### Abstract

The time evolution of unstable particles that occur in the expanding universe is investigated. The off-shell effect not included in the Boltzmann-like equation is important for the decay process when the temperature becomes much below the mass of unstable particle. When the off-shell effect is taken into account, the thermal abundance of unstable particles at low temperatures has a power law behavior of temperature [Formula Presented] [Formula Presented] unlike the Boltzmann suppressed [Formula Presented] with the power [Formula Presented] related to the spectral rise near the threshold of the decay and with [Formula Presented] the decay rate. Moreover, the relaxation time towards the thermal value is not governed by the exponential law; instead, it is the power law of time. The evolution equation for the occupation number and the number density of the unstable particle is derived, when both of these effects, along with the cosmic expansion, are included. We also critically examine how the scattering of thermal particles may affect the off-shell effect to the unstable particle. As an application showing the importance of the off-shell effect we compute the time evolution of the baryon asymmetry generated by the heavy [Formula Presented] boson decay. It is shown that the out-of equilibrium kinematics previously discussed is changed; this change becomes considerable for large values of [Formula Presented] where [Formula Presented] is the Hubble rate at the temperature equal to the [Formula Presented]-boson mass, while we confirm the previous result for small values of [Formula Presented].

Original language | English |
---|---|

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

Volume | 58 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jan 1 1998 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

### Cite this

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

*58*(4). https://doi.org/10.1103/PhysRevD.58.043507

**Prolonged decay and [Formula Presented] asymmetry.** / Joichi, I.; Matsumoto, Sh; Yoshimura, Motohiko.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 58, no. 4. https://doi.org/10.1103/PhysRevD.58.043507

}

TY - JOUR

T1 - Prolonged decay and [Formula Presented] asymmetry

AU - Joichi, I.

AU - Matsumoto, Sh

AU - Yoshimura, Motohiko

PY - 1998/1/1

Y1 - 1998/1/1

N2 - The time evolution of unstable particles that occur in the expanding universe is investigated. The off-shell effect not included in the Boltzmann-like equation is important for the decay process when the temperature becomes much below the mass of unstable particle. When the off-shell effect is taken into account, the thermal abundance of unstable particles at low temperatures has a power law behavior of temperature [Formula Presented] [Formula Presented] unlike the Boltzmann suppressed [Formula Presented] with the power [Formula Presented] related to the spectral rise near the threshold of the decay and with [Formula Presented] the decay rate. Moreover, the relaxation time towards the thermal value is not governed by the exponential law; instead, it is the power law of time. The evolution equation for the occupation number and the number density of the unstable particle is derived, when both of these effects, along with the cosmic expansion, are included. We also critically examine how the scattering of thermal particles may affect the off-shell effect to the unstable particle. As an application showing the importance of the off-shell effect we compute the time evolution of the baryon asymmetry generated by the heavy [Formula Presented] boson decay. It is shown that the out-of equilibrium kinematics previously discussed is changed; this change becomes considerable for large values of [Formula Presented] where [Formula Presented] is the Hubble rate at the temperature equal to the [Formula Presented]-boson mass, while we confirm the previous result for small values of [Formula Presented].

AB - The time evolution of unstable particles that occur in the expanding universe is investigated. The off-shell effect not included in the Boltzmann-like equation is important for the decay process when the temperature becomes much below the mass of unstable particle. When the off-shell effect is taken into account, the thermal abundance of unstable particles at low temperatures has a power law behavior of temperature [Formula Presented] [Formula Presented] unlike the Boltzmann suppressed [Formula Presented] with the power [Formula Presented] related to the spectral rise near the threshold of the decay and with [Formula Presented] the decay rate. Moreover, the relaxation time towards the thermal value is not governed by the exponential law; instead, it is the power law of time. The evolution equation for the occupation number and the number density of the unstable particle is derived, when both of these effects, along with the cosmic expansion, are included. We also critically examine how the scattering of thermal particles may affect the off-shell effect to the unstable particle. As an application showing the importance of the off-shell effect we compute the time evolution of the baryon asymmetry generated by the heavy [Formula Presented] boson decay. It is shown that the out-of equilibrium kinematics previously discussed is changed; this change becomes considerable for large values of [Formula Presented] where [Formula Presented] is the Hubble rate at the temperature equal to the [Formula Presented]-boson mass, while we confirm the previous result for small values of [Formula Presented].

UR - http://www.scopus.com/inward/record.url?scp=85039030021&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85039030021&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.58.043507

DO - 10.1103/PhysRevD.58.043507

M3 - Article

VL - 58

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 0556-2821

IS - 4

ER -