Skip to main content
SpringerLink
Log in

Baryon electric dipole moments from strong CP violation

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

The electric dipole form factors and moments of the ground state baryons are calculated in chiral perturbation theory at next-to-leading order. We show that the baryon electric dipole form factors at this order depend only on two combinations of low-energy constants. We also derive various relations that are free of unknown low-energy constants. We use recent lattice QCD data to calculate all baryon EDMs. In particular, we find d n = −2.9 ± 0.9 and d p = 1.1 ± 1.1 in units of 10−16 e θ 0 cm. Finite volume corrections to the electric dipole moments are also worked out. We show that for a precision extraction from lattice QCD data, the next-to-leading order terms have to be accounted for.

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. C. Baker, D. Doyle, P. Geltenbort, K. Green, M. van der Grinten, et al., An Improved experimental limit on the electric dipole moment of the neutron, Phys. Rev. Lett. 97 (2006) 131801 [hep-ex/0602020] [INSPIRE].

    Article  ADS  Google Scholar 

  2. M. Pospelov and A. Ritz, Electric dipole moments as probes of new physics, Annals Phys. 318 (2005)119 [hep-ph/0504231] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  3. S. Lamoreaux and R. Golub, Experimental searches for the neutron electric dipole moment, J. Phys. G 36 (2009) 104002 [INSPIRE].

    ADS  Google Scholar 

  4. F. Farley, K. Jungmann, J. Miller, W. Morse, Y. Orlov, et al., A New method of measuring electric dipole moments in storage rings, Phys. Rev. Lett. 93 (2004) 052001 [hep-ex/0307006] [INSPIRE].

    Article  ADS  Google Scholar 

  5. Storage Ring EDM collaboration, Y.K. Semertzidis, A Storage Ring proton Electric Dipole Moment experiment: most sensitive experiment to CP-violation beyond the Standard Model, arXiv:1110.3378 [INSPIRE].

  6. F. Rathmann and N. Nikolaev, Precursor experiments to search for permanent electric dipole moments (EDMs) of protons and deuterons at COSY, PoS(STORI11)029 (2011).

  7. A. Lehrach, B. Lorentz, W. Morse, N. Nikolaev and F. Rathmann, Precursor Experiments to Search for Permanent Electric Dipole Moments (EDMs) of Protons and Deuterons at COSY, arXiv:1201.5773 [INSPIRE].

  8. S. Aoki and A. Gocksch, The neutron electric dipole moment in lattice QCD, Phys. Rev. Lett. 63 (1989) 1125 [Erratum ibid. 65 (1990) 1172] [INSPIRE].

    Article  ADS  Google Scholar 

  9. S. Aoki, A. Gocksch, A. Manohar and S.R. Sharpe, Calculating the neutron electric dipole moment on the lattice, Phys. Rev. Lett. 65 (1990) 1092 [INSPIRE].

    Article  ADS  Google Scholar 

  10. E. Shintani, S. Aoki, N. Ishizuka, K. Kanaya, Y. Kikukawa, et al., Neutron electric dipole moment with external electric field method in lattice QCD, Phys. Rev. D 75 (2007) 034507 [hep-lat/0611032] [INSPIRE].

    ADS  Google Scholar 

  11. E. Shintani, S. Aoki and Y. Kuramashi, Full QCD calculation of neutron electric dipole moment with the external electric field method, Phys. Rev. D 78 (2008) 014503 [arXiv:0803.0797] [INSPIRE].

    ADS  Google Scholar 

  12. E. Shintani, S. Aoki, N. Ishizuka, K. Kanaya, Y. Kikukawa, et al., Neutron electric dipole moment from lattice QCD, Phys. Rev. D 72 (2005) 014504 [hep-lat/0505022] [INSPIRE].

    ADS  Google Scholar 

  13. F. Berruto, T. Blum, K. Orginos and A. Soni, Calculation of the neutron electric dipole moment with two dynamical flavors of domain wall fermions, Phys. Rev. D 73 (2006) 054509 [hep-lat/0512004] [INSPIRE].

    ADS  Google Scholar 

  14. T. Izubuchi, S. Aoki, K. Hashimoto, Y. Nakamura, T. Sekido and G. Schierholz, Dynamical QCD simulation with theta terms, PoS(LATTICE 2007)016 (2007) [arXiv:0802.1470] [INSPIRE].

  15. S. Aoki, R. Horsley, T. Izubuchi, Y. Nakamura, D. Pleiter, et al., The Electric dipole moment of the nucleon from simulations at imaginary vacuum angle theta, arXiv:0808.1428 [INSPIRE].

  16. E. Shintani, talk given at the Xth Quark Confinement and the Hadron Spectrum, Garching, Germany, Oct. 8–12, 2012.

  17. G. Schierholz, talk given at the ECT* Workshop on EDM Searches at Storage Rings, Trento, Italy, Oct. 2–5, 2012.

  18. S.J. Brodsky, S. Gardner and D.S. Hwang, Discrete symmetries on the light front and a general relation connecting nucleon electric dipole and anomalous magnetic moments, Phys. Rev. D 73 (2006) 036007 [hep-ph/0601037] [INSPIRE].

    ADS  Google Scholar 

  19. K.-F. Liu, Neutron Electric Dipole Moment at Fixed Topology, Mod. Phys. Lett. A 24 (2009) 1971 [arXiv:0807.1365] [INSPIRE].

    ADS  Google Scholar 

  20. E. Mereghetti, W. Hockings and U. van Kolck, The Effective Chiral Lagrangian From the Theta Term, Annals Phys. 325 (2010) 2363 [arXiv:1002.2391] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  21. S.D. Thomas, Electromagnetic contributions to the Schiff moment, Phys. Rev. D 51 (1995) 3955 [hep-ph/9402237] [INSPIRE].

    ADS  Google Scholar 

  22. B. Borasoy, The Electric dipole moment of the neutron in chiral perturbation theory, Phys. Rev. D 61 (2000) 114017 [hep-ph/0004011] [INSPIRE].

    ADS  Google Scholar 

  23. R.J. Crewther, P. Di Vecchia, G. Veneziano and E. Witten, Chiral Estimate of the Electric Dipole Moment of the Neutron in Quantum Chromodynamics, Phys. Lett. B 88 (1979) 123 [Erratum ibid. B 91 (1980) 487] [INSPIRE].

    ADS  Google Scholar 

  24. A. Pich and E. de Rafael, Strong CP-violation in an effective chiral Lagrangian approach, Nucl. Phys. B 367 (1991) 313 [INSPIRE].

    Article  ADS  Google Scholar 

  25. S. Narison, A Fresh Look into the Neutron EDM and Magnetic Susceptibility, Phys. Lett. B 666 (2008)455 [arXiv:0806.2618] [INSPIRE].

    ADS  Google Scholar 

  26. W.H. Hockings and U. van Kolck, The Electric dipole form factor of the nucleon, Phys. Lett. B 605 (2005) 273 [nucl-th/0508012] [INSPIRE].

    ADS  Google Scholar 

  27. K. Ottnad, B. Kubis, U.-G. Meißner and F.-K. Guo, New insights into the neutron electric dipole moment, Phys. Lett. B 687 (2010) 42 [arXiv:0911.3981] [INSPIRE].

    ADS  Google Scholar 

  28. E. Mereghetti, J. de Vries, W. Hockings, C. Maekawa and U. van Kolck, The Electric Dipole Form Factor of the Nucleon in Chiral Perturbation Theory to Sub-leading Order, Phys. Lett. B 696 (2011) 97 [arXiv:1010.4078] [INSPIRE].

    ADS  Google Scholar 

  29. D. O’Connell and M.J. Savage, Extrapolation formulas for neutron EDM calculations in lattice QCD, Phys. Lett. B 633 (2006) 319 [hep-lat/0508009] [INSPIRE].

    ADS  Google Scholar 

  30. J.-W. Chen, D. O’Connell and A. Walker-Loud, Universality of mixed action extrapolation formulae, JHEP 04 (2009) 090 [arXiv:0706.0035] [INSPIRE].

    Article  ADS  Google Scholar 

  31. J.F. Donoghue, E. Golowich and B.R. Holstein, Dynamics of the Standard Model, Cambridge University Press, Cambridge (1992).

    Book  MATH  Google Scholar 

  32. J. Gasser and H. Leutwyler, Chiral Perturbation Theory: Expansions in the Mass of the Strange Quark, Nucl. Phys. B 250 (1985) 465 [INSPIRE].

    Article  ADS  Google Scholar 

  33. H. Leutwyler, Bounds on the light quark masses, Phys. Lett. B 374 (1996) 163 [hep-ph/9601234] [INSPIRE].

    ADS  Google Scholar 

  34. P. Herrera-Siklody, J. Latorre, P. Pascual and J. Taron, Chiral effective Lagrangian in the large-N c limit: the nonet case, Nucl. Phys. B 497 (1997) 345 [hep-ph/9610549] [INSPIRE].

    Article  ADS  Google Scholar 

  35. K. Ottnad, The electric dipole form factor of the neutron in chiral perturbation theory, Diploma thesis, University of Bonn (2009).

  36. T. Becher and H. Leutwyler, Baryon chiral perturbation theory in manifestly Lorentz invariant form, Eur. Phys. J. C 9 (1999) 643 [hep-ph/9901384] [INSPIRE].

    ADS  Google Scholar 

  37. B. Borasoy and U.-G. Meißner, Chiral expansion of baryon masses and sigma terms, Annals Phys. 254 (1997) 192 [hep-ph/9607432] [INSPIRE].

    Article  ADS  Google Scholar 

  38. J. Bsaisou, C. Hanhart, S. Liebig, U.-G. Meißner, A. Nogga, et al., The electric dipole moment of the deuteron from the QCD θ-term, arXiv:1209.6306 [INSPIRE].

  39. Particle Data Group collaboration, J. Beringer et al., Review of Particle Physics (RPP), Phys. Rev. D 86 (2012) 010001 [INSPIRE].

    ADS  Google Scholar 

  40. P. Herrera-Siklody, J. Latorre, P. Pascual and J. Taron, η − η ′ mixing from U (3) L ⊗ U (3) R chiral perturbation theory, Phys. Lett. B 419 (1998) 326 [hep-ph/9710268] [INSPIRE].

    ADS  Google Scholar 

  41. B.C. Tiburzi, External momentum, volume effects and the nucleon magnetic moment, Phys. Rev. D 77 (2008) 014510 [arXiv:0710.3577] [INSPIRE].

    ADS  Google Scholar 

  42. L. Greil, T.R. Hemmert and A. Schafer, Finite Volume Corrections to the Electromagnetic Current of the Nucleon, Eur. Phys. J. A 48 (2012) 53 [arXiv:1112.2539] [INSPIRE].

    ADS  Google Scholar 

  43. J. Gasser and H. Leutwyler, Spontaneously Broken Symmetries: Effective Lagrangians at Finite Volume, Nucl. Phys. B 307 (1988) 763 [INSPIRE].

    Article  ADS  Google Scholar 

  44. L.-s. Geng, X.-l. Ren, J. Martin-Camalich and W. Weise, Finite-volume effects on octet-baryon masses in covariant baryon chiral perturbation theory, Phys. Rev. D 84 (2011) 074024 [arXiv:1108.2231] [INSPIRE].

    ADS  Google Scholar 

  45. J. Gasser and H. Leutwyler, Light Quarks at Low Temperatures, Phys. Lett. B 184 (1987) 83 [INSPIRE].

    ADS  Google Scholar 

  46. B.C. Tiburzi, Volume Effects for Pion Two-Point Functions in Constant Electric and Magnetic Fields, Phys. Lett. B 674 (2009) 336 [arXiv:0809.1886] [INSPIRE].

    ADS  Google Scholar 

  47. J. Gasser, M. Sainio and A. Svarc, Nucleons with Chiral Loops, Nucl. Phys. B 307 (1988) 779 [INSPIRE].

    Article  ADS  Google Scholar 

  48. E.E. Jenkins and A.V. Manohar, Baryon chiral perturbation theory using a heavy fermion Lagrangian, Phys. Lett. B 255 (1991) 558 [INSPIRE].

    ADS  Google Scholar 

  49. V. Bernard, N. Kaiser and U.-G. Meißner, Chiral dynamics in nucleons and nuclei, Int. J. Mod. Phys. E 4 (1995) 193 [hep-ph/9501384] [INSPIRE].

    ADS  Google Scholar 

  50. V. Bernard, Chiral Perturbation Theory and Baryon Properties, Prog. Part. Nucl. Phys. 60 (2008)82 [arXiv:0706.0312] [INSPIRE].

    Article  ADS  Google Scholar 

  51. P.J. Ellis and H.-B. Tang, Pion nucleon scattering in a new approach to chiral perturbation theory, Phys. Rev. C 57 (1998) 3356 [hep-ph/9709354] [INSPIRE].

    ADS  Google Scholar 

  52. S.R. Beane, Nucleon masses and magnetic moments in a finite volume, Phys. Rev. D 70 (2004)034507 [hep-lat/0403015] [INSPIRE].

    ADS  Google Scholar 

  53. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical tables, Dover, New York (1972).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, D-53115, Bonn, Germany

    Feng-Kun Guo & Ulf-G. Meißner

  2. Institute for Advanced Simulation, Institut für Kernphysik and Jülich Center for Hadron Physics, JARA-FAME and JARA-HPC, Forschungszentrum Jülich, D-52425, Jülich, Germany

    Ulf-G. Meißner

Authors
  1. Feng-Kun Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ulf-G. Meißner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Feng-Kun Guo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Guo, FK., Meißner, UG. Baryon electric dipole moments from strong CP violation. J. High Energ. Phys. 2012, 97 (2012). https://doi.org/10.1007/JHEP12(2012)097

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP12(2012)097

Keywords

Search

Navigation