Skip to main content
SpringerLink
Log in

Hadronic contributions to (g−2) of the leptons and to the effective fine structure constant α(M 2Z )

  • Published:
Zeitschrift für Physik C Particles and Fields

Abstract

The new experiment planned at Brookhaven to measure the anomalous magnetic moment of the muona μ≡(g μ−2)/2 will improve the present accuracy of 7 ppm by about a factor of 20. This requires a careful reconsideration of the theoretical uncertainties of theg−2 predictions, which are dominated by the error of the contribution from the light quarks to the photon vacuum polarization. This issue is cruicial also for the precise determination of the running fine structure constant at theZ-peak as LEP/SLC experiments continue to increase their precision. In this paper we present an updated analysis of the hadronic vacuum polarization using all presently availablee +e− data. This seems to be justified because previous work on the subject was based to some extent on preliminary or incomplete experimental data. Contributions from different energy ranges are presented separately forg−2 of the muon and the τ-lepton and for α(M 2Z ). We obtain the resultsa had*μ =(725±16)×10−10 anda had*τ =(351±10)×10−8, where the asterisk indicates the dressed (renormalization group improved) value. For the effective fine structure constant atM Z=91.1888 GeV we obtainΔα (5)had =0.0280±0.0007 and α(M 2Z )−1=128.896±0.090. Further improvement in the accuracy of theoretical predictions which depend on the hadronic vacuum polarization requires more precise measurements ofe +e− cross-sections at energies below about 12 GeV in future experiments.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Bailey et al. Phys. Lett. 68B (1977) 191; F.J.M. Farley and E. Picasso, Ann. Rev. Nucl. Sci. 29 (1979) 243; in “Quantum Electrodynamics”, ed. T. Kinoshita, World Scientific, Singapore, F.J.M. Farley, Z. Phys. C56 (1992) S88.

    Google Scholar 

  2. T. Kinoshita, Past, Present and Future of Leptong−2, in Proc. of the 10th Inter. Symposium on “High Energy Spin Physics”, Nagoya, Japan, 1992; Z. Phys. C56 (1992) S80; T. Kinoshita, in “Quantum Electrodynamics”, ed. T. Kinoshita, World Scientific, Singapore, 1990, pp. 218–321.

  3. T. Kinoshita and W.B. Lindquist, Phys. Rev. D41 (1990) 593; M.A. Samuel and G. Li, Phys. Rev. D44 (1991) 3935; S. Laporta and E. Remiddi, Phys. Lett. B301 (1993) 440.

    Google Scholar 

  4. D.J. Broadhurst, A.L. Kataev and O.V. Tarasov, Phys. Lett. B298 (1993) 445; T. Kinoshita, Phys. Rev. D47 (1993) 5013.

    Google Scholar 

  5. T. Kinoshita and W. J. Marciano, in: “Quantum Electrodynamics”, ed. T. Kinoshita, World Scientific, Singapore, 1990, pp. 419–478, and references therein.

    Google Scholar 

  6. P. Mery, S.E. Moubarik, M. Perrottet and F.M. Renard, Z. Phys. C46 (1990) 229.

    Google Scholar 

  7. W. Bernreuther, Z. Phys. C56 (1992) S97.

    Google Scholar 

  8. C. Arzt, M.B. Einhorn and J. Wudka, Phys. Rev. D49 (1994) 1370.

    Google Scholar 

  9. M.A. Samuel, G. Li and R. Mendel, Phys. Rev. Lett. 67 (1991) 668.

    Google Scholar 

  10. M. Benmerrouche, G. Orlandini and T.G. Steele, Phys. Lett. B316 (1993) 381.

    Google Scholar 

  11. L. Vuilleumier, Ph.D. Thesis, University of Lausanne, 1994.

  12. B. Lee Roberts (BNL E821), Z. Phys. C56 (1992) S101.

    Google Scholar 

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

    Google Scholar 

  14. L. Durand, III., Phys. Rev. 128 (1962) 441.

    Google Scholar 

  15. M. Gourdin and E. de Rafael, Nucl. Phys. B10 (1969) 667.

    Google Scholar 

  16. V. Barger, W.F. Long and M.G. Olsson, Phys. Lett. 60B (1975) 89.

    Google Scholar 

  17. J. Calmet, S. Narison, M. Perrottet and E. de Rafael, Phys. Lett. 61B (1976) 283; Rev. Mod. Phys. 49 (1977) 21. S. Narison, J. Phys. G: Nucl. Phys. 4 (1978) 1849.

    Google Scholar 

  18. L.M. Barkov et al., (OLYA, CMD), Nucl. Phys. B256 (1985) 365.

    Google Scholar 

  19. T. Kinoshita, B. Nižić and Y. Okamata, Phys. Rev. Lett. 52 (1984) 717; Phys. Rev. D31 (1985) 2108.

    Google Scholar 

  20. J.A. Casas, C. López and F.J. Ynduráin, Phys. Rev. D32 (1985) 736.

    Google Scholar 

  21. Ľ. Martinovič and S. Dubnička, Phys. Rev. D42 (1990) 884.

    Google Scholar 

  22. F. Jegerlehner, private communication to V.W. Hughes, 1991.

  23. A.Z. Dubničková, S. Dubnička and P. Strizenec, New Evaluation of Hadronicc Contributions to the Anomalous Magnetic, Moment of Charged Leptons, Dubna-Report, JINR-E2-92-281 (Dec. 1992).

  24. D. Schaile (LEP Collaboration), CERN-PPE-94-162, 1994; Talk given at 27th International Conference on High Energy Physics (ICHEP), Glasgow, Scotland, 20–27 July 1994.

  25. F. Jegerlehner, Z. Phys. C32 (1986) 195.

    Google Scholar 

  26. B. W. Lynn, G. Penso, C. Verzegnassi, Phys. Rev. D35 (1987) 42.

    Google Scholar 

  27. H. Burkhardt, F. Jegerlehner, G. Penso, C. Verzegnassi, Z. Phys. C42 (1989) 497.

    Google Scholar 

  28. F. Jegerlehner, in “Testing the Standard Model”, eds. M. Cvetič, P. Langacker, World Scientific, Singapore, 1991, p. 476; Prog. Part. Nucl. Phys. 27 (1991) 32.

    Google Scholar 

  29. M.L. Swartz, Preprint SLAC-PUB-6710, 1994.

  30. A.D. Martin and D. Zeppenfeld, Preprint MAD/PH/855, 1994.

  31. F.A. Berends and G.J. Komen, Phys. Lett. 63B (1976) 432; E.A. Paschos, Nucl. Phys. B159 (1979) 285; J. Ellis, M.K. Gaillard, D.V. Nanopoulos and S. Rugaz, Nucl. Phys. B176 (1980) 61; W. Wetzel, Z. Phys. C11 (1981) 117.

    Google Scholar 

  32. R. Barbieri and E. Remiddi, in “The DAΦNE physics handbook” Vol. II, eds. L. Maiani et al., (INFN, Frascati, 1992) p. 301; M.B. Einhorn, Phys. Rev. D49 (1994) 1668; E. de Rafael, Phys. Lett. B322 (1994) 239.

    Google Scholar 

  33. S.G. Gorishny, A.L. Kataev and S.A. Larin, Phys. Lett. B259 (1991) 144, L.R. Surguladze, M.A. Samuel, Phys. Rev. Lett. 66 (1991) 560;id.Phys. Rev. Lett., 2416(E).

    Google Scholar 

  34. K.G. Chetyrkin and J.H. Kühn, Phys. Lett. B342 (1995) 356 and references therein.

    Google Scholar 

  35. G. Bonneau and F. Martin, Nucl. Phys. B27 (1971) 381; D.R. Yennie, Phys. Rev. Lett. 34 (1975) 239; J.D. Jackson and D.L. Scharre, Nucl. Instrum. Methods 128 (1975) 13; M. Greco, G. Pancheri-Srivastava and Y. Srivastava, Nucl. Phys. B101 (1975) 234; B202 (1980) 118.

    Google Scholar 

  36. Y.S. Tsai, SLAC-PUB-1515 (1975); SLAC-PUB-3129 (1983).

  37. F.A. Berends et al., Nucl. Phys. B57 (1973) 381; Nucl. Phys. B68 (1974) 541; F.A. Berends and R. Kleiss, Nucl. Phys. B178 (1981) 141; F.A. Berends, R. Kleiss and S. Jadach, Nucl. Phys. B202 (1982) 63; F.A. Berends and R. Kleiss, Nucl. Phys. B228 (1983) 537.

    Google Scholar 

  38. S.I. Eidelman and E.A. Kuraev, Phys. Lett. 80B (1978) 94; V.N. Baier, V.S. Fadin, V.A. Khoze and E.A. Kuraev, Phys. Rep. C78 (1981) 293; E.A. Kuraev and V.S. Fadin, Sov. J. Nucl. Phys. 41 (1985) 466.

    Google Scholar 

  39. F.A. Berends and A. Böhm, in “High Energy Electron-Positron Physics”, eds. A. Ali and P. Söding, World Scientific, Singapore, 1988, p. 27–140 (see Fig. 8.5).

    Google Scholar 

  40. N. Cabbibo and R. Gatto, Phys. Rev. Lett. 4 (1960) 313, Phys. Rev. 124 (1961) 1577.

    Google Scholar 

  41. G. Gounaris, J. Sakurai, Phys. Rev. Lett. 21 (1968) 244; M. Gourdin et al., Phys. Lett. 30B (1969) 347; A. Quenzer et al., Phys. Lett. 76B (1978) 512.

    Google Scholar 

  42. L. Montanet et al. (Review of Particle Properties), Phys. Rev. D50 (1994) p. 1, 1173.

    Google Scholar 

  43. G.P. Yost et al. (Review of Particle Properties), Phys. Lett. B204 (1988) p. 339.

    Google Scholar 

  44. W. Buchmüller and S. Cooper, in “High Energy Electron-Positron Physics”, eds. A. Ali and P. Söding, World Scientific, Singapore, 1988, p. 410–487.

    Google Scholar 

  45. K. Königsmann, DESY 87-046 (1987).

  46. J.P. Alexander, G. Bonvicini, P.S. Drell and R. Frey, Phys. Rev. D37 (1988) 56; J.P. Alexander, G. Bonvicini, P.S. Drell, R. Frey and V. Lüth, Nucl. Phys. B320 (1989) 45.

    Google Scholar 

  47. V.M. Aulchenko et al., Phys. Lett. 186B (1987) 432.

    Google Scholar 

  48. F.M. Renard, Nucl. Phys. B82 (1974) 1; N.N. Achasov, N.M. Budnev, A.A. Kozhevnikov and G.N. Shestakov, Sov. J. Nucl. Phys. 23 (1976) 320; N.N. Achasov, A.A. Kozhevnikov, M.S. Dubrovin, V.N. Ivanchenko and E. V. Pakhtusova, Int. J. Mod. Phys. A 7 (1992) 3187.

    Google Scholar 

  49. J. Gasser, U.-G. Meißner, Nucl. Phys. B357 (1991) 90.

    Google Scholar 

  50. S.R. Amendolia et al. (NA7); Nucl. Phys. B277 (1986) 168.

    Google Scholar 

  51. J.E. Augustin, Proc. EPS Int.Conf.on HEP, CERN, Geneva, 1979; Proc. of the 1979 Cargése Summer Institute on Quarks and Leptons, eds. M. Lévy et al., Plenum Press, New York, 1980.

  52. G. D' Agostini, Preprint DESY 93-175, 1993.

  53. T. Sjöstrand and M. Bengtson, Comp. Phys. Comm. 27 (1982) 243; T. Sjöstrand, Comp. Phys. Comm. 28 (1983) 229.

    Google Scholar 

  54. A.B. Clegg and A. Donnachie, Z. Phys. C62 (1994) 455.

    Google Scholar 

  55. I.B. Vasserman et al. (OLYA), Sov. J. Nucl. Phys. 30 (1979) 519.

    Google Scholar 

  56. I.B. Vasserman et al. (TOF), Sov. J. Nucl. Phys. 33 (1981) 709.

    Google Scholar 

  57. S.R. Amendolia et al. (NA7), Phys. Lett. 138B (1984) 454.

    Google Scholar 

  58. L.M. Barkov et al. (VEPP-2M), Preprint INP 79-117, Novosibirsk, 1979.

  59. A. Quenzer et al. (DM1), Phys. Lett. 76B (1978) 512.

    Google Scholar 

  60. D. Bisello et al. (DM2), Phys. Lett. B220 (1989) 321.

    Google Scholar 

  61. G. Barbiellini et al.(μπ), Lett. Nuovo Cim. 6 (1973) 557.

    Google Scholar 

  62. D. Bollini et al. (BCF), Lett. Nuovo Cim. 14 (1975) 418.

    Google Scholar 

  63. B. Esposito et al. (MEA), Phys. Lett. 67B (1977) 239; Lett. Nuovo Cim. 28 (1980) 337.

    Google Scholar 

  64. L.M. Barkov et al. (CMD), Preprint INP 89-15, Novosibirsk, 1989.

  65. S.I. Dolinsky et al. (ND), Phys. Rep. C202 (1991) 99.

    Google Scholar 

  66. G. Cosme et al. (M2N), Phys. Lett. 63B (1976) 349; G. Parrour et al. (M2N), Phys. Lett. 63B (1976) 357.

    Google Scholar 

  67. G. Cosme et al. (M3N), Nucl. Phys. B152 (1979) 215; C. Paulot (M3N), Preprint LAL-79-14, Orsay, 1979.

    Google Scholar 

  68. B. Esposito et al. (MEA), Lett. Nuovo Cim. 28 (1980) 195.

    Google Scholar 

  69. A. Cordier et al. (DM1), Nucl. Phys. B172 (1980) 13.

    Google Scholar 

  70. A. Antonelli et al. (DM2), Z. Phys. C56 (1992) 15.

    Google Scholar 

  71. L.M. Kurdadze et al. (OLYA), JETP Lett. 43 (1986) 643.

    Google Scholar 

  72. L.M. Kurdadze et al. (OLYA), JETP Lett. 47 (1988) 512.

    Google Scholar 

  73. L.M. Barkov et al. (CMD), Sov. J. Nucl. Phys. 47 (1988) 248.

    Google Scholar 

  74. A. Cordier et al. (DM1), Phys. Lett. 109B (1982) 129.

    Google Scholar 

  75. D. Bisello et al. (DM2), Preprint LAL-90-71, Orsay, 1990; M. Schioppa, Thesis, Rome, 1986.

  76. D. Bisello et al. (DM2), Preprint LAL-91-64, Orsay, 1991.

  77. A. Cordier et al. (DM1), Phys. Lett. 106B (1981) 155.

    Google Scholar 

  78. A. Pais, Ann. Phys. N.Y. 9 (1960) 548.

    Google Scholar 

  79. C. Bacci et al. (γγ2), Phys. Lett. 86B (1979) 234.

    Google Scholar 

  80. D. Bisello et al. (DM1), Phys. Lett. 107B (1981) 145.

    Google Scholar 

  81. A. Antonelli et al. (DM2), Phys. Lett. B212 (1988) 133.

    Google Scholar 

  82. S.I. Dolinsky et al. (ND), Phys. Lett. B174 (1986) 453.

    Google Scholar 

  83. P.M. Ivanov et al. (OLYA), Phys. Lett. 107B (1981) 297.

    Google Scholar 

  84. P.M. Ivanov et al. (OLYA), JETP Lett. 36 (1982) 112.

    Google Scholar 

  85. G.V. Anikin et al. (CMD), Preprint INP 83-85, Novosibirsk, 1983; E.P. Solodov, Thesis, Novosibirsk, 1984.

  86. G. Grosdidier et al. (DM1), Preprint LAL-80-35, Orsay, 1980; B. Delcourt et al. (DM1), Phys. Lett. 99B (1981) 257; F. Mane et al. (DM1), Phys. Lett. 99B (1981) 261.

  87. M. Bernardini et al. (BCF), Phys. Lett. 46B, (1973) 261.

    Google Scholar 

  88. D. Bisello et al. (DM2), Z. Phys. C39 (1988) 13.

    Google Scholar 

  89. A. Cordier et al. (DM1), Phys. Lett 110B (1982) 335; F. Mane et al. (DM1), Phys. Lett. 112B (1982) 178.

    Google Scholar 

  90. G. Bassompierre et al., Phys. Lett. 68B (1977) 477; B. Delcourt et al. (DM1), Phys. Lett. 86B (1979) 395.

    Google Scholar 

  91. D. Bisello et al. (DM2), Nucl. Phys. B224 (1983) 379; Z. Phys. C48 (1990) 23.

    Google Scholar 

  92. A. Antonelli et al. (FENICE), Phys. Lett. B334 (1994) 431.

    Google Scholar 

  93. M. Ambrosio et al., (B\({\bar B}\)), Phys. Lett. 91B (1980) 155.

    Google Scholar 

  94. B. Esposito et al. (MEA), Lett. Nuovo Cim. 19 (1977) 21; 30 (1981) 65.

    Google Scholar 

  95. M. Bernardini et al. (BCF), Phys. Lett. 51B (1974) 200; 53B (1974) 384.

    Google Scholar 

  96. P.A. Rapidis et al. (Mark I/Lead Glass Wall), Phys. Rev. Lett. 39 (1977) 526; W. Bacino et al. (Mark I/Lead Glass Wall), Phys. Rev. Lett. 40 (1978) 671.

    Google Scholar 

  97. J.L. Siegrist et al. (Mark I), Phys. Rev. D26 (1982) 969; J.L. Siegrist, SLAC-Report No. 225, 1979.

    Google Scholar 

  98. R. Brandelik et al. (DASP), Phys. Lett. 76B (1978) 361; H. Albrecht et al. (DASP), Phys. Lett. 116B (1982) 383.

    Google Scholar 

  99. J. Burmeister et al. (PLUTO), Phys. Lett. 66B (1977) 395; Ch. Berger et al. (PLUTO), Phys. Lett. 81B (1979) 410; L. Criegee and G. Knies (PLUTO), Phys. Rep. C83 (1982) 151.

    Google Scholar 

  100. B. Niczyporuk, et al. (LENA), Z. Phys. C15 (1982) 299.

    Google Scholar 

  101. Z. Jakubowsky et al. (Crystal Ball), Z. Phys. C40 (1988) 49; C. Edwards et al. (Crystal Ball), SLAC-PUB-5160, 1990.

    Google Scholar 

  102. A.E. Blinov et al. (MD-1), Z. Phys. C49 (1991) 239; A.E. Blinov et al. (MD-1), Preprint BudkerINP 93-54, Novosibirsk, 1993.

    Google Scholar 

  103. H. J. Behrend et al. (CELLO), Phys. Lett. B183 (1987) 400.

    Google Scholar 

  104. W. Bartel et al. (JADE), Phys. Lett. 129B (1983) 145; 160B (1985) 337; B. Naroska et al. (JADE), Phys. Rep. C148 (1987) 67.

    Google Scholar 

  105. B. Adeva et al. (MARK J), Phys. Rev. Lett. 50 (1983) 799, 2051; Phys. Rep. C109 (1984) 131; Phys. Rev. D34 (1986) 681.

    Google Scholar 

  106. R. Brandelik et al. (TASSO), Phys. Lett. 113B (1982) 499; M. Althoff et al. (TASSO), Phys. Lett. 138B (1984) 441.

    Google Scholar 

  107. P. Bock et al. (DHHM), Z. Phys. C6 (1980) 125.

    Google Scholar 

  108. R. Giles et al. (CLEO), Phys. Rev. D29 (1984) 1285; D. Besson et al. (CLEO), Phys. Rev. Lett. 54 (1985) 381.

    Google Scholar 

  109. E. Rice et al. (CUSB), Phys. Rev. Lett. 48 (1982) 906.

    Google Scholar 

  110. D. Bender et al. (HRS), Phys. Rev. D31 (1985) 1.

    Google Scholar 

  111. E. Fernandez et al. (MAC), Phys. Rev. D31 (1985) 1537.

    Google Scholar 

  112. Numerical Data and Functional Relationships in Science and Technology: Group. 1: Nuclear and Particle Physics. Vol. 14: Electron-Positron Interactions, by H. Schopper, (ed.), D.R.O. Morrison, V.V. Ezhela, Yu.G. Stroganov, O.P. Yushchenko, V. Flaminio, (ed.), M.R. Whalley, (ed.), Springer, Berlin, 1992 (Landolt-Boernstein. New Series, 1.14).

  113. T.H. Chang, K.J.F. Gaemers and W.L.V. van Neerven, Nucl. Phys. B202 (1982) 407.

    Google Scholar 

  114. N.A. Papadopoulos, J.A. Peñarrocha, F.Scheck and K. Schilcher, Phys. Lett. 140B (1984) 213; Nucl. Phys. B258 (1985) 1.

    Google Scholar 

  115. V.A. Novikov, L.B. Okun and M.I. Vysotskii, Phys. Lett. B324 (1994) 89.

    Google Scholar 

  116. B.V. Geshkenbein and V.L. Morgunov, Phys. Lett. B340 (1994) 185; Preprint ITEP-70-94, 1994.

    Google Scholar 

  117. E. Pallante, Phys. Lett. B341 (1994) 221.

    Google Scholar 

  118. F. Jegerlehner and J. Fleischer, Phys. Lett. 151B (1985) 65; Acta Phys. Polonica B17 (1986) 709.

    Google Scholar 

  119. B.I. Khazin, Talk given at 27th International Conference on High Energy Physics (ICHEP), Glasgow, Scotland, 20–27 July 1994.

  120. Paolo Franzini, The Muon Gyromagnetic Ratio andR H at DAΦNE, in the “Second DAΦNE Physics Handbook”, ed. L. Maiani, L. Pancheri and N. Paver, to appear, 1995.

Download references

Author information

Authors and Affiliations

  1. Budker Institute for Nuclear Physics, 630090, Novosibirsk, Russia

    S. Eidelman

  2. Paul Scherrer Institute, Villigen PSI, CH-5232, Villigen, Switzerland

    F. Jegerlehner

Authors
  1. S. Eidelman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Jegerlehner
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Eidelman, S., Jegerlehner, F. Hadronic contributions to (g−2) of the leptons and to the effective fine structure constant α(M 2Z ). Z. Phys. C - Particles and Fields 67, 585–601 (1995). https://doi.org/10.1007/BF01553984

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01553984

Keywords

Search

Navigation