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Volumn 56, Issue 1, 1997, Pages 80-89

Time-reversal violation in β decay in the standard model

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EID: 0004184228     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.56.80     Document Type: Article
Times cited : (42)

References (58)
  • 2
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    • The electroweak component of the standard model will be understood here to be the minimal version of the (Formula presented) gauge theory, containing three families of leptons and quarks, one Higgs doublet, and only left-handed neutrinos
    • The electroweak component of the standard model will be understood here to be the minimal version of the (Formula presented) gauge theory, containing three families of leptons and quarks, one Higgs doublet, and only left-handed neutrinos.
  • 6
    • 0001493343 scopus 로고
    • We follow the treatment of these results in I. B. Khriplovich and S. K. Lamoreaux, CP-Violation Without Strangeness (Springer-Verlag, Berlin, in press)
    • K. F. Smith et al., 234, 191 (1990).We follow the treatment of these results in I. B. Khriplovich and S. K. Lamoreaux, CP-Violation Without Strangeness (Springer-Verlag, Berlin, in press).
    • (1990) , vol.234 , pp. 191
    • Smith, K.F.1
  • 11
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    • M. Kobayashi and T. Maskawa 1
    • M. Kobayashi and T. Maskawa 1. The reason for the absence of (Formula presented) violation is that as a consequence of the (Formula presented) structure of the weak currents a (Formula presented)-violating phase associated with a term in the semileptonic Hamiltonian describing a particular quark transition must be an overall phase, which has no observable consequences in first order in the weak interaction.
  • 12
    • 0004332375 scopus 로고
    • Progress in Nuclear Physics, edited by W-Y. Pauchy Hwang, S-C. Lee, C-E. Lee, and D. J. Ernst (North-Holland, New York, 1991), p. 171;, in Precision Tests of the Standard Electroweak Model, edited by P. Langacker, Advanced Series on Directions in High Energy Physics Vol. 14 (World Scientific, Singapore, 1995), p. 786
    • In some extensions of the standard model where (Formula presented) violation in β decay appears already at the tree level, (Formula presented) and (Formula presented) [see Eqs. (4) and (5) in the text] can be as large as or close to the present limits on (Formula presented) and (Formula presented) See P. Herczeg, Phys. Rev. D 28, 200 (1983); in Progress in Nuclear Physics, edited by W-Y. Pauchy Hwang, S-C. Lee, C-E. Lee, and D. J. Ernst (North-Holland, New York, 1991), p. 171;in Precision Tests of the Standard Electroweak Model, edited by P. Langacker, Advanced Series on Directions in High Energy Physics Vol. 14 (World Scientific, Singapore, 1995), p. 786.
    • (1983) Phys. Rev. D , vol.28 , pp. 200
    • Herczeg, P.1
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    • The (Formula presented) coefficient in supersymmetric models has been considered in E. Christova and M. Fabbrichesi, Phys. Lett. B 315, 113 (1993).
    • (1993) Phys. Lett. B , vol.315 , pp. 113
    • Christova, E.1    Fabbrichesi, M.2
  • 14
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    • Our metric and γ matrices are the same as in J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics (McGraw-Hill, New York, 1963)
    • Our metric and γ matrices are the same as in J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics (McGraw-Hill, New York, 1963).
  • 23
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    • Particle Data Group, R. M. Barnett et al., Phys. Rev. D 54, 1 (1996).
    • (1996) Phys. Rev. D , vol.54 , pp. 1
    • Barnett, R.M.1
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    • Proceedings of the XXX Rencontre de Moriond, edited by B. Guiderdoni, G. Greene, E. Hinds, and J. Tra⁁n Thanh Va⁁n (Editions Frontieres, Gif-sur-Yvette, 1995), p. 613
    • For a review see E. Wasserman, in Dark Matter in Cosmology, Clocks, and Tests of Fundamental Laws, Proceedings of the XXX Rencontre de Moriond, edited by B. Guiderdoni, G. Greene, E. Hinds, and J. Tra⁁n Thanh Va⁁n (Editions Frontieres, Gif-sur-Yvette, 1995), p. 613.
    • Dark Matter in Cosmology, Clocks, and Tests of Fundamental Laws
    • Wasserman, E.1
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    • For a review see A. R. Young et al., in Dark Matter in Cosmology, Clocks, and Tests of Fundamental Laws 15
    • For a review see A. R. Young et al., in Dark Matter in Cosmology, Clocks, and Tests of Fundamental Laws 15, p. 539.
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    • The contribution of the final-state interactions to (Formula presented) in (Formula presented) decay is (Formula presented) [P. Vogel and B. Werner, Nucl. Phys. A404, 345 (1983);
    • (1983) Nucl. Phys. , vol.A404 , pp. 345
    • Vogel, P.1    Werner, B.2
  • 31
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    • The present bound on the coupling constant (Formula presented) of the (Formula presented)- and (Formula presented)-violating tensor electron-nucleon interaction used to derive this limit is (Formula presented) [J. P. Jacobs, W. M. Klipstein, S. K. Lamoreaux, B. R. Heckel, and E. N. Fortson, Phys. Rev. A 52, 3521 (1995)].
    • (1995) Phys. Rev. A , vol.52 , pp. 3521
    • Jacobs, J.P.1    Klipstein, W.M.2    Lamoreaux, S.K.3    Heckel, B.R.4    Fortson, E.N.5
  • 32
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    • This feature is analogous to the result of B. W. Lee and A. R. Swift, Phys. Rev. 136, B228 (1964), which states that the (Formula presented) matrix elements (where (Formula presented) (Formula presented) are states of the baryon octet) of a (Formula presented)-violating, (Formula presented)-invariant Hamiltonian which transforms as the 6th component of an octet vanish in the limit of SU(3) symmetry. Note that the octet part of (Formula presented) transforms as (Formula presented)
    • (1964) Phys. Rev. , vol.136
    • Lee, B.W.1    Swift, A.R.2
  • 33
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    • Our phase conventions are such that the (Formula presented)-violating amplitudes (Formula presented) are real. Note also that (Formula presented) [Eq. (9)] is (Formula presented) invariant
    • Our phase conventions are such that the (Formula presented)-violating amplitudes (Formula presented) are real. Note also that (Formula presented) [Eq. (9)] is (Formula presented) invariant.
  • 43
    • 85038307980 scopus 로고    scopus 로고
    • This can be shown by using in the factor (Formula presented) in the vacuum saturation part of (Formula presented) the divergence equation (Formula presented) One obtains then (Formula presented) where (Formula presented) is the vector form factor in (Formula presented) Assuming SU(3) symmetry for (Formula presented) (as we did for (Formula presented) and (Formula presented)) the stated result follows
    • This can be shown by using in the factor (Formula presented) in the vacuum saturation part of (Formula presented) the divergence equation (Formula presented) One obtains then (Formula presented) where (Formula presented) is the vector form factor in (Formula presented) Assuming SU(3) symmetry for (Formula presented) (as we did for (Formula presented) and (Formula presented)) the stated result follows.
  • 44
    • 85038347887 scopus 로고    scopus 로고
    • For comparison, the vacuum saturation part of (Formula presented) is (Formula presented)(Formula presented)(Formula presented) where (Formula presented)(Formula presented)(Formula presented) similarly, (Formula presented) note that (Formula presented) We used (Formula presented)(Formula presented) (Formula presented) and (Formula presented) (see Ref. 34
    • For comparison, the vacuum saturation part of (Formula presented) is (Formula presented)(Formula presented)(Formula presented) where (Formula presented)(Formula presented)(Formula presented) similarly, (Formula presented) note that (Formula presented) We used (Formula presented)(Formula presented) (Formula presented) and (Formula presented) (see Ref. 34 below).
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    • R. J. Crewther et al. 35.
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    • First-class” and “second-class” currents of a given parity have opposite (Formula presented) parities. See S. Weinberg, Phys. Rev. 112, 1375 (1958).
    • (1958) Phys. Rev. , vol.112 , pp. 1375
    • Weinberg, S.1
  • 58
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    • No experiments have been carried out so far to search for (Formula presented) violation in muon capture. For a review of aspects of this field see, e.g., J. Deutsch, in The Future of Muon Physics, edited by K. Jungmann, V. W. Hughes, and G. zu Putlitz (Springer-Verlag, Berlin, 1992), p. 143., A study of (Formula presented) violation in muon capture in extensions of the standard model is in preparation by N. C. Mukhopadhyay and P. Herczeg
    • No experiments have been carried out so far to search for (Formula presented) violation in muon capture. For a review of aspects of this field see, e.g., J. Deutsch, in The Future of Muon Physics, edited by K. Jungmann, V. W. Hughes, and G. zu Putlitz (Springer-Verlag, Berlin, 1992), p. 143.A study of (Formula presented) violation in muon capture in extensions of the standard model is in preparation by N. C. Mukhopadhyay and P. Herczeg.


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