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Foot, R.1
Volkas, R.R.2
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The possibility that the solar neutrino problem can be solved just by maximal neutrino oscillations (in the energy independent range (Formula presented) was earlier proposed in the papers: R. Foot, H. Lew, and R. R. Volkas, Mod. Phys. Lett. A7, 2567 (1992);
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In the context of large angle (or maximal) ordinary-ordinary neutrino oscillations, energy independent oscillations have also been put forward as a solution to the solar neutrino problem in the papers: A. Acker, S. Pakvasa, J. Learned, and T. J. Weiler, Phys. Lett. B298, 149 (1993);
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Note that the conclusion that an energy independent flux reduction can lead to an acceptable solution to the solar neutrino problem has been disputed in the paper, P. Krastev and S. Petcov, Phys. Rev. D53, 1665 (1996).
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The possibility that large lepton number asymmetry can suppress transitions from ordinary to sterile neutrinos and thus weaken the BBN bounds has been studied recently by R. Foot and R. R. Volkas, Phys. Rev. Lett.75, 4350 (1995). In this paper it was assumed that the asymmetry was generated at some early time by some unspecified mechanism.
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85038342840
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We have implicitly assumed that the collision rate for neutrinos, (Formula presented), is equal to the collision rate for antineutrinos, (Formula presented). Of course, in a (Formula presented) asymmetric background the collision rate for neutrinos will be slightly different from the collision rate for antineutrinos. However, as shown in 18
-
We have implicitly assumed that the collision rate for neutrinos, (Formula presented), is equal to the collision rate for antineutrinos, (Formula presented). Of course, in a (Formula presented) asymmetric background the collision rate for neutrinos will be slightly different from the collision rate for antineutrinos. However, as shown in 18, (Formula presented) and hence to a good approximation (Formula presented).
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47
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85038302841
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The condition that (Formula presented) and (Formula presented) are approximately constant over the time scale (Formula presented) can be expressed by the equations (Formula presented)Expanding these conditions out, using the fact (Formula presented) (and similarly for (Formula presented) and (Formula presented) (where (Formula presented) is the Hubble parameter), it is straightforward to show that the above conditions are satisfied provided that (Formula presented), i.e., for (Formula presented) MeV
-
The condition that (Formula presented) and (Formula presented) are approximately constant over the time scale (Formula presented) can be expressed by the equations (Formula presented)Expanding these conditions out, using the fact (Formula presented) (and similarly for (Formula presented) and (Formula presented) (where (Formula presented) is the Hubble parameter), it is straightforward to show that the above conditions are satisfied provided that (Formula presented), i.e., for (Formula presented) MeV.
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48
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0007744596
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See K. Enqvist et al., Nucl. Phys.B349, 754 (1991).
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85038345459
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The quantity (Formula presented) can be taken outside the integral (to a good approximation) provided that (Formula presented). This equation implies that (Formula presented)Using (Formula presented), and (Formula presented) (where (Formula presented) is the Hubble parameter), it follows that the above condition holds provided that (Formula presented), i.e., for (Formula presented)
-
The quantity (Formula presented) can be taken outside the integral (to a good approximation) provided that (Formula presented). This equation implies that (Formula presented)Using (Formula presented), and (Formula presented) (where (Formula presented) is the Hubble parameter), it follows that the above condition holds provided that (Formula presented), i.e., for (Formula presented).
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52
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85038324318
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Recently, D. P. Kirilova and M. V. Chizhov [Teoretisk Astrofysik Center CopenhagenReport No. TAC-1996-018 (unpublished)] have examined the BBN bounds on (Formula presented)-(Formula presented) oscillations for (Formula presented) including the effects of the neutrino asymmetry and momentum distribution.
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Kirilova, D.P.1
Chizhov, M.V.2
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The possibility that a large electron lepton number can modify BBN has been discussed from time to time. See, e.g., Y. David and H. Reeves, Philos. Trans. R. Soc. London, Ser. A296, 415 (1980);
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The possibility that the solar neutrino deficit is due to vacuum neutrino oscillations was first proposed in the paper V. Gribov and B. Pontecorvo, Phys. Lett. B28B, 493 (1969).
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D. R. O. Morrison [CERN Report No. PPE/95-47, (1995) (unpublished)]. Table I also includes the most recent data from GALLEX and SAGE (GALLEX: (Formula presented) SNU, SAGE: (Formula presented) SNU which combine to give an average of (Formula presented) SNU), which was presented at the XVII International Conference on Neutrino Physics and Astrophysics in Helsinki (1996)
-
The theoretical predictions for the (Formula presented)Be, (Formula presented) and (Formula presented) neutrinos were taken from the paper by J. N. Bahcall in 40. These results have been obtained by examining 10 different solar models. For CNO neutrinos we have used Table 18 of S. Turck-Chièze et al., Phys. Rep.230, 57 (1993), and derived the error from the range of predictions. Note that the Homestake value (Formula presented) SNU represents the average of the data taken from the last run (1986–1993). We take this value because the pre-1986 data may be unreliable because it contains significant fluctuations. For a discussion about this point, see D. R. O. Morrison [CERN Report No. PPE/95-47, (1995) (unpublished)]. Table I also includes the most recent data from GALLEX and SAGE (GALLEX: (Formula presented) SNU, SAGE: (Formula presented) SNU which combine to give an average of (Formula presented) SNU), which was presented at the XVII International Conference on Neutrino Physics and Astrophysics in Helsinki (1996).
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For example, the following three predictions for the boron flux have been recently obtained by three different groups (in units of (Formula presented): (Formula presented)by J. N. Bahcall and M. H. Pinsonneault, Rev. Mod. Phys.67, 781 (1995)
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For a review of BBN see, e.g., S. Sarkar, Rep. Prog. Phys.59, 1493 (1996).
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For the case of the exact parity symmetric model, it is necessary to assume that an initial macroscopic asymmetry between the ordinary and mirror matter exists. This can be arranged through the inflationary scenario proposed by E. W. Kolb, D. Seckel, and M. S. Turner, Nature (London)314, 415 (1985) (for example).
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We will suppose that ordinary matter dominates mirror matter immediately after the big bang. Note that in addition to ordinary-mirror neutrino mass mixing, the mirror world can interact with the ordinary particles through photon-mirror photon mixing [discussed byB. Holdom, Phys. Lett.166B, 196 (1985);
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Higgs-boson-mirror–Higgs-boson mixing [discussed in the previous paper and in H. Lew (unpublished)]. We assume that these interactions are either zero or small enough so as to preserve the dominance of matter over mirror matter
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and independently in a slightly different way by R. Foot, H. Lew, and R. R. Volkas, 272, 67 (1991)], and Higgs-boson-mirror–Higgs-boson mixing [discussed in the previous paper and in H. Lew (unpublished)]. We assume that these interactions are either zero or small enough so as to preserve the dominance of matter over mirror matter.
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For a recent analysis, see, e.g., E. Calabresu et al., Astropart. Phys.4, 159 (1995).
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Note that the LSND experiment 3
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Note that the LSND experiment 3 suggests that (Formula presented). This also implies that (Formula presented) because (Formula presented) and (Formula presented).
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85038307304
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the case where (Formula presented) oscillations are very significant (this should happen when the mixing angle (Formula presented) is relatively large), it may be possible that the rate of change of (Formula presented) can be large enough to make (Formula presented). In this case one then has approximately only one differential equation rather than two coupled differential equations. Even in this case, it is possible to show that the (Formula presented) created by (Formula presented) oscillations cannot get destroyed by (Formula presented) oscillations provided that (Formula presented)
-
In the case where (Formula presented) oscillations are very significant (this should happen when the mixing angle (Formula presented) is relatively large), it may be possible that the rate of change of (Formula presented) can be large enough to make (Formula presented). In this case one then has approximately only one differential equation rather than two coupled differential equations. Even in this case, it is possible to show that the (Formula presented) created by (Formula presented) oscillations cannot get destroyed by (Formula presented) oscillations provided that (Formula presented).
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83
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One way to enable the neutrinos to decay rapidly enough to be consistent with the cosmology bound is if a singlet Majoron exists, as suggested by Y. Chikashige, R. N. Mohapatra, and R. D. Peccei, Phys. Rev. Lett.45, 1926 (1980).
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Note that (Formula presented) follows because (Formula presented)
-
Note that (Formula presented) follows because (Formula presented)
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88
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0000328194
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see also 7
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Another way in which the sterile neutrinos can have a significant effective potential is if interactions with light particles such as Majorons exist. This possibility has been discussed in the paper, K. S. Babu and I. Z. Rothstein, Phys. Lett. B275, 112 (1992); see also 7.
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85038272434
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From Eq. (A18), using the result that the cosine is bounded by 1, it is straightforward to show that (Formula presented) provided that (Formula presented)
-
From Eq. (A18), using the result that the cosine is bounded by 1, it is straightforward to show that (Formula presented) provided that (Formula presented).
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90
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85038303364
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hep-ph/9612245
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R. Foot and R. R. Volkas, University of Melbourne Report No. UM-P-96/102, hep-ph/9612245, 1996 (unpublished).
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Volkas, R.R.2
|