Abstract
We derive a Wilson coefficient of a CP-violating purely gluonic dimension-6 operator called the Weinberg operator \( \left(GG\overset{\sim }{G}\right) \) generated by a scalar and two fermions at the two-loop level. We do not specify the representation of SU(3)c for the scalar and the fermions, and thus our result can be applied to a variety of models beyond the standard model. We estimate the nucleon EDMs induced by the Weinberg operator in some examples and discuss the importance of measuring EDMs. It is found that future measurements of the EDMs can probe physics at higher energy scale beyond the reach of collider experiments.
Similar content being viewed by others
References
M.B. Gavela, A. Le Yaouanc, L. Oliver, O. Pene, J.C. Raynal and T.N. Pham, CP violation induced by penguin diagrams and the neutron electric dipole moment, Phys. Lett. B 109 (1982) 215 [INSPIRE].
I.B. Khriplovich and A.R. Zhitnitsky, What is the value of the neutron electric dipole moment in the Kobayashi-Maskawa model?, Phys. Lett. B 109 (1982) 490 [INSPIRE].
B.H.J. McKellar, S.R. Choudhury, X.-G. He and S. Pakvasa, The neutron electric dipole moment in the standard KM model, Phys. Lett. B 197 (1987) 556 [INSPIRE].
J.O. Eeg and I. Picek, Two loop diagrams for the electric dipole moment of the neutron, Nucl. Phys. B 244 (1984) 77 [INSPIRE].
M. Pospelov and A. Ritz, Electric dipole moments as probes of new physics, Annals Phys. 318 (2005) 119 [hep-ph/0504231] [INSPIRE].
M.E. Pospelov and I.B. Khriplovich, Electric dipole moment of the W boson and the electron in the Kobayashi-Maskawa model, Sov. J. Nucl. Phys. 53 (1991) 638 [Yad. Fiz. 53 (1991) 1030] [INSPIRE].
C.A. Baker et al., An improved experimental limit on the electric dipole moment of the neutron, Phys. Rev. Lett. 97 (2006) 131801 [hep-ex/0602020] [INSPIRE].
ACME collaboration, J. Baron et al., Order of magnitude smaller limit on the electric dipole moment of the electron, Science 343 (2014) 269 [arXiv:1310.7534] [INSPIRE].
S. Weinberg, Larger Higgs exchange terms in the neutron electric dipole moment, Phys. Rev. Lett. 63 (1989) 2333 [INSPIRE].
D.A. Dicus, Neutron electric dipole moment from charged Higgs exchange, Phys. Rev. D 41 (1990) 999 [INSPIRE].
J. Dai, H. Dykstra, R.G. Leigh, S. Paban and D. Dicus, CP violation from three gluon operators in the supersymmetric Standard Model, Phys. Lett. B 237 (1990) 216 [Erratum ibid. B 242 (1990) 547] [INSPIRE].
D. Chang, C.S. Li and T.C. Yuan, Larger neutron electric dipole moment in left-right symmetric models, Phys. Rev. D 42 (1990) 867 [INSPIRE].
I.Z. Rothstein, Three gluon contribution to the neutron electric dipole moment in a model without the strong CP problem, Phys. Lett. B 249 (1990) 467 [INSPIRE].
E. Braaten, C.-S. Li and T.-C. Yuan, The evolution of Weinberg’s gluonic CP violation operator, Phys. Rev. Lett. 64 (1990) 1709 [INSPIRE].
G. Boyd, A.K. Gupta, S.P. Trivedi and M.B. Wise, Effective Hamiltonian for the electric dipole moment of the neutron, Phys. Lett. B 241 (1990) 584 [INSPIRE].
D. Chang, W.-Y. Keung, C.S. Li and T.C. Yuan, QCD corrections to CP violation from color electric dipole moment of b quark, Phys. Lett. B 241 (1990) 589 [INSPIRE].
M. Dine and W. Fischler, Constraints on new physics from Weinberg’s analysis of the neutron electric dipole moment, Phys. Lett. B 242 (1990) 239 [INSPIRE].
V.A. Novikov, M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Calculations in external fields in quantum chromodynamics. Technical review, Fortsch. Phys. 32 (1984) 585 [INSPIRE].
J. Hisano, K. Ishiwata and N. Nagata, Gluon contribution to the dark matter direct detection, Phys. Rev. D 82 (2010) 115007 [arXiv:1007.2601] [INSPIRE].
R. Mertig, M. Böhm and A. Denner, FEYN CALC: computer algebraic calculation of Feynman amplitudes, Comput. Phys. Commun. 64 (1991) 345 [INSPIRE].
V. Shtabovenko, R. Mertig and F. Orellana, New developments in FeynCalc 9.0, Comput. Phys. Commun. 207 (2016) 432 [arXiv:1601.01167] [INSPIRE].
D. Chang, T.W. Kephart, W.-Y. Keung and T.C. Yuan, The chromoelectric dipole moment of the heavy quark and purely gluonic CP-violating operators, Phys. Rev. Lett. 68 (1992) 439 [INSPIRE].
D. Chang, T.W. Kephart, W.-Y. Keung and T.C. Yuan, An effective field theory for the neutron electric dipole moment, Nucl. Phys. B 384 (1992) 147 [INSPIRE].
D.A. Demir, M. Pospelov and A. Ritz, Hadronic EDMs, the Weinberg operator and light gluinos, Phys. Rev. D 67 (2003) 015007 [hep-ph/0208257] [INSPIRE].
A. Manohar and H. Georgi, Chiral quarks and the nonrelativistic quark model, Nucl. Phys. B 234 (1984) 189 [INSPIRE].
D. Chang, X.-G. He, W.-Y. Keung, B.H.J. McKellar and D. Wyler, Neutron electric dipole moment due to Higgs exchange in left-right symmetric models, Phys. Rev. D 46 (1992) 3876 [hep-ph/9209284] [INSPIRE].
D. Chang, X.-G. He and B.H.J. McKellar, Ruling out the Weinberg model of spontaneous CP-violation, Phys. Rev. D 63 (2001) 096005 [hep-ph/9909357] [INSPIRE].
G. Degrassi, E. Franco, S. Marchetti and L. Silvestrini, QCD corrections to the electric dipole moment of the neutron in the MSSM, JHEP 11 (2005) 044 [hep-ph/0510137] [INSPIRE].
Particle Data Group collaboration, C. Patrignani et al., Review of particle physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].
I. Altarev et al., Towards a new measurement of the neutron electric dipole moment, Nucl. Instrum. Meth. A 611 (2009) 133 [INSPIRE].
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].
J. Dragos, T. Luu, A. Shindler and J. de Vries, Electric dipole moment results from lattice QCD, in 35th International Symposium on Lattice Field Theory (Lattice 2017), Granada Spain, 18-24 June 2017 [arXiv:1711.04730] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1712.09503
Rights and permissions
About this article
Cite this article
Abe, T., Hisano, J. & Nagai, R. Model independent evaluation of the Wilson coefficient of the Weinberg operator in QCD. J. High Energ. Phys. 2018, 175 (2018). https://doi.org/10.1007/JHEP03(2018)175
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2018)175