Three-Loop Slope of the Dirac Form Factor and the 1S Lamb Shift in Hydrogen

  • Kirill Melnikov
  • Timo van Ritbergen
Part of the Lecture Notes in Physics book series (LNP, volume 570)


The calculation of the last unknown contribution to hydrogen energy levels at order mα7, due to the three loop slope of the Dirac form factor, is described. The resulting shift of the nS energy level is found to be 3.16/n 3 kHz. Adding this result to many known contributions to the 1S Lamb shift and comparing with experimental value, we derive the value of the proton charge radius \( r_p = 0.883 \pm 0.014 \) fm.


Anomalous Magnetic Moment Master Integral Lamb Shift Loop Momentum Pauli Form Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Weitz et al.: Phys. Rev. Lett. 72, 328 (1994)CrossRefADSGoogle Scholar
  2. 2.
    D.J. Berkeland et al.: Phys. Rev. Lett. 75, 2470 (1995)CrossRefADSGoogle Scholar
  3. 3.
    S. Bourzeix et al.: Phys. Rev. Lett. 76, 384 (1996)CrossRefADSGoogle Scholar
  4. 4.
    B. de Beauvoir et al.: Phys. Rev. Lett. 78, 440 (1997)CrossRefADSGoogle Scholar
  5. 5.
    Th. Udem et al.: Phys. Rev. Lett. 79, 2646 (1997)CrossRefADSGoogle Scholar
  6. 6.
    G. Schwob et. al.: Phys. Rev. Lett. 82, 4960 (1999)CrossRefADSGoogle Scholar
  7. 7.
    P. Mohr: in Atomic, Molecular and Optical Physics Handbook, edited by G.W.F. Drake, pp. 341–351, (AIP Press, Woodbory, New York, 1996)Google Scholar
  8. 8.
    K. Melnikov and T. van Ritbergen: Phys. Rev. Lett. 84, 1673 (2000)CrossRefADSGoogle Scholar
  9. 9.
    F. Tkachov: Phys. Lett. B 100, 65 (1981); K.G. Chetyrkin and F. Tkachov: Nucl. Phys. B 192, 159 (1981)CrossRefADSMathSciNetGoogle Scholar
  10. 10.
    S. Laporta and E. Remiddi: Phys. Lett. B 379, 283 (1996)CrossRefADSGoogle Scholar
  11. 11.
    K. Melnikov and T. van Ritbergen: The three loop on-shell renormalization of QCD and QED, hep-ph/0005131Google Scholar
  12. 12.
    P.J. Mohr and B.N. Taylor: Rev. Mod. Phys. 72, 351 (2000)CrossRefADSGoogle Scholar
  13. 13.
    P. Baikov and D.J. Broadhurst: hep-ph/9504398Google Scholar
  14. 14.
    G.G. Simon et al.: Nucl. Phys. A333, 381 (1980)CrossRefADSGoogle Scholar
  15. 15.
    Ch.W. Wong: Int. J. Mod. Phys. 3, 821 (1994)ADSGoogle Scholar
  16. 16.
    R. Rosenfelder: Phys. Lett. B 479, 381 (2000)CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Kirill Melnikov
    • 1
  • Timo van Ritbergen
    • 2
  1. 1.Stanford Linear Accelerator CenterStanford UniversityUSA
  2. 2.Institut für Theoretische TeilchenphysikUniversität KarlsruheKarlsruheGermany

Personalised recommendations