Spontaneous <i>CP</i> violation in theories with low-energy supersymmetry

S. M. Barr; A. Masiero

doi:10.1103/PhysRevD.38.366

Access by Xinjiang University

Spontaneous CP violation in theories with low-energy supersymmetry

S. M. Barr

A. Masiero

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

Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Via F. Marzolo, 8, I-35100 Padova, Italy

PDF

Phys. Rev. D 38, 366 – Published 1 July, 1988

DOI: https://doi.org/10.1103/PhysRevD.38.366

Abstract

The problem of strong CP violation in theories with low-energy supersymmetry is studied. Special emphasis is given to theories with spontaneous CP violation. It is found that supersymmetric versions of the Nelson models only receive contributions to Θ¯ of order ( $m_{g}$ / $M_{GUT}$ ) or at the three-loop level. The resulting Θ is of order $10^{- 13}$ or less. This improves on the nonsupersymmetric Nelson models where Θ arises at the one-loop level. Constraints on the mechanism for spontaneously breaking CP invariance in supersymmetric models are found.

References (17)

For a clear discussion of the extra phases in general N=1 supergravity models and in their minimal version, see M. Dugan, B. Grinstein and L. Hall, Nucl. Phys. B255, 413 (1985).
R. Peccei and H. Quinn, Phys. Rev. Lett. 38, 1440 (1977).
M. A. B. Beg and H. S. Tsao, Phys. Rev. Lett. 41, 278 (1978); R. N. Mohapatra and G. Senjanović, Phys. Lett. 79B, 283 (1978); H. Georgi, Had. J. 1, 155 (1978); G. Segre` and H. A. Weldon, Phys. Rev. Lett. 42, 1191 (1979); S. Barr and P. Langacker, ibid. 42, 1654 (1979).
A. Nelson, Phys. Lett. 136B, 387 (1984); S. M. Barr, Phys. Rev. Lett. 53, 329 (1984); Phys. Rev. D 30, 1805 (1984) A. Nelson, Phys. Lett. 143B, 165 (1984).
S. M. Barr and D. Seckel, Nucl. Phys. B233, 116 (1984); S. M. Barr and A. Zee, Phys. Rev. Lett. 55, 2253 (1985); A. Dannenberg, L. Hall and L. Randall, Nucl. Phys. B271, 574 (1986); L. Hall and L. Randall, ibid. B274, 157 (1986); S. M. Barr, Phys. Rev. D 34, 1567 (1986).
For a review of N=1 supergravity models, see, for instance, H. P. Nilles, Phys. Rep. 110, 1 (1984).
See references in L. Hall, J. Lykken and S. Weinberg, Phys. Rev. D 27, 2359 (1983); S. K. Soni and H. A. Weldon, Phys. Lett. 126B, 215 (1983).
The trilinear soft-breaking terms are A $m_{g}$ g ${hat}_{s}$ , where g ${hat}_{s}$ is obtained from the trilinear terms in the superpotential $g_{3}$ by taking the scalar component of each superfield. Neglecting the contribution due to the VEV's of possible superheavy fields, the bilinear soft-breaking term is (A-1) $m_{g}$ μ HH prime. The effect of the superheavy fields on this bilinear term and, more generally, for our discussion of the strong CP problem is dealt with in Appendix B (Ref. 7).
We understand that the tiny window of small gluino masses, of the order of some GeV, although not completely ruled out yet, is however very unlikely.
J. Polchinski and M. Wise, Phys. Lett. 125B, 393 (1983); see, also, F. del Aguila, M. B. Gavela, J. A. Grifols and A. Mendez, ibid. 126B, 71 (1983); W. Buchmüller and D. Wyler, ibid. 121B, 321 (1982); E. Franco and M. Mangano, ibid. 135B, 445 (1984).
M. Dugan, B. Grinstein and L. Hall, Nucl. Phys. B255, 413 (1985).
$m_{\tilde{d}}$ denotes an average squark mass of the ${\tilde{d}}_{L}$ and ${\tilde{d}}_{R}$ eigenvectors of the ${\tilde{d}}_{L}$ -& ${dtilde}_{R}$ mass matrix.
Spontaneous breaking of CP leads to cosmological domain walls. These must be ``inflated away'' which presumably is not possible unless CP is broken at a very large scale.
Dannenberg, Hall, and Randall (Ref. 5).
Barr and Zee (Ref. 5).
J. Ellis, S. Ferrara and D. V. Nanopoulos, Phys. Lett. 114B, 231 (1982).
For a review of axion cosmology, see J. E. Kim, Phys. Rep. 150, 1 (1987).

[c1] For a clear discussion of the extra phases in general N=1 supergravity models and in their minimal version, see M. Dugan, B. Grinstein and L. Hall, Nucl. Phys. B255, 413 (1985).

[c2] R. Peccei and H. Quinn, Phys. Rev. Lett. 38, 1440 (1977).

[c3] M. A. B. Beg and H. S. Tsao, Phys. Rev. Lett. 41, 278 (1978); R. N. Mohapatra and G. Senjanović, Phys. Lett. 79B, 283 (1978); H. Georgi, Had. J. 1, 155 (1978); G. Segre` and H. A. Weldon, Phys. Rev. Lett. 42, 1191 (1979); S. Barr and P. Langacker, ibid. 42, 1654 (1979).

[c4] A. Nelson, Phys. Lett. 136B, 387 (1984); S. M. Barr, Phys. Rev. Lett. 53, 329 (1984); Phys. Rev. D 30, 1805 (1984) A. Nelson, Phys. Lett. 143B, 165 (1984).

[c5] S. M. Barr and D. Seckel, Nucl. Phys. B233, 116 (1984); S. M. Barr and A. Zee, Phys. Rev. Lett. 55, 2253 (1985); A. Dannenberg, L. Hall and L. Randall, Nucl. Phys. B271, 574 (1986); L. Hall and L. Randall, ibid. B274, 157 (1986); S. M. Barr, Phys. Rev. D 34, 1567 (1986).

[c6] For a review of N=1 supergravity models, see, for instance, H. P. Nilles, Phys. Rep. 110, 1 (1984).

[c7] See references in L. Hall, J. Lykken and S. Weinberg, Phys. Rev. D 27, 2359 (1983); S. K. Soni and H. A. Weldon, Phys. Lett. 126B, 215 (1983).

[c8] The trilinear soft-breaking terms are A $m_{g}$ g ${hat}_{s}$ , where g ${hat}_{s}$ is obtained from the trilinear terms in the superpotential $g_{3}$ by taking the scalar component of each superfield. Neglecting the contribution due to the VEV's of possible superheavy fields, the bilinear soft-breaking term is (A-1) $m_{g}$ μ HH prime. The effect of the superheavy fields on this bilinear term and, more generally, for our discussion of the strong CP problem is dealt with in Appendix B (Ref. 7).

[c9] We understand that the tiny window of small gluino masses, of the order of some GeV, although not completely ruled out yet, is however very unlikely.

[c10] J. Polchinski and M. Wise, Phys. Lett. 125B, 393 (1983); see, also, F. del Aguila, M. B. Gavela, J. A. Grifols and A. Mendez, ibid. 126B, 71 (1983); W. Buchmüller and D. Wyler, ibid. 121B, 321 (1982); E. Franco and M. Mangano, ibid. 135B, 445 (1984).

[c11] M. Dugan, B. Grinstein and L. Hall, Nucl. Phys. B255, 413 (1985).

[c12] $m_{\tilde{d}}$ denotes an average squark mass of the ${\tilde{d}}_{L}$ and ${\tilde{d}}_{R}$ eigenvectors of the ${\tilde{d}}_{L}$ -& ${dtilde}_{R}$ mass matrix.

[c13] Spontaneous breaking of CP leads to cosmological domain walls. These must be ``inflated away'' which presumably is not possible unless CP is broken at a very large scale.

[c14] Dannenberg, Hall, and Randall (Ref. 5).

[c15] Barr and Zee (Ref. 5).

[c16] J. Ellis, S. Ferrara and D. V. Nanopoulos, Phys. Lett. 114B, 231 (1982).

[c17] For a review of axion cosmology, see J. E. Kim, Phys. Rep. 150, 1 (1987).

Physical Review D

Export citation

Export citation

Spontaneous CP violation in theories with low-energy supersymmetry

Abstract

References (17)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation