### Abstract

Pair annihilation of heavy stable particles that occurs in the early universe is investigated, and a quantum kinetic equation for the momentum distribution of the annihilating particle is derived, using the influence functional method. A bosonic field theory model is used to describe the pair annihilation in the presence of decay product particles making up a thermal environment. A crossing symmetric Hartree approximation that determines self-consistently the equilibrium distribution is developed for an otherwise intractable theory. The time evolution equation and its Markovian approximation are derived to give a generalized Boltzmann equation including off-shell effects. The narrow width approximation to an energy integral in this equation gives the usual Boltzmann equation in a thermal bath of light particles. The off-shell effect is a correction to the Boltzmann equation at high temperatures, but is dominant at low temperatures. The effect changes the equilibrium distribution from the familiar 1/(e^{ωk/T}-1) to a modified one given by a Gibbs formula. Integrated over momenta, the particle number density becomes roughly of order (coupling) X √T/MT^{3} at low temperatures for S-wave annihilation. The relic mass density in the present universe is insensitive to the coupling strength in a large range of the mass and the coupling parameters, and scales with the WIMP mass as ≈6×10^{4} eV cm^{-3} (M/GeV)^{4/3}. The bound from the closure density gives an upper WIMP mass bound roughly of order 1 GeV in the present model.

Original language | English |
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Article number | 123511 |

Pages (from-to) | 1-30 |

Number of pages | 30 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 59 |

Issue number | 12 |

Publication status | Published - Jun 15 1999 |

Externally published | Yes |

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

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## Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*59*(12), 1-30. [123511].