Journal of High Energy Physics

, 2012:97 | Cite as

Baryon electric dipole moments from strong CP violation

Article

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 dn = −2.9 ± 0.9 and dp = 1.1 ± 1.1 in units of 10−16e θ0 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.

Keywords

Chiral Lagrangians Lattice QCD CP violation 

References

  1. [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].ADSCrossRefGoogle Scholar
  2. [2]
    M. Pospelov and A. Ritz, Electric dipole moments as probes of new physics, Annals Phys. 318 (2005)119 [hep-ph/0504231] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  3. [3]
    S. Lamoreaux and R. Golub, Experimental searches for the neutron electric dipole moment, J. Phys. G 36 (2009) 104002 [INSPIRE].ADSGoogle Scholar
  4. [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].ADSCrossRefGoogle Scholar
  5. [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. [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).Google Scholar
  7. [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. [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].ADSCrossRefGoogle Scholar
  9. [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].ADSCrossRefGoogle Scholar
  10. [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].ADSGoogle Scholar
  11. [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].ADSGoogle Scholar
  12. [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].ADSGoogle Scholar
  13. [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].ADSGoogle Scholar
  14. [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. [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. [16]
    E. Shintani, talk given at the Xth Quark Confinement and the Hadron Spectrum, Garching, Germany, Oct. 8–12, 2012.Google Scholar
  17. [17]
    G. Schierholz, talk given at the ECT* Workshop on EDM Searches at Storage Rings, Trento, Italy, Oct. 2–5, 2012.Google Scholar
  18. [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].ADSGoogle Scholar
  19. [19]
    K.-F. Liu, Neutron Electric Dipole Moment at Fixed Topology, Mod. Phys. Lett. A 24 (2009) 1971 [arXiv:0807.1365] [INSPIRE].ADSGoogle Scholar
  20. [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].ADSCrossRefMATHGoogle Scholar
  21. [21]
    S.D. Thomas, Electromagnetic contributions to the Schiff moment, Phys. Rev. D 51 (1995) 3955 [hep-ph/9402237] [INSPIRE].ADSGoogle Scholar
  22. [22]
    B. Borasoy, The Electric dipole moment of the neutron in chiral perturbation theory, Phys. Rev. D 61 (2000) 114017 [hep-ph/0004011] [INSPIRE].ADSGoogle Scholar
  23. [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].ADSGoogle Scholar
  24. [24]
    A. Pich and E. de Rafael, Strong CP-violation in an effective chiral Lagrangian approach, Nucl. Phys. B 367 (1991) 313 [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    S. Narison, A Fresh Look into the Neutron EDM and Magnetic Susceptibility, Phys. Lett. B 666 (2008)455 [arXiv:0806.2618] [INSPIRE].ADSGoogle Scholar
  26. [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].ADSGoogle Scholar
  27. [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].ADSGoogle Scholar
  28. [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].ADSGoogle Scholar
  29. [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].ADSGoogle Scholar
  30. [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].ADSCrossRefGoogle Scholar
  31. [31]
    J.F. Donoghue, E. Golowich and B.R. Holstein, Dynamics of the Standard Model, Cambridge University Press, Cambridge (1992).CrossRefMATHGoogle Scholar
  32. [32]
    J. Gasser and H. Leutwyler, Chiral Perturbation Theory: Expansions in the Mass of the Strange Quark, Nucl. Phys. B 250 (1985) 465 [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    H. Leutwyler, Bounds on the light quark masses, Phys. Lett. B 374 (1996) 163 [hep-ph/9601234] [INSPIRE].ADSGoogle Scholar
  34. [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].ADSCrossRefGoogle Scholar
  35. [35]
    K. Ottnad, The electric dipole form factor of the neutron in chiral perturbation theory, Diploma thesis, University of Bonn (2009).Google Scholar
  36. [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].ADSGoogle Scholar
  37. [37]
    B. Borasoy and U.-G. Meißner, Chiral expansion of baryon masses and sigma terms, Annals Phys. 254 (1997) 192 [hep-ph/9607432] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [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. [39]
    Particle Data Group collaboration, J. Beringer et al., Review of Particle Physics (RPP), Phys. Rev. D 86 (2012) 010001 [INSPIRE].ADSGoogle Scholar
  40. [40]
    P. Herrera-Siklody, J. Latorre, P. Pascual and J. Taron, ηη mixing from U (3)LU (3)R chiral perturbation theory, Phys. Lett. B 419 (1998) 326 [hep-ph/9710268] [INSPIRE].ADSGoogle Scholar
  41. [41]
    B.C. Tiburzi, External momentum, volume effects and the nucleon magnetic moment, Phys. Rev. D 77 (2008) 014510 [arXiv:0710.3577] [INSPIRE].ADSGoogle Scholar
  42. [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].ADSGoogle Scholar
  43. [43]
    J. Gasser and H. Leutwyler, Spontaneously Broken Symmetries: Effective Lagrangians at Finite Volume, Nucl. Phys. B 307 (1988) 763 [INSPIRE].ADSCrossRefGoogle Scholar
  44. [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].ADSGoogle Scholar
  45. [45]
    J. Gasser and H. Leutwyler, Light Quarks at Low Temperatures, Phys. Lett. B 184 (1987) 83 [INSPIRE].ADSGoogle Scholar
  46. [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].ADSGoogle Scholar
  47. [47]
    J. Gasser, M. Sainio and A. Svarc, Nucleons with Chiral Loops, Nucl. Phys. B 307 (1988) 779 [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    E.E. Jenkins and A.V. Manohar, Baryon chiral perturbation theory using a heavy fermion Lagrangian, Phys. Lett. B 255 (1991) 558 [INSPIRE].ADSGoogle Scholar
  49. [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].ADSGoogle Scholar
  50. [50]
    V. Bernard, Chiral Perturbation Theory and Baryon Properties, Prog. Part. Nucl. Phys. 60 (2008)82 [arXiv:0706.0312] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [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].ADSGoogle Scholar
  52. [52]
    S.R. Beane, Nucleon masses and magnetic moments in a finite volume, Phys. Rev. D 70 (2004)034507 [hep-lat/0403015] [INSPIRE].ADSGoogle Scholar
  53. [53]
    M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical tables, Dover, New York (1972).MATHGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  1. 1.Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical PhysicsUniversität BonnBonnGermany
  2. 2.Institute for Advanced Simulation, Institut für Kernphysik and Jülich Center for Hadron PhysicsJARA-FAME and JARA-HPC, Forschungszentrum JülichJülichGermany

Personalised recommendations