 65, 073034 (2002).

    Google Scholar 

  • 136. M. Hayakawa and T. Kinoshita, arXiv:hep-ph/0112102, and the erratum to [136] published in Phys. Rev. D 66, 019902(E) (2002).

    Google Scholar 

  • 137. J. Bijnens, E. Pallante and J. Prades, Nucl. Phys. B 626, 410 (2002).

    Google Scholar 

  • 138. J. Wess and B. Zumino, Phys. Lett. 37B, 95 (1971).

    Google Scholar 

  • 139. E. Witten, Nucl. Phys. B223, 422 (1983).

    Google Scholar 

  • 140. S. L. Adler, Phys. Rev. 177, 2426 (1969).

    Google Scholar 

  • 141. J. S. Bell and R. Jackiw, Nuovo Cimento A 60, 47 (1969).

    Google Scholar 

  • 142. E. de Rafael, Phys. Lett. B322, 239 (1994).

    Google Scholar 

  • 143. J. Bijnens and F. Persson, arXiv:hep-ph/0106130.

    Google Scholar 

  • 144. M. Knecht and A. Nyffeler, Eur. Phys. J. C 21, 659 (2001).

    Google Scholar 

  • 145. J. L. Rosner, Ann. Phys. (N.Y.) 44, 11 (1967).

    Google Scholar 

  • 146. M. J. Levine and R. Roskies, Phys. Rev. D 9, 421 (1974); M. J. Levine, E. Remiddi, and R. Roskies, ibid. 20, 2068 (1979).

    Google Scholar 

  • 147. M. Knecht, A. Nyffeler, M. Perrottet and E. de Rafael, Phys. Rev. Lett. 88, 071802 (2002).

    Google Scholar 

  • 148. I. Blokland, A. Czarnecki and K. Melnikov, Phys. Rev. Lett. 88, 071803 (2002).

    Google Scholar 

  • 149. W. J. Bardeen and A. de Gouvea, private communication.

    Google Scholar 

  • 150. W.A. Bardeen, R. Gastmans and B.E. Lautrup, Nucl. Phys. B46, 315 (1972).

    Google Scholar 

  • 151. G. Altarelli, N. Cabbibo and L. Maiani, Phys. Lett. 40B, 415 (1972).

    Google Scholar 

  • 152. R. Jackiw and S. Weinberg, Phys. Rev. D 5, 2473 (1972).

    Google Scholar 

  • 153. I. Bars and M. Yoshimura, Phys. Rev. D 6, 374 (1972).

    Google Scholar 

  • 154. M. Fujikawa, B.W. Lee and A.I. Sanda, Phys. Rev. D 6, 2923 (1972).

    Google Scholar 

  • 155. V.A. Smirnov, Mod. Phys. Lett. A 10, 1485 (1995).

    Google Scholar 

  • 156. S. Peris, M. Perrottet and E. de Rafael, Phys. Lett. B355, 523 (1995).

    Google Scholar 

  • 157. A. Czarnecki, B. Krause and W. Marciano, Phys. Rev. D 52, R2619 (1995).

    Google Scholar 

  • 158. T.V. Kukhto, E.A. Kuraev, A. Schiller and Z.K. Silagadze, Nucl. Phys. B 371, 567 (1992).

    Google Scholar 

  • 159. M. Knecht, S. Peris, M. Perrottet and E. de Rafael, JHEP 0211, 003 (2002).

    Google Scholar 

  • 160. A. Czarnecki, W. J. Marciano and A. Vainshtein, Phys. Rev. D 67, 073006 (2003).

    Google Scholar 

  • 161. A. Vainshtein, arXiv:hep-ph/0212231.

    Google Scholar 

  • 162. M. Knecht, S. Peris, M. Perrottet and E. de Rafael, in preparation.

    Google Scholar 

  • 163. G. Degrassi and G.F. Giudice, Phys. Rev. 58D (1998) 053007.

    Google Scholar 

  • 164. R. R. Akhmetshin et al. [CMD-2 Collaboration], arXiv:hep-ex/0308008.

    Google Scholar 

  • 165. M. Davier, S. Eidelman, A. Höcker and Z. Zhang, arXiv:hep-ph/0308213.

    Google Scholar 

  • 166. P. Achard et al. [L3 Collaboration], CERN-EP/2003-19.

    Google Scholar 

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Knecht, M. The Anomalous Magnetic Moment of the Muon: A Theoretical Introduction. In: Meissner, UG., Plessas, W. (eds) Lectures on Flavor Physics. Lecture Notes in Physics, vol 629. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44457-2_2

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