Tying in CP and flavor violations with fermion masses and neutrino oscillations

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 71, Issue 1, 2005, Pages

  Babu, K S ^a   Pati, Jogesh C ^b   Rastogi, Parul ^b  

^a OKLAHOMA STATE UNIVERSITY   (United States)

^b University of Maryland   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CALCULATION; ELECTRON TRANSPORT; FERMION; MOLECULAR INTERACTION; MOLECULAR MODEL; MOLECULAR WEIGHT; NEUTRINO; NEUTRON; OSCILLATION; PREDICTION; QUANTUM THEORY;

EID: 84927743639     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.71.015005     Document Type: Article

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25. The zeros in "11," "13," and "31" elements signify that they are relatively small quantities (specified below). While the "22" elements were set to zero in Ref. [9], because they are meant to be <"23" "32"/"33" ∼ 10-2 (see below), and thus unimportant for purposes of Ref. [9], they are retained here, because such small ζ22u and ζ22 d [∼ (1/3) × 10-2] can still be important for CP violation and leptogenesis.
26. For G(224), one can choose the corresponding submultiplets-that is, (1, 1, 15)H, (1, 2, 4)H, (1, 2, 4)H, (2, 2, 1) H-together with a singlet S, and write a super-potential analogous to Eq. (4).
27. If the effective nonrenormalizable operator like 16216 310H45H/M1 is induced through exchange of states with GUT-scale masses involving renormalizable couplings, rather than through quantum gravity, M1 would, however, be of order GUT scale. In this case 〈45H〉/M1 ∼ 1, rather than 1/10.
28. While 16H has a GUT-scale VEV along the SM singlet, it turns out that it can also have a VEV of EW scale along the " ν̃L" direction due to its mixing with 10 Hd, so that the Hd of MSSM is a mixture of 10Hd and 16Hd. This turns out to be the origin of nontrivial CKM mixings (see Ref. [9]).
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48. For a partial list of references for works along these lines see, e.g., H. Arason et al., Phys. Rev. D 46, 3945 (1992); D. J. Castano, E. J. Pirad, and P. Ramond, Phys. Rev. D 49, 4882 (1994); K. S. Babu, C. N. Leung, and J. Pantaleone, Phys. Lett. B 319, J91 (1993); H. Fusaoka and Y. Koide, Phys. Rev. D 57, 3986 (1998); C. R. Das and M. K. Parida, Eur. Phys. J. C 20, 121 (2001).
49. For a partial list of references for works along these lines see, e.g., H. Arason et al., Phys. Rev. D 46, 3945 (1992); D. J. Castano, E. J. Pirad, and P. Ramond, Phys. Rev. D 49, 4882 (1994); K. S. Babu, C. N. Leung, and J. Pantaleone, Phys. Lett. B 319, J91 (1993); H. Fusaoka and Y. Koide, Phys. Rev. D 57, 3986 (1998); C. R. Das and M. K. Parida, Eur. Phys. J. C 20, 121 (2001).
50. For a partial list of references for works along these lines see, e.g., H. Arason et al., Phys. Rev. D 46, 3945 (1992); D. J. Castano, E. J. Pirad, and P. Ramond, Phys. Rev. D 49, 4882 (1994); K. S. Babu, C. N. Leung, and J. Pantaleone, Phys. Lett. B 319, J91 (1993); H. Fusaoka and Y. Koide, Phys. Rev. D 57, 3986 (1998); C. R. Das and M. K. Parida, Eur. Phys. J. C 20, 121 (2001).
51. For a partial list of references for works along these lines see, e.g., H. Arason et al., Phys. Rev. D 46, 3945 (1992); D. J. Castano, E. J. Pirad, and P. Ramond, Phys. Rev. D 49, 4882 (1994); K. S. Babu, C. N. Leung, and J. Pantaleone, Phys. Lett. B 319, J91 (1993); H. Fusaoka and Y. Koide, Phys. Rev. D 57, 3986 (1998); C. R. Das and M. K. Parida, Eur. Phys. J. C 20, 121 (2001).
52. For a partial list of references for works along these lines see, e.g., H. Arason et al., Phys. Rev. D 46, 3945 (1992); D. J. Castano, E. J. Pirad, and P. Ramond, Phys. Rev. D 49, 4882 (1994); K. S. Babu, C. N. Leung, and J. Pantaleone, Phys. Lett. B 319, J91 (1993); H. Fusaoka and Y. Koide, Phys. Rev. D 57, 3986 (1998); C. R. Das and M. K. Parida, Eur. Phys. J. C 20, 121 (2001).
53. For very recent improved lattice results on light quark masses, see HPQCD Collaboration, MILC Collaboration, UKQCD Collaboration, C. Aubin et al., Phys. Rev. D 70, 031504 (2004); MILC Collaboration. Aubin et al., hep-lat/0407028. These papers give msMS̄(2 GeV) = 76(0) × (3)(7)(0) MeV, 1/2(mu + md)MS̄(2 GeV) = 2.8(0)(1) × (3)(0) MeV, and mu/md = 0.43(0)(1)(8). Using these results and extrapolating to 1 GeV, one gets mu(1 GeV) ≃ 2.1 ± 0.5 MeV, md(1 GeV) ≃ 4.9 ± 0.6 MeV, and ms(1 GeV) ≃ 95 ± 10 MeV. Note that these values are considerably smaller than those commonly used in literature. Somewhat larger values of the masses are quoted in a paper, also based on improved lattice calculation, by QCDSF-UKQCD Collaboration, M. Goeckeler et al., hep-ph/0409312, which appeared on the web just before the completion of this paper.
54. For very recent improved lattice results on light quark masses, see HPQCD Collaboration, MILC Collaboration, UKQCD Collaboration, C. Aubin et al., Phys. Rev. D 70, 031504 (2004); MILC Collaboration. Aubin et al., hep-lat/0407028. These papers give msMS̄(2 GeV) = 76(0) × (3)(7)(0) MeV, 1/2(mu + md)MS̄(2 GeV) = 2.8(0)(1) × (3)(0) MeV, and mu/md = 0.43(0)(1)(8). Using these results and extrapolating to 1 GeV, one gets mu(1 GeV) ≃ 2.1 ± 0.5 MeV, md(1 GeV) ≃ 4.9 ± 0.6 MeV, and ms(1 GeV) ≃ 95 ± 10 MeV. Note that these values are considerably smaller than those commonly used in literature. Somewhat larger values of the masses are quoted in a paper, also based on improved lattice calculation, by QCDSF-UKQCD Collaboration, M. Goeckeler et al., hep-ph/0409312, which appeared on the web just before the completion of this paper.
55. For very recent improved lattice results on light quark masses, see HPQCD Collaboration, MILC Collaboration, UKQCD Collaboration, C. Aubin et al., Phys. Rev. D 70, 031504 (2004); MILC Collaboration. Aubin et al., hep-lat/0407028. These papers give msMS̄(2 GeV) = 76(0) × (3)(7)(0) MeV, 1/2(mu + md)MS̄(2 GeV) = 2.8(0)(1) × (3)(0) MeV, and mu/md = 0.43(0)(1)(8). Using these results and extrapolating to 1 GeV, one gets mu(1 GeV) ≃ 2.1 ± 0.5 MeV, md(1 GeV) ≃ 4.9 ± 0.6 MeV, and ms(1 GeV) ≃ 95 ± 10 MeV. Note that these values are considerably smaller than those commonly used in literature. Somewhat larger values of the masses are quoted in a paper, also based on improved lattice calculation, by QCDSF-UKQCD Collaboration, M. Goeckeler et al., hep-ph/0409312, which appeared on the web just before the completion of this paper.
56. For CKM-elements see, e.g., Ref. [1] or a most recent update by M. Bona et al., hep-ph/0408079 in Ref. [2]. The bottom quark mass quoted in C. W. Bauer et al., Phys. Rev. D 67, 054012 (2003) is mb(mb) = 4.22 ± 0.09 GeV, which is lower than our value given in Eq. (21) by about 10%-12%. Gluino-loop corrections to mb for μ < 0 and tanβ = 10 can, however, reduce mb by about 6%-7%.
57. For CKM-elements see, e.g., Ref. [1] or a most recent update by M. Bona et al., hep-ph/0408079 in Ref. [2]. The bottom quark mass quoted in C. W. Bauer et al., Phys. Rev. D 67, 054012 (2003) is mb(mb) = 4.22 ± 0.09 GeV, which is lower than our value given in Eq. (21) by about 10%-12%. Gluino-loop corrections to mb for μ < 0 and tanβ = 10 can, however, reduce mb by about 6%-7%.
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