General references
143
6. Verify equation (4.86).
7. If the S0(10) GUT symmetry-breaking Higgs transforms as the 16dimensional representation, show that the gauge group breaks to SU(5) x
U (1). and if the Higgs transforms as the S4-dimensioinal representation, then
the gauge group breaks to G422 given in equation (4.97).
8. Verify equations (4.130) and (4.131).
9. Verify equation (4.136).
10. Show that in the standard model the communication of CP-violation to the
baryon-numbernon-conserving processes, via the phase in the CKM matrix,
arises first in 12th order perturbation theory, as given in equation (4.210).
Verify equation (4.214).
11. Verify that decoupling of the baryon-number non-conserving interactions
occurs at a temperature T* given by equation (4.223).
12. Verify equation (4.240) relating the asymmetry nA to the chemical potential
/La·
13. Show that in the direction (4.249) all of the F -terms derived from the
superpotential (4.248) are zero.
14. Show that in the direction (4.249) all of the D-terms are also zero.
15. Verify that the potentia] (4.258) has a minimum of the form given in (4.259).
16. Verify (4.264).
17. Show that in the MSSM the subspace of field directions in which all D-terms
vanish is 37-dimensional [72].
4.14 General references
• Riotto A 1998 Trieste 1998, High Energy Physics and Cosmology pp 326436, arXiv:hep-ph/9807454
• Trodden M 1999 Rev. Mod. Phys. 71 1463, arXiv:hep-ph/9803479
• Cline J M, Joyce M and Kainulainen K 2000 lHEP 0007 018, arXiv:hepph/0006119
Bibliography
[1] Saeki T et al 1998 Phys. Len. B 422 319
[2] Sleeker F W. Morgan D L and Bredekamp J 1971 Phys. Rev. Len. 27 1469
Steeker F W 1985 Nucl. Phys. B 252 25
MohanlY A K and Sleeker F W 1984 Phys. Lett. B 143 351
Gao Y T. Sleeker F W. Gleiser M and Klein D B 1990 Astrophys. 1. Len. 37 361
[3] Steigrnan G 1976 Ann. Rev. Astron. Astrophys. 14334
[4] MalherJ C 1999 et at Astrophys. 1 512 511
[5] Spergel D N et al2oo3 Astrophys. J. Sup pt. 148 175. arXiv:astro-phl0302209
143
6. Verify equation (4.86).
7. If the S0(10) GUT symmetry-breaking Higgs transforms as the 16dimensional representation, show that the gauge group breaks to SU(5) x
U (1). and if the Higgs transforms as the S4-dimensioinal representation, then
the gauge group breaks to G422 given in equation (4.97).
8. Verify equations (4.130) and (4.131).
9. Verify equation (4.136).
10. Show that in the standard model the communication of CP-violation to the
baryon-numbernon-conserving processes, via the phase in the CKM matrix,
arises first in 12th order perturbation theory, as given in equation (4.210).
Verify equation (4.214).
11. Verify that decoupling of the baryon-number non-conserving interactions
occurs at a temperature T* given by equation (4.223).
12. Verify equation (4.240) relating the asymmetry nA to the chemical potential
/La·
13. Show that in the direction (4.249) all of the F -terms derived from the
superpotential (4.248) are zero.
14. Show that in the direction (4.249) all of the D-terms are also zero.
15. Verify that the potentia] (4.258) has a minimum of the form given in (4.259).
16. Verify (4.264).
17. Show that in the MSSM the subspace of field directions in which all D-terms
vanish is 37-dimensional [72].
4.14 General references
• Riotto A 1998 Trieste 1998, High Energy Physics and Cosmology pp 326436, arXiv:hep-ph/9807454
• Trodden M 1999 Rev. Mod. Phys. 71 1463, arXiv:hep-ph/9803479
• Cline J M, Joyce M and Kainulainen K 2000 lHEP 0007 018, arXiv:hepph/0006119
Bibliography
[1] Saeki T et al 1998 Phys. Len. B 422 319
[2] Sleeker F W. Morgan D L and Bredekamp J 1971 Phys. Rev. Len. 27 1469
Steeker F W 1985 Nucl. Phys. B 252 25
MohanlY A K and Sleeker F W 1984 Phys. Lett. B 143 351
Gao Y T. Sleeker F W. Gleiser M and Klein D B 1990 Astrophys. 1. Len. 37 361
[3] Steigrnan G 1976 Ann. Rev. Astron. Astrophys. 14334
[4] MalherJ C 1999 et at Astrophys. 1 512 511
[5] Spergel D N et al2oo3 Astrophys. J. Sup pt. 148 175. arXiv:astro-phl0302209