Spontaneous <i>CP</i> violation in the supersymmetric Higgs sector

K. S. Babu; S. M. Barr

doi:10.1103/PhysRevD.49.R2156

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Spontaneous CP violation in the supersymmetric Higgs sector

K. S. Babu and S. M. Barr

Bartol Research Institute, University of Delaware, Newark, Delaware 19716

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Phys. Rev. D 49, R2156(R) – Published 1 March, 1994

DOI: https://doi.org/10.1103/PhysRevD.49.R2156

Abstract

Spontaneous CP violation in the minimal supersymmetric standard model with a gauge singlet and a cubic superpotential is examined. Although the tree-level Higgs potential conserves CP, it is shown that with the inclusion of the one-loop top-quark radiative effects CP may be broken spontaneously. The CP-violating minimum requires two neutral ( $h_{1}$ , $h_{2}$ ) and one charged ( $H^{\pm}$ ) Higgs boson to be relatively light with $m_{h 1}$ + $m_{h 2}$ ≲100 GeV and $m_{H}^{\pm}$ ≲110 GeV. The electric dipole moment of the electron is in the observable range of (1/3 to 3)× $10^{- 27}$ e cm.

References (12)

S. Weinberg, Phys. Rev. Lett. 63, 2333 (1989); S.M. Barr and A. Zee, ibid. 65, 21 (1990); J. Gunion and R. Vega, Phys. Lett. B 251, 157 (1990); D. Chang, W. Y. Keung and T.C. Yuan, Phys. Rev. D 43, 14 (1991); R.G. Leigh, S. Paban and R M. Xu, Nucl. Phys. B352, 45 (1991). For a review of atomic searches, see S.M. Barr, Int. J. Mod. Phys. A 8, 209 (1993).
V.A. Kuzmin, V.A. Rubakov and M.E. Shaposhnikov, Phys. Lett. 155B, 36 (1985).
See, for example, A. Pomarol, Phys. Rev. D 47, 273 (1993).
It has been argued that spontaneous CP violation may occur in the MSSM after radiative corrections are included, see N. Maekawa, Phys. Lett. B 282, 387 (1992). However, this is inconsistent with LEP limits on light Higgs boson searches, see A. Pomarol, ibid. 287, 331 (1992). See also G. Branco and N. Oshimo, Report No. IFM 1/93, 1993 (unpublished).
H. Nilles, M. Srednicki and D. Wyler, Phys. Lett. 120B, 346 (1983); J.P. Derendinger and C. Savoy, Nucl Phys. B237, 307 (1984); J. Gunion and H. Haber, ibid. B272, 1 (1986); J. Ellis, J. Gunion, H. Haber, L. Roskowski and F. Zwirner, Phys. Rev. D 39, 844 (1989); M. Drees, Int. J. Mod. Phys. A 4, 3635 (1989); L. Durand and J. Lopez, Phys. Lett. B 217, 463 (1989); J. Espinosa and M. Quiros, ibid. 279, 92 (1992); T. Moroi and Y. Okada, ibid. 295, 73 (1992); U. Ellwanger and M. Rausch de Traubenberg, Z. Phys. C 53, 521 (1992); T. Elliot, S.F. King and P.L. White, Phys. Lett. B 305, 71 (1993); G. Kane, C. Kolda and J. Wells, Phys. Rev. Lett. 70, 2686 (1993); W. ter Veldhuis, Purdue Report No. PURD TH 92 11, 1992 (unpublished); C. Savoy, SACLAY Report No. T93/060, 1993 (unpublished).
J. Romao, Phys. Lett. B 173, 309 (1986).
Y. Okada, M. Yamaguchi and T. Yanagida, Prog. Theor. Phys. 85, 1 (1991); J. Ellis, G. Ridolfi and F. Zwirner, Phys. Lett. B 257, 83 (1991); H. Haber and R. Hempfling, Phys. Rev. Lett. 66, 1815 (1991); R. Barbieri, M. Frigeni and F. Caravaglios, Phys. Lett. B 258, 167 (1991); A. Yamada, ibid. 263, 233 (1991).
Superficially this would seem to contradict the Georgi Pais theorem: H. Georgi and A. Pais, Phys. Rev. D 10, 1246 (1974); ibid. 16, 3520 (1977). But does not since the radiative corrections here are not small in the sense assumed in the proof of that theorem.
In supergravity models with a canonical Kahler potential r=1 (and thus real) at the unification scale. r can develop a phase in the process of running only through complex gaugino mass terms, but this effect will be small due to constraints on the gaugino phase from the neutron EDM.
The radiative corrections are treated more exactly in a forthcoming paper, K.S. Babu and S.M. Barr (unpublished).
Particle Data Group, K. Hikasa et al., Phys. Rev. D 45, S1 (1992).
ALEPH Collaboration, D. Decamp et al., Phys. Lett. B 265, 475 (1991).

[c1] S. Weinberg, Phys. Rev. Lett. 63, 2333 (1989); S.M. Barr and A. Zee, ibid. 65, 21 (1990); J. Gunion and R. Vega, Phys. Lett. B 251, 157 (1990); D. Chang, W. Y. Keung and T.C. Yuan, Phys. Rev. D 43, 14 (1991); R.G. Leigh, S. Paban and R M. Xu, Nucl. Phys. B352, 45 (1991). For a review of atomic searches, see S.M. Barr, Int. J. Mod. Phys. A 8, 209 (1993).

[c2] V.A. Kuzmin, V.A. Rubakov and M.E. Shaposhnikov, Phys. Lett. 155B, 36 (1985).

[c3] See, for example, A. Pomarol, Phys. Rev. D 47, 273 (1993).

[c4] It has been argued that spontaneous CP violation may occur in the MSSM after radiative corrections are included, see N. Maekawa, Phys. Lett. B 282, 387 (1992). However, this is inconsistent with LEP limits on light Higgs boson searches, see A. Pomarol, ibid. 287, 331 (1992). See also G. Branco and N. Oshimo, Report No. IFM 1/93, 1993 (unpublished).

[c5] H. Nilles, M. Srednicki and D. Wyler, Phys. Lett. 120B, 346 (1983); J.P. Derendinger and C. Savoy, Nucl Phys. B237, 307 (1984); J. Gunion and H. Haber, ibid. B272, 1 (1986); J. Ellis, J. Gunion, H. Haber, L. Roskowski and F. Zwirner, Phys. Rev. D 39, 844 (1989); M. Drees, Int. J. Mod. Phys. A 4, 3635 (1989); L. Durand and J. Lopez, Phys. Lett. B 217, 463 (1989); J. Espinosa and M. Quiros, ibid. 279, 92 (1992); T. Moroi and Y. Okada, ibid. 295, 73 (1992); U. Ellwanger and M. Rausch de Traubenberg, Z. Phys. C 53, 521 (1992); T. Elliot, S.F. King and P.L. White, Phys. Lett. B 305, 71 (1993); G. Kane, C. Kolda and J. Wells, Phys. Rev. Lett. 70, 2686 (1993); W. ter Veldhuis, Purdue Report No. PURD TH 92 11, 1992 (unpublished); C. Savoy, SACLAY Report No. T93/060, 1993 (unpublished).

[c6] J. Romao, Phys. Lett. B 173, 309 (1986).

[c7] Y. Okada, M. Yamaguchi and T. Yanagida, Prog. Theor. Phys. 85, 1 (1991); J. Ellis, G. Ridolfi and F. Zwirner, Phys. Lett. B 257, 83 (1991); H. Haber and R. Hempfling, Phys. Rev. Lett. 66, 1815 (1991); R. Barbieri, M. Frigeni and F. Caravaglios, Phys. Lett. B 258, 167 (1991); A. Yamada, ibid. 263, 233 (1991).

[c8] Superficially this would seem to contradict the Georgi Pais theorem: H. Georgi and A. Pais, Phys. Rev. D 10, 1246 (1974); ibid. 16, 3520 (1977). But does not since the radiative corrections here are not small in the sense assumed in the proof of that theorem.

[c9] In supergravity models with a canonical Kahler potential r=1 (and thus real) at the unification scale. r can develop a phase in the process of running only through complex gaugino mass terms, but this effect will be small due to constraints on the gaugino phase from the neutron EDM.

[c10] The radiative corrections are treated more exactly in a forthcoming paper, K.S. Babu and S.M. Barr (unpublished).

[c11] Particle Data Group, K. Hikasa et al., Phys. Rev. D 45, S1 (1992).

[c12] ALEPH Collaboration, D. Decamp et al., Phys. Lett. B 265, 475 (1991).

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Spontaneous CP violation in the supersymmetric Higgs sector

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