New cosmological limit on neutrino mass

George M. Fuller; Robert A. Malaney

doi:10.1103/PhysRevD.43.3136

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New cosmological limit on neutrino mass

George M. Fuller

Robert A. Malaney

Physics Department, University of California, San Diego, California 92093

Institute of Geophysics and Planetary Physics, University of California, Lawrence Livermore National Laboratory, Livermore, California 94550

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Phys. Rev. D 43, 3136 – Published 15 May, 1991

DOI: https://doi.org/10.1103/PhysRevD.43.3136

Abstract

We show that considerations of the equilibration of right- and left-handed neutrino seas in the early Universe and the well-known ${}^{4}{He}$ constraint on the number of relativistic degrees of freedom extant at the nucleosynthesis epoch lead to a new limit on the Dirac neutrino mass of $m_{ν}$ ≪300 keV. This constraint would apply to any neutrino so long as it had a purely Dirac mass and a lifetime exceeding the nucleosynthesis time scale.

References (24)

G. Steigman, D. N. Schramm and J. E. Gunn, Phys. Lett. 66B, 202 (1977); R. V. Wagoner, Astrophys. J. 179, 343 (1973); R. V. Wagoner, W. A. Fowler and F. Hoyle, ibid. 148, 3 (1967); F. Hoyle and R. J. Tayler, Nature (London) 203, 1108 (1964); and cf. E. W. Kolb and M. S. Turner, The Early Universe (Addison-Wesley, Redwood City, CA, 1990), pp. 95–113, and references therein.
ALEPH, DELPHI, L3, OPAL, and Mark II Collaborations, in Proceedings of the XXVth International Conference on High Energy Physics, Singapore, 1990, edited by K. K. Phua and Y. Yamaguchi (World Scientific, Singapore, 1991).
J. A. Morgan, Phys. Lett. 102B, 247 (1981).
R. Barbieri and A. Dolgov, Phys. Lett. B 237, 440 (1990); M. Yu. Khlopov and S. T. Petcov, Phys. Lett. 99B, 117 (1981); A. Manohar, Phys. Lett. B 186, 370 (1987).
G. Steigman, K. A. Olive and D. N. Schramm, Phys. Lett. 43, 239 (1979).
J. R. Bond, G. Efstathiou and J. Silk, Phys. Rev. Lett. 45, 1980 (1980).
S. L. Shapiro, S. A. Teukolsky and I. Wasserman, Phys. Rev. Lett. 45, 669 (1980).
A. Perez and R. Gandhi, Phys. Rev. D 41, 2374 (1990); in this reference an argument similar to ours, involving Dirac neutrino helicity flip in supernova cores, has been used to set an upper limit on neutrino mass ( $m_{ν}$ <1 ndash100 MeV). The helicity-flip amplitude for $e^{+}$ $e^{-}$ annihilation is explicitly calculated in this reference and the authors point out that the flip and no-flip cross sections differ by more than a factor of ( $m_{ν}$ / ${2 E}_{ν}$ $)^{2}$ . We argue that when averaged over all neutrino-scattering channels in the early Universe this factor is adequate for our purposes. Note added in proof: A paper by R. Gandhi and A. Burrows [Phys. Lett. B 246, 149 (1990)] has come to our attention, which improves on the Perez and Gandhi result by taking into account nu-nucleon scattering. Their Dirac mass limit is 14 keV.
Compare J. Kogut, Phys. Rev. Lett. 56, 2557 (1986); L. G. Yaffe and B. Svetitsky, Phys. Rev. D 26, 963 (1982); R. D. Pisarski and F. Wilczek, ibid. 29, 338 (1984).
Compare G. M. Fuller, G. J. Mathews and C. R. Alcock, Phys. Rev. D 37, 1380 (1988); E. Witten, ibid. 30, 272 (1984).
K. A. Olive, D. N. Schramm, G. Steigman and T. P. Walker, Phys. Lett. B 236, 454 (1990).
W. Mampe, P. Ageron, C. Bates, J. M. Pendlebury and A. Steyeul, Phys. Rev. Lett. 63, 593 (1989).
B. E. J. Pagel, in A Unified View of the Macro- and Micro-Cosmos, edited by A. De Rújula, D. V. Nanopoulos, and P. A. Shaver (World Scientific, Singapore, 1988), p. 399.
E. W. Kolb and R. J. Scherrer, Phys. Rev. D 25, 1481 (1982). Note added in proof: An updated and refined version of Kolb and Scherrer's paper can be found in a paper by E. Kolb, M. Turner, A. Chakravorty, and D. Schramm, FNAL PUB. 91/28-A, 1991 (unpublished). In this work a more detailed account of all scattering neutrino processes has been taken into account [such detailed analysis has also been carried out recently by M. Savage (private communication)]. Our Dirac neutrino mass limit is in good agreement with these more sophisticated analyses.
Particle Data Group, G. P. Yost et al., Phys. Lett B 204, 1 (1988).
J. Gunn, B. Lee, I. Lerche, D. Schramm and G. Steigman, Astrophys. J. 223, 1015 (1978).
R. Cowsik and J. McClelland, Phys. Rev. Lett. 29, 669 (1972).
B. Lee and S. Weinberg, Phys. Rev. Lett. 39, 165 (1977); L. Krauss, Phys. Lett. 128B, 37 (1983); R. Kolb and K. Olive, Phys. Rev. D 33, 1202 (1983).
D. Dicus, E. Kolb and V. Teplitz, Astrophys. J. 221, 327 (1978).
D. Dicus, E. Kolb and V. Teplitz, Phys. Rev. Lett. 39, 169 (1977).
R. Cowsik, Phys. Rev. Lett. 39, 784 (1977).
M. Turner, G. Steigman and L. Krauss, Phys. Rev. Lett. 52, 2090 (1984).
G. Gelmini and M. Roncadelli, Phys. Lett. 99B, 411 (1982); H. Georgi, S. L. Glashow and S. Nussinov, Nucl. Phys. B193, 297 (1982); only the singlet Majoron models are not in conflict with $Z^{0}$ width experiments.
See the review of neutrino properties by P. Langacker, in Neutrinos Physics, Proceedings of the Workshop, Heidelberg, West Germany, 1987, edited by H. V. Klapdor and B. Povh (Springer, Berlin, 1988), p. 71.

[c1] G. Steigman, D. N. Schramm and J. E. Gunn, Phys. Lett. 66B, 202 (1977); R. V. Wagoner, Astrophys. J. 179, 343 (1973); R. V. Wagoner, W. A. Fowler and F. Hoyle, ibid. 148, 3 (1967); F. Hoyle and R. J. Tayler, Nature (London) 203, 1108 (1964); and cf. E. W. Kolb and M. S. Turner, The Early Universe (Addison-Wesley, Redwood City, CA, 1990), pp. 95–113, and references therein.

[c2] ALEPH, DELPHI, L3, OPAL, and Mark II Collaborations, in Proceedings of the XXVth International Conference on High Energy Physics, Singapore, 1990, edited by K. K. Phua and Y. Yamaguchi (World Scientific, Singapore, 1991).

[c3] J. A. Morgan, Phys. Lett. 102B, 247 (1981).

[c4] R. Barbieri and A. Dolgov, Phys. Lett. B 237, 440 (1990); M. Yu. Khlopov and S. T. Petcov, Phys. Lett. 99B, 117 (1981); A. Manohar, Phys. Lett. B 186, 370 (1987).

[c5] G. Steigman, K. A. Olive and D. N. Schramm, Phys. Lett. 43, 239 (1979).

[c6] J. R. Bond, G. Efstathiou and J. Silk, Phys. Rev. Lett. 45, 1980 (1980).

[c7] S. L. Shapiro, S. A. Teukolsky and I. Wasserman, Phys. Rev. Lett. 45, 669 (1980).

[c8] A. Perez and R. Gandhi, Phys. Rev. D 41, 2374 (1990); in this reference an argument similar to ours, involving Dirac neutrino helicity flip in supernova cores, has been used to set an upper limit on neutrino mass ( $m_{ν}$ <1 ndash100 MeV). The helicity-flip amplitude for $e^{+}$ $e^{-}$ annihilation is explicitly calculated in this reference and the authors point out that the flip and no-flip cross sections differ by more than a factor of ( $m_{ν}$ / ${2 E}_{ν}$ $)^{2}$ . We argue that when averaged over all neutrino-scattering channels in the early Universe this factor is adequate for our purposes. Note added in proof: A paper by R. Gandhi and A. Burrows [Phys. Lett. B 246, 149 (1990)] has come to our attention, which improves on the Perez and Gandhi result by taking into account nu-nucleon scattering. Their Dirac mass limit is 14 keV.

[c9] Compare J. Kogut, Phys. Rev. Lett. 56, 2557 (1986); L. G. Yaffe and B. Svetitsky, Phys. Rev. D 26, 963 (1982); R. D. Pisarski and F. Wilczek, ibid. 29, 338 (1984).

[c10] Compare G. M. Fuller, G. J. Mathews and C. R. Alcock, Phys. Rev. D 37, 1380 (1988); E. Witten, ibid. 30, 272 (1984).

[c11] K. A. Olive, D. N. Schramm, G. Steigman and T. P. Walker, Phys. Lett. B 236, 454 (1990).

[c12] W. Mampe, P. Ageron, C. Bates, J. M. Pendlebury and A. Steyeul, Phys. Rev. Lett. 63, 593 (1989).

[c13] B. E. J. Pagel, in A Unified View of the Macro- and Micro-Cosmos, edited by A. De Rújula, D. V. Nanopoulos, and P. A. Shaver (World Scientific, Singapore, 1988), p. 399.

[c14] E. W. Kolb and R. J. Scherrer, Phys. Rev. D 25, 1481 (1982). Note added in proof: An updated and refined version of Kolb and Scherrer's paper can be found in a paper by E. Kolb, M. Turner, A. Chakravorty, and D. Schramm, FNAL PUB. 91/28-A, 1991 (unpublished). In this work a more detailed account of all scattering neutrino processes has been taken into account [such detailed analysis has also been carried out recently by M. Savage (private communication)]. Our Dirac neutrino mass limit is in good agreement with these more sophisticated analyses.

[c15] Particle Data Group, G. P. Yost et al., Phys. Lett B 204, 1 (1988).

[c16] J. Gunn, B. Lee, I. Lerche, D. Schramm and G. Steigman, Astrophys. J. 223, 1015 (1978).

[c17] R. Cowsik and J. McClelland, Phys. Rev. Lett. 29, 669 (1972).

[c18] B. Lee and S. Weinberg, Phys. Rev. Lett. 39, 165 (1977); L. Krauss, Phys. Lett. 128B, 37 (1983); R. Kolb and K. Olive, Phys. Rev. D 33, 1202 (1983).

[c19] D. Dicus, E. Kolb and V. Teplitz, Astrophys. J. 221, 327 (1978).

[c20] D. Dicus, E. Kolb and V. Teplitz, Phys. Rev. Lett. 39, 169 (1977).

[c21] R. Cowsik, Phys. Rev. Lett. 39, 784 (1977).

[c22] M. Turner, G. Steigman and L. Krauss, Phys. Rev. Lett. 52, 2090 (1984).

[c23] G. Gelmini and M. Roncadelli, Phys. Lett. 99B, 411 (1982); H. Georgi, S. L. Glashow and S. Nussinov, Nucl. Phys. B193, 297 (1982); only the singlet Majoron models are not in conflict with $Z^{0}$ width experiments.

[c24] See the review of neutrino properties by P. Langacker, in Neutrinos Physics, Proceedings of the Workshop, Heidelberg, West Germany, 1987, edited by H. V. Klapdor and B. Povh (Springer, Berlin, 1988), p. 71.

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New cosmological limit on neutrino mass

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