Skip to main content
Log in

The electric dipole moment of the deuteron from the QCD θ-term

  • Regular Article - Theoretical Physics
  • Published:
The European Physical Journal A Aims and scope Submit manuscript

Abstract

The two-nucleon contributions to the electric dipole moment (EDM) of the deuteron, induced by the QCD θ-term, are calculated in the framework of effective field theory up-to-and-including next-to-next-to-leading order. In particular we find for the difference of the deuteron EDM and the sum of proton and neutron EDM induced by the QCD θ-term a value of \(( - 5.4 \pm 3.9) \bar \theta \times 10^{ - 4}\) e fm. The by far dominant uncertainty comes from the CP- and isospin-violating πNN coupling constant.

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

Access this article

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. I.B. Khriplovich, S.K. Lamoreaux, CP Violation Without Strangeness: Electric Dipole Moments of Particles, Atoms, and Molecules (Springer, Berlin, Germany, 1997).

  2. I.I.Y. Bigi, A.I. Sanda, CP Violation, 2nd edition (Cambridge University Press, Cambridge, UK, 2009).

  3. M. Pospelov, A. Ritz, Ann. Phys. 318, 119 (2005) hep-ph/0504231.

    Article  ADS  MATH  Google Scholar 

  4. V. Baluni, Phys. Rev. D 19, 2227 (1979).

    Article  ADS  Google Scholar 

  5. R.J. Crewther, P. Di Vecchia, G. Veneziano, E. Witten, Phys. Lett. B 88, 123 (1979) 91.

    Article  ADS  Google Scholar 

  6. G. ’t Hooft, Phys. Rev. Lett. 37, 8 (1976).

    Article  ADS  Google Scholar 

  7. W. Buchmüller, D. Wyler, Nucl. Phys. B 268, 621 (1986).

    Article  ADS  Google Scholar 

  8. A. De Rujula, M.B. Gavela, O. Pene, F.J. Vegas, Nucl. Phys. B 357, 311 (1991).

    Article  ADS  Google Scholar 

  9. B. Grzadkowski, M. Iskrzynski, M. Misiak, J. Rosiek, JHEP 10, 085 (2010) arXiv:1008.4884 [hep-ph].

    Article  ADS  Google Scholar 

  10. C.M. Maekawa, E. Mereghetti, J. de Vries, U. van Kolck, Nucl. Phys. A 872, 117 (2011).

    Article  ADS  Google Scholar 

  11. J. de Vries, E. Mereghetti, R.G.E. Timmermans, U. van Kolck, arXiv:1212.0990 [hep-ph].

  12. M.J. Ramsey-Musolf, S. Su, Phys. Rep. 456, 1 (2008) hep-ph/0612057.

    Article  ADS  Google Scholar 

  13. S. Weinberg, Phys. Rev. Lett. 63, 2333 (1989).

    Article  ADS  Google Scholar 

  14. T. Mannel, N. Uraltsev, Phys. Rev. D 85, 096002 (2012) arXiv:1202.6270 [hep-ph].

    Article  ADS  Google Scholar 

  15. T. Mannel, N. Uraltsev, arXiv:1205.0233 [hep-ph].

  16. LHCb Collaboration (R. Aaij et al.), Phys. Rev. Lett. 108, 111602 (2012) arXiv:1112.0938 [hep-ex].

    Article  ADS  Google Scholar 

  17. CDF Collaboration (T. Aaltonen et al.), Phys. Rev. D 85, 012009 (2012) arXiv:1111.5023 [hep-ex].

    Article  ADS  Google Scholar 

  18. I.B. Khriplovich, R.A. Korkin, Nucl. Phys. A 665, 365 (2000) nucl-th/9904081.

    Article  ADS  Google Scholar 

  19. O. Lebedev, K.A. Olive, M. Pospelov, A. Ritz, Phys. Rev. D 70, 016003 (2004) hep-ph/0402023.

    Article  ADS  Google Scholar 

  20. C.-P. Liu, R.G.E. Timmermans, Phys. Rev. C 70, 055501 (2004) nucl-th/0408060.

    Article  ADS  Google Scholar 

  21. I. Stetcu, C.-P. Liu, J.L. Friar, A.C. Hayes, P. Navratil, Phys. Lett. B 665, 168 (2008) arXiv:0804.3815 [nucl-th].

    Article  ADS  Google Scholar 

  22. J. de Vries, E. Mereghetti, R.G.E. Timmermans, U. van Kolck, Phys. Rev. Lett. 107, 091804 (2011) arXiv:1102.4068 [hep-ph].

    Article  ADS  Google Scholar 

  23. J. de Vries, R. Higa, C.-P. Liu, E. Mereghetti, I. Stetcu, R.G.E. Timmermans, U. van Kolck, Phys. Rev. C 84, 065501 (2011) arXiv:1109.3604 [hep-ph].

    Article  ADS  Google Scholar 

  24. I.R. Afnan, B.F. Gibson, Phys. Rev. C 82, 064002 (2010) arXiv:1011.4968 [nucl-th].

    Article  ADS  Google Scholar 

  25. B.F. Gibson, I.R. Afnan, AIP Conf. Proc. 1441, 579 (2012).

    Article  ADS  Google Scholar 

  26. EDM Collaboration (Y.K. Semertzidis et al.), AIP Conf. Proc. 698, 200 (2004) hep-ex/0308063.

    Article  ADS  Google Scholar 

  27. Y.F. Orlov, W.M. Morse, Y.K. Semertzidis, Phys. Rev. Lett. 96, 214802 (2006) hep-ex/0605022.

    Article  ADS  Google Scholar 

  28. D. Anastassopoulos, AGS Proposal, April 2008, available from http://www.bnl.gov/edm/.

  29. A. Lehrach, B. Lorentz, W. Morse, N.N. Nikolaev, F. Rathmann, arXiv:1201.5773 [hep-ex].

  30. JEDI Collaboration (R. Engels), COSY proposal #216, May 2012, available from http://collaborations.fz-juelich.de/ikp/jedi/documents/proposals.shtml.

  31. E. Mereghetti, W.H. Hockings, U. van Kolck, Ann. Phys. 325, 2363 (2010) arXiv:1002.2391 [hep-ph].

    Article  ADS  MATH  Google Scholar 

  32. A. Pich, E. de Rafael, Nucl. Phys. B 367, 313 (1991).

    Article  ADS  Google Scholar 

  33. K. Ottnad, B. Kubis, U.-G. Meißner, F.-K. Guo, Phys. Lett. B 687, 42 (2010) arXiv:0911.3981 [hep-ph].

    Article  ADS  Google Scholar 

  34. K. Ottnad, Diplom thesis, University of Bonn (2009) unpublished.

  35. F.-K. Guo, U.-G. Meißner, JHEP 12, 097 (2012) arXiv:1210.5887 [hep-ph].

    Article  ADS  Google Scholar 

  36. Particle Data Group (J. Beringer et al.), Phys. Rev. D 86, 010001 (2012).

    Article  ADS  Google Scholar 

  37. V. Bernard, N. Kaiser, U.-G. Meißner, Int. J. Mod. Phys. E 4, 193 (1995) hep-ph/9501384.

    Article  ADS  Google Scholar 

  38. M. Cini, E. Ferrair, R. Gatto, Phys. Rev. Lett. 2, 7 (1959).

    Article  ADS  Google Scholar 

  39. W. Cottingham, Ann. Phys. 25, 424 (1963).

    Article  ADS  Google Scholar 

  40. J. Gasser, H. Leutwyler, Phys. Rep. 87, 77 (1982).

    Article  ADS  Google Scholar 

  41. A. Walker-Loud, C.E. Carlson, G.A. Miller, Phys. Rev. Lett. 108, 232301 (2012) arXiv:1203.0254 [nucl-th].

    Article  ADS  Google Scholar 

  42. S.R. Beane, K. Orginos, M.J. Savage, Nucl. Phys. B 768, 38 (2007).

    Article  ADS  Google Scholar 

  43. A. Filin et al., Phys. Lett. B 681, 423 (2009) arXiv:0907.4671 [nucl-th].

    Article  ADS  Google Scholar 

  44. E. Mereghetti, J. de Vries, W.H. Hockings, C.M. Maekawa, U. van Kolck, Phys. Lett. B 696, 97 (2011) arXiv:1010.4078 [hep-ph].

    Article  ADS  Google Scholar 

  45. V. Baru, C. Hanhart, M. Hoferichter, B. Kubis, A. Nogga, D.R. Phillips, Nucl. Phys. A 872, 69 (2011) arXiv:1107.5509 [nucl-th].

    Article  ADS  Google Scholar 

  46. T. Becher, H. Leutwyler, JHEP 06, 017 (2001) arXiv:hep-ph/0103263.

    Article  ADS  Google Scholar 

  47. J. Gasser, M.A. Ivanov, E. Lipartia, M. Mojžiš, A. Rusetsky, Eur. Phys. J. C 26, 13 (2002) arXiv:hep-ph/0206068.

    Article  ADS  Google Scholar 

  48. P. Büttiker, U.-G. Meißner, Nucl. Phys. A 668, 97 (2000) arXiv:hep-ph/9908247.

    Article  Google Scholar 

  49. N. Fettes, U.-G. Meißner, Nucl. Phys. A 676, 311 (2000) arXiv:hep-ph/0002162.

    Article  ADS  Google Scholar 

  50. J. Gasser, H. Leutwyler, Nucl. Phys. B 250, 539 (1985).

    Article  ADS  Google Scholar 

  51. A.M. Gasparyan, J. Haidenbauer, C. Hanhart, J. Speth, Phys. Rev. C 68, 045207 (2003) nucl-th/0307072.

    Article  ADS  Google Scholar 

  52. S. Weinberg, Phys. Lett. B 295, 114 (1992) hep-ph/9209257.

    Article  ADS  Google Scholar 

  53. S. Liebig et al., Eur. Phys. J. A 47, 69 (2011) arXiv:1003.3826 [nucl-th].

    Article  ADS  Google Scholar 

  54. V. Baru, C. Hanhart, A. Nogga, in preparation.

  55. U. van Kolck, M.C.M. Rentmeester, J.L. Friar, J.T. Goldman, J.J. de Swart, Phys. Rev. Lett. 80, 4386 (1998) nucl-th/9710067.

    Article  ADS  Google Scholar 

  56. R. Machleidt, Phys. Rev. C 63, 024001 (2001) nucl-th/0006014.

    Article  ADS  Google Scholar 

  57. J. Haidenbauer, W. Plessas, Phys. Rev. C 30, 1822 (1984).

    Article  ADS  Google Scholar 

  58. N. Kaiser, R. Brockmann, W. Weise, Nucl. Phys. A 625, 758 (1997) nucl-th/9706045.

    Article  ADS  Google Scholar 

  59. N. Kaiser, Phys. Rev. C 62, 024001 (2000) nucl-th/9912054.

    Article  ADS  Google Scholar 

  60. S.-L. Zhu, C.M. Maekawa, B.R. Holstein, M.J. Ramsey-Musolf, U. van Kolck, Nucl. Phys. A 748, 435 (2005) nucl-th/0407087.

    Article  ADS  Google Scholar 

  61. R.B. Wiringa, V.G.J. Stoks, R. Schiavilla, Phys. Rev. C 51, 38 (1995) nucl-th/9408016.

    Article  ADS  Google Scholar 

  62. V.G.J. Stoks, R.A.M. Klomp, C.P.F. Terheggen, J.J. de Swart, Phys. Rev. C 49, 2950 (1994) nucl-th/9406039.

    Article  ADS  Google Scholar 

  63. R. Timmermans, private communication.

  64. V. Bernard, Prog. Part. Nucl. Phys. 60, 82 (2008) arXiv:0706.0312 [hep-ph].

    Article  ADS  Google Scholar 

  65. J. de Vries, R.G.E. Timmermans, E. Mereghetti, U. van Kolck, Phys. Lett. B 695, 268 (2011) arXiv:1006.2304 [hep-ph].

    Article  ADS  Google Scholar 

  66. R.F. Dashen, Phys. Rev. D 3, 1879 (1971).

    Article  MathSciNet  ADS  Google Scholar 

  67. J. Gasser, H. Leutwyler, Ann. Phys. 158, 142 (1984).

    Article  MathSciNet  ADS  Google Scholar 

  68. N. Fettes, U.-G. Meißner, S. Steininger, Nucl. Phys. A 640, 199 (1998) hep-ph/9803266.

    Article  ADS  Google Scholar 

  69. B. Borasoy, U.-G. Meißner, Ann. Phys. 254, 192 (1997) hep-ph/9607432.

    Article  ADS  Google Scholar 

  70. J.M. Alarcon, J. Martin Camalich, J.A. Oller, Phys. Rev. D 85, 051503 (2012) arXiv:1110.3797 [hep-ph].

    Article  ADS  Google Scholar 

  71. J. Martin Camalich, J.M. Alarcon, J.A. Oller, Prog. Part. Nucl. Phys. 67, 327 (2012) arXiv:1111.4934 [hep-ph].

    Article  ADS  Google Scholar 

  72. J.M. Alarcon, L.S. Geng, J.M. Camalich, J.A. Oller, arXiv:1209.2870 [hep-ph].

  73. M. Mai, P.C. Bruns, B. Kubis, U.-G. Meißner, Phys. Rev. D 80, 094006 (2009) arXiv:0905.2810 [hep-ph].

    Article  ADS  Google Scholar 

  74. M. Frink, U.-G. Meißner, JHEP 07, 028 (2004) hep-lat/0404018.

    Article  ADS  Google Scholar 

  75. R.F. Dashen, Phys. Rev. 183, 1245 (1969).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. Bsaisou.

Additional information

Communicated by M.C. Birse

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bsaisou, J., Hanhart, C., Liebig, S. et al. The electric dipole moment of the deuteron from the QCD θ-term. Eur. Phys. J. A 49, 31 (2013). https://doi.org/10.1140/epja/i2013-13031-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epja/i2013-13031-x

Keywords

Navigation