Relic neutrino asymmetries and big bang nucleosynthesis in a four neutrino model

N. F. Bell; R. Foot; R. R. Volkas

doi:10.1103/PhysRevD.58.105010

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Relic neutrino asymmetries and big bang nucleosynthesis in a four neutrino model

N. F. Bell^*, R. Foot^†, and R. R. Volkas^‡

School of Physics, Research Centre for High Energy Physics, The University of Melbourne, Parkville 3052 Australia

^*Email address: n.bell@physics.unimelb.edu.au
^†Email address: foot@physics.unimelb.edu.au
^‡Email address: r.volkas@physics.unimelb.edu.au

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Phys. Rev. D 58, 105010 – Published 8 October, 1998

DOI: https://doi.org/10.1103/PhysRevD.58.105010

Abstract

Oscillations between ordinary and sterile neutrinos can generate large neutrino asymmetries in the early universe. These asymmetries can significantly affect big bang nucleosynthesis (BBN) through modification of nuclear reaction rates. We study this phenomenon within a model consisting of the three ordinary neutrinos plus one sterile neutrino that can be motivated by the neutrino anomalies and the dark matter problem. We calculate how the lepton asymmetries produced, evolve at temperatures where they impact on BBN. The effect of the asymmetries on primordial helium production is determined, leading to an effective number of neutrino flavors during BBN of either about 2.7 or 3.1 depending on the sign of the lepton asymmetry.

References (21)

K. Enqvist, K. Kainulainen and M. Thomson, Nucl. Phys. B373, 498 (1992); ibid.K. Enqvist, K. Kainulainen and J. Maalampi, B349, 754 (1991); Phys. Lett. B 244, 186 (1990); ibid.R. Barbieri and A. Dolgov, 237, 440 (1990); Nucl. Phys. B349, 743 (1991); J. Cline, Phys. Rev. Lett. 68, 3137 (1992); X. Shi, D. N. Schramm and B. D. Fields, Phys. Rev. D 48, 2563 (1993); R. Foot and R. R. Volkas, Phys. Rev. Lett. 75, 4350 (1995).
For foundational work on ordinary-sterile neutrino oscillations in the early universe see: A. Dolgov, Sov. J. Nucl. Phys. 33, 700 (1981); R. A. Harris and L. Stodolsky, Phys. Lett. 116B, 464 (1982); L. Stodolsky, Phys. Rev. D 36, 2273 (1987); G. Raffelt, G. Sigl and L. Stodolsky, Phys. Rev. Lett. 70, 2363 (1993); B. H. J. McKellar and M. J. Thomson, Phys. Rev. D 49, 2710 (1994); M. J. Thomson, Phys. Rev. A 45, 2243 (1992).
D. P. Kirilova and M. V. Chizhov, Phys. Lett. B 393, 375 (1997); Phys. Rev. D.58, 073004 (1998).
R. Foot and R. R. Volkas, Phys. Rev. D 55, 5147 (1997); ibid.R. Foot, M. J. Thomson and R. R. Volkas, 53, 5349 (1996).
X. Shi, Phys. Rev. D 54, 2753 (1996).
R. Foot and R. R. Volkas, Phys. Rev. D 56, 6653 (1997).
D. O. Caldwell and R. N. Mohapatra, Phys. Rev. D 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); D. O. Caldwell and R. N. Mohapatra, Phys. Rev. D 50, 3477 (1994); D. O. Caldwell, in Proceedings of the Cosmo ’97 Conference, hep-ph/9804367.
M. Rugers and C. J. Hogan, Astrophys. J. Lett. 459, 1 (1996).
S. Burles and D. Tytler, astro-ph/9712265; S. Burles, X. Fan and D. Tytler, in Proceedings of the ISSI Workshop, astro-ph/9603069; S. Burles and D. Tytler, astro-ph/9603070.
N. Hata, G. Steigman, S. Bludman and P. Langacker, Phys. Rev. D 55, 540 (1997).
P. J. Kernan and S. Sarkar, Phys. Rev. D 54, 3681 (1996); Y. Cardall and G. M. Fuller, astro-ph/9603071; C. Copi, D. N. Schramm and M. S. Turner, Phys. Rev. D 55, 3389 (1997); K. A. Olive and D. Thomas, Astropart. Phys. 7, 27 (1997).
D. N. Schramm and M. S. Turner, Rev. Mod. Phys. 70, 303 (1998).
See, for example, T. P. Walker et al., Astrophys. J. 376, 51 (1991).
V. Barger et al., Phys. Rev. D 43, 1759 (1991).
J. G. Learned, S. Pakvasa and T. J. Weiler, Phys. Lett. B 207, 79 (1988); ibid.V. Barger and K. Whisnant, 209, 365 (1988); K. Hidaka, M. Honda and S. Midorikawa, Phys. Rev. Lett. 61, 1537 (1988).
LSND Collaboration, C. Athanassopoulos et al., Phys. Rev. C (to be published), nucl-ex/9706006; C. AthanassopoulosPhys. Rev. Lett.77, 3082 (1996); ibid.75, 2650 (1995).
J. Primack, J. Holtzman, A. Klypin and D. O. Caldwell, Phys. Rev. Lett. 74, 2160 (1995); S. Ghigna et al., Astrophys. J. 479, 580 (1997); J. Primack, astro-ph/9707285.
L. Wolfenstein, Phys. Rev. D 17, 2369 (1978); ibid.20, 2634 (1979); S. P. Mikheyev and A. Y. Smirnov, Nuovo Cimento C 9, 17 (1986). For a review see, e.g., T. K. Kuo and J. Pantaleone, Rev. Mod. Phys. 61, 937 (1989).
D. Notzold and G. Raffelt, Nucl. Phys. B307, 924 (1988).
L. DiLella, in Proceedings of the TAUP ’97, LNGS, Assergi, Italy, 1997.
Of course this assumes that $\sin^{2} 2 θ_{0} ≳ 3 \times 10^{- 10} .$ If the mixing angle is smaller than this, the lepton number is not generated by oscillations and consequently $m_{ν_{τ}} {= m}_{ν_{μ}} = 2.4 eV$ would remain as the favored neutrino mass for $h o t + c o l d$ dark matter scenarios.

[c1] K. Enqvist, K. Kainulainen and M. Thomson, Nucl. Phys. B373, 498 (1992); ibid.K. Enqvist, K. Kainulainen and J. Maalampi, B349, 754 (1991); Phys. Lett. B 244, 186 (1990); ibid.R. Barbieri and A. Dolgov, 237, 440 (1990); Nucl. Phys. B349, 743 (1991); J. Cline, Phys. Rev. Lett. 68, 3137 (1992); X. Shi, D. N. Schramm and B. D. Fields, Phys. Rev. D 48, 2563 (1993); R. Foot and R. R. Volkas, Phys. Rev. Lett. 75, 4350 (1995).

[c2] For foundational work on ordinary-sterile neutrino oscillations in the early universe see: A. Dolgov, Sov. J. Nucl. Phys. 33, 700 (1981); R. A. Harris and L. Stodolsky, Phys. Lett. 116B, 464 (1982); L. Stodolsky, Phys. Rev. D 36, 2273 (1987); G. Raffelt, G. Sigl and L. Stodolsky, Phys. Rev. Lett. 70, 2363 (1993); B. H. J. McKellar and M. J. Thomson, Phys. Rev. D 49, 2710 (1994); M. J. Thomson, Phys. Rev. A 45, 2243 (1992).

[c3] D. P. Kirilova and M. V. Chizhov, Phys. Lett. B 393, 375 (1997); Phys. Rev. D.58, 073004 (1998).

[c4] R. Foot and R. R. Volkas, Phys. Rev. D 55, 5147 (1997); ibid.R. Foot, M. J. Thomson and R. R. Volkas, 53, 5349 (1996).

[c5] X. Shi, Phys. Rev. D 54, 2753 (1996).

[c6] R. Foot and R. R. Volkas, Phys. Rev. D 56, 6653 (1997).

[c7] D. O. Caldwell and R. N. Mohapatra, Phys. Rev. D 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); D. O. Caldwell and R. N. Mohapatra, Phys. Rev. D 50, 3477 (1994); D. O. Caldwell, in Proceedings of the Cosmo ’97 Conference, hep-ph/9804367.

[c8] M. Rugers and C. J. Hogan, Astrophys. J. Lett. 459, 1 (1996).

[c9] S. Burles and D. Tytler, astro-ph/9712265; S. Burles, X. Fan and D. Tytler, in Proceedings of the ISSI Workshop, astro-ph/9603069; S. Burles and D. Tytler, astro-ph/9603070.

[c10] N. Hata, G. Steigman, S. Bludman and P. Langacker, Phys. Rev. D 55, 540 (1997).

[c11] P. J. Kernan and S. Sarkar, Phys. Rev. D 54, 3681 (1996); Y. Cardall and G. M. Fuller, astro-ph/9603071; C. Copi, D. N. Schramm and M. S. Turner, Phys. Rev. D 55, 3389 (1997); K. A. Olive and D. Thomas, Astropart. Phys. 7, 27 (1997).

[c12] D. N. Schramm and M. S. Turner, Rev. Mod. Phys. 70, 303 (1998).

[c13] See, for example, T. P. Walker et al., Astrophys. J. 376, 51 (1991).

[c14] V. Barger et al., Phys. Rev. D 43, 1759 (1991).

[c15] J. G. Learned, S. Pakvasa and T. J. Weiler, Phys. Lett. B 207, 79 (1988); ibid.V. Barger and K. Whisnant, 209, 365 (1988); K. Hidaka, M. Honda and S. Midorikawa, Phys. Rev. Lett. 61, 1537 (1988).

[c16] LSND Collaboration, C. Athanassopoulos et al., Phys. Rev. C (to be published), nucl-ex/9706006; C. AthanassopoulosPhys. Rev. Lett.77, 3082 (1996); ibid.75, 2650 (1995).

[c17] J. Primack, J. Holtzman, A. Klypin and D. O. Caldwell, Phys. Rev. Lett. 74, 2160 (1995); S. Ghigna et al., Astrophys. J. 479, 580 (1997); J. Primack, astro-ph/9707285.

[c18] L. Wolfenstein, Phys. Rev. D 17, 2369 (1978); ibid.20, 2634 (1979); S. P. Mikheyev and A. Y. Smirnov, Nuovo Cimento C 9, 17 (1986). For a review see, e.g., T. K. Kuo and J. Pantaleone, Rev. Mod. Phys. 61, 937 (1989).

[c19] D. Notzold and G. Raffelt, Nucl. Phys. B307, 924 (1988).

[c20] L. DiLella, in Proceedings of the TAUP ’97, LNGS, Assergi, Italy, 1997.

[c21] Of course this assumes that $\sin^{2} 2 θ_{0} ≳ 3 \times 10^{- 10} .$ If the mixing angle is smaller than this, the lepton number is not generated by oscillations and consequently $m_{ν_{τ}} {= m}_{ν_{μ}} = 2.4 eV$ would remain as the favored neutrino mass for $h o t + c o l d$ dark matter scenarios.

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Relic neutrino asymmetries and big bang nucleosynthesis in a four neutrino model

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References (21)

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