Proton polarisability contribution to the Lamb shift in muonic hydrogen at fourth order in chiral perturbation theory

  • M. C. Birse
  • J. A. McGovern
Regular Article - Theoretical Physics

Abstract

We calculate the amplitude T1 for forward doubly virtual Compton scattering in heavy-baryon chiral perturbation theory, to fourth order in the chiral expansion and with the leading contribution of the \( \gamma\)N\( \Delta\) form factor. This provides a model-independent expression for the amplitude in the low-momentum region, which is the dominant one for its contribution to the Lamb shift. It allows us to significantly reduce the theoretical uncertainty in the proton polarisability contributions to the Lamb shift in muonic hydrogen. We also stress the importance of consistency between the definitions of the Born and structure parts of the amplitude. Our result leaves no room for any effect large enough to explain the discrepancy between proton charge radii as determined from muonic and normal hydrogen.

References

  1. 1.
    R. Pohl et al., Nature 466, 213 (2010)ADSCrossRefGoogle Scholar
  2. 2.
    P.J. Mohr, B.N. Taylor, D.B. Newell, Rev. Mod. Phys. 80, 633 (2008) arXiv:0801.0028 ADSCrossRefGoogle Scholar
  3. 3.
    A1 Collaboration (J.C. Bernauer et al.), Phys. Rev. Lett. 105, 242001 (2010) arXiv:1007.5076 ADSCrossRefGoogle Scholar
  4. 4.
    U.D. Jentschura, Ann. Phys. 326, 500 (2011) arXiv:1011.5275 MathSciNetADSCrossRefMATHGoogle Scholar
  5. 5.
    U.D. Jentschura, Ann. Phys. 326, 516 (2011) arXiv:1011.5453 MathSciNetADSCrossRefMATHGoogle Scholar
  6. 6.
    E. Borie, Ann. Phys. 327, 733 (2012) arXiv:1103.1772 ADSCrossRefMATHGoogle Scholar
  7. 7.
    P.J. Mohr, B.N. Taylor, D.B. Newell, arXiv:1203.5425
  8. 8.
    J. Bernabéu, R. Tarrach, Ann. Phys. 102, 323 (1976)ADSCrossRefGoogle Scholar
  9. 9.
    J. Bernabéu, C. Jarlskog, Nucl. Phys. B 60, 347 (1973)ADSCrossRefGoogle Scholar
  10. 10.
    K. Pachucki, Phys. Rev. A 60, 3593 (1999) arXiv:physics/9906002 ADSCrossRefGoogle Scholar
  11. 11.
    S. Scherer, A.Yu. Korchin, J.H. Koch, Phys. Rev. C 54, 904 (1996) arXiv:nucl-th/9605030 ADSCrossRefGoogle Scholar
  12. 12.
    D. Drechsel, G. Knoechlein, A. Metz, S. Scherer, Phys. Rev. C 55, 424 (1997) arXiv:nucl-th/9608061 ADSCrossRefGoogle Scholar
  13. 13.
    H.W. Fearing, S. Scherer, Few-Body Syst. 23, 111 (1998) arXiv:nucl-th/9607056 ADSCrossRefGoogle Scholar
  14. 14.
    A.P. Martynenko, Phys. At. Nucl. 69, 1309 (2006) arXiv:hep-ph/0509236 CrossRefGoogle Scholar
  15. 15.
    A. Zee, Phys. Rep. 3, 127 (1972)ADSCrossRefGoogle Scholar
  16. 16.
    J. Gasser, H. Leutwyler, Phys. Rep. 87, 77 (1982)ADSCrossRefGoogle Scholar
  17. 17.
    A. Walker-Loud, C.E. Carlson, G.A. Miller, Phys. Rev. Lett. 108, 232301 (2012) arXiv:1203.0254 ADSCrossRefGoogle Scholar
  18. 18.
    G.A. Miller, A.W. Thomas, J.D. Carroll, J. Rafelski, Phys. Rev. A 84, 020101 (2011) arXiv:1101.4073 ADSCrossRefGoogle Scholar
  19. 19.
    C.E. Carlson, M. Vanderhaeghen, Phys. Rev. A 84, 020102 (2011) arXiv:1101.5965 ADSCrossRefGoogle Scholar
  20. 20.
    R.J. Hill, G. Paz, Phys. Rev. Lett. 107, 160402 (2011) arXiv:1103.4617 ADSCrossRefGoogle Scholar
  21. 21.
    C.E. Carlson, M. Vanderhaeghen, arXiv:1109.3779
  22. 22.
    D. Nevado, A. Pineda, Phys. Rev. C 77, 035202 (2008) arXiv:0712.1294 ADSCrossRefGoogle Scholar
  23. 23.
    V. Bernard, N. Kaiser, A. Schmidt, U.-G. Meissner, Phys. Lett. B 319, 269 (1993) arXiv:hep-ph/9309211 ADSCrossRefGoogle Scholar
  24. 24.
    V. Bernard, N. Kaiser, U.-G. Meissner, A. Schmidt, Z. Phys. A 348, 317 (1994) arXiv:hep-ph/9311354 ADSCrossRefGoogle Scholar
  25. 25.
    M.N. Butler, M.J. Savage, Phys. Lett. 294, 369 (1992) arXiv:hep-ph/9209204 CrossRefGoogle Scholar
  26. 26.
    T.R. Hemmert, B.R. Holstein, J. Kambor, Phys. Rev. D 55, 5598 (1997) arXiv:hep-ph/9612374 ADSCrossRefGoogle Scholar
  27. 27.
    V. Pascalutsa, D.R. Phillips, Phys. Rev. C 67, 055202 (2003) arXiv:nucl-th/0212024 ADSCrossRefGoogle Scholar
  28. 28.
    A. Pineda, Phys. Rev. C 71, 065205 (2005) arXiv:hep-ph/0412142 ADSCrossRefGoogle Scholar
  29. 29.
    V. Bernard, N. Kaiser, U.-G. Meissner, Phys. Rev. D 48, 3062 (1993) arXiv:hep-ph/9212257 ADSCrossRefGoogle Scholar
  30. 30.
    X. Ji, C.-W. Kao, J. Osborne, Phys. Lett. B 472, 1 (2000) arXiv:hep-ph/9910256 ADSCrossRefGoogle Scholar
  31. 31.
    V. Bernard, T.R. Hemmert, U.-G. Meissner, Phys. Lett. B 545, 105 (2002) arXiv:hep-ph/0203167 ADSCrossRefGoogle Scholar
  32. 32.
    V. Bernard, T.R. Hemmert, U.-G. Meissner, Phys. Rev. D 67, 076008 (2003) arXiv:hep-ph/0212033 ADSCrossRefGoogle Scholar
  33. 33.
    H.W. Griesshammer, J.A. McGovern, D.R. Phillips, G. Feldman, Prog. Part. Nucl. Phys. 67, 841 (2012) arXiv:1203.6834 ADSCrossRefGoogle Scholar
  34. 34.
    J.C. Collins, Nucl. Phys. B 149, 90 (1979)ADSCrossRefGoogle Scholar
  35. 35.
    W.A. Bardeen, W.-K. Tung, Phys. Rev. 173, 1423 (1968)ADSCrossRefGoogle Scholar
  36. 36.
    R. Tarrach, Nuovo Cimento A 28, 409 (1975)ADSCrossRefGoogle Scholar
  37. 37.
    V. Bernard, N. Kaiser, U.-G. Meissner, Int. J. Mod. Phys. E 4, 193 (1995) arXiv:hep-ph/9501385 ADSCrossRefGoogle Scholar
  38. 38.
    M.E. Luke, A.V. Manohar, Phys. Lett. B 286, 348 (1992) arXiv:hep-ph/9205228 ADSCrossRefGoogle Scholar
  39. 39.
    A.V. Manohar, Phys. Rev. D 56, 230 (1997) arXiv:hep-ph/9701294 ADSCrossRefGoogle Scholar
  40. 40.
    N. Fettes, U.-G. Meissner, M. Mojzis, S. Steininger, Ann. Phys. 283, 273 (2000) 288ADSCrossRefGoogle Scholar
  41. 41.
    V. Bernard, N. Kaiser, U.-G. Meissner, Nucl. Phys. B 373, 346 (1992)ADSCrossRefGoogle Scholar
  42. 42.
    J.A. McGovern, Phys. Rev. C 63, 064608 (2001) 66ADSCrossRefGoogle Scholar
  43. 43.
    M.C. Birse, X. Ji, J.A. McGovern, Phys. Rev. Lett. 86, 3204 (2001) arXiv:nucl-th/0011054 ADSCrossRefGoogle Scholar
  44. 44.
    V. Pascalutsa, M. Vanderhaeghen, Phys. Rev. D 73, 034003 (2006) arXiv:hep-ph/0512244 ADSCrossRefGoogle Scholar
  45. 45.
    V. Pascalutsa, M. Vanderhaeghen, S.N. Yang, Phys. Rep. 437, 125 (2007) arXiv:hep-ph/0609004 ADSCrossRefGoogle Scholar
  46. 46.
    V. Bernard, Prog. Part. Nucl. Phys. 60, 82 (2008) arXiv:0706.0312 ADSCrossRefGoogle Scholar
  47. 47.
    M.C.M. Rentmeester, R.G.E. Timmermans, J.J. de Swart, Phys. Rev. C 67, 044001 (2003) arXiv:nucl-th/0302080 ADSCrossRefGoogle Scholar
  48. 48.
    R.P. Hildebrandt, H.W. Griehammer, T.R. Hemmert, B. Pasquini, Eur. Phys. J. A 20, 293 (2004) arXiv:nucl-th/0307070 ADSCrossRefGoogle Scholar
  49. 49.
    A.I. Vainstein, V.I. Zakharov, Phys. Lett. B 72, 368 (1978)ADSCrossRefGoogle Scholar
  50. 50.
    C.E. Carlson, F. Gross, Phys. Rev. Lett. 53, 127 (1984)ADSCrossRefGoogle Scholar
  51. 51.
    V. Bernard, N. Kaiser, J. Kambor, U.-G. Meissner, Nucl. Phys. B 388, 287 (1992)ADSCrossRefGoogle Scholar
  52. 52.
    V. Bernard, H.W. Fearing, T.R. Hemmert, U.-G. Meissner, Nucl. Phys. A 635, 121 (1998) arXiv:hep-ph/9801297 ADSCrossRefGoogle Scholar
  53. 53.
    K. Pachucki, Phys. Rev. A 53, 2093 (1996)ADSCrossRefGoogle Scholar
  54. 54.
    J. Arrington, W. Melnitchouk, J.A. Tjon, Phys. Rev. C 76, 035205 (2007) arXiv:0707.1861 ADSCrossRefGoogle Scholar
  55. 55.
    I.T. Lorenz, H.-W. Hammer, U.-G. Meissner, arXiv:1205:6628Google Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • M. C. Birse
    • 1
  • J. A. McGovern
    • 1
  1. 1.Theoretical Physics Division, School of Physics and AstronomyThe University of ManchesterManchesterUK

Personalised recommendations