Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Early Universe production of $W$ bosons in neutrino decays

Amalia Dariana Fodor, Andru Mihai Buga, Cosmin Crucean

TL;DR

This work investigates the production of charged $W^{\pm}$ bosons in the early Universe by perturbative electroweak processes in de Sitter spacetime. It derives the first-order transition amplitude for neutrino decays emitting a transversal Proca $W$ boson, obtains the corresponding transition rate using Hankel/Bessel representations, and regularizes divergent momentum integrals via dimensional regularization with minimal subtraction. In the large-expansion limit, the authors extract finite total rates, yielding explicit expressions for $R_{\nu \rightarrow W^{+}+e^{-}}$ and its antiparticle counterpart, and they define the density number of $W$ bosons as production minus decay per unit time and volume, showing explicit momentum and renormalization-parameter dependence. The results demonstrate that such production channels are viable only when the expansion rate $\omega$ is large (Early Universe) and vanish in the Minkowski limit, providing a quantitative framework for non-equilibrium gauge-boson production in an expanding background and laying groundwork for further exploration of temperature dependence and quark decay channels.

Abstract

In this paper we study, via perturbative methods, the rates of production of $W$ bosons emitted in neutrino decays during the early stages of the Universe. We compute the transition amplitude corresponding to the first order of de Sitter electroweak perturbation theory and study its various limiting cases. The transition rates are derived using minimal subtraction and dimensional regularization. In the end we attempt to obtain the density number of $W$ bosons produced in perturbative transitions in de Sitter spacetime, using the rates obtained in this paper and in previous ones, and analyze the density number with respect to the particle momenta and renormalisation mass $μ$.

Early Universe production of $W$ bosons in neutrino decays

TL;DR

This work investigates the production of charged bosons in the early Universe by perturbative electroweak processes in de Sitter spacetime. It derives the first-order transition amplitude for neutrino decays emitting a transversal Proca boson, obtains the corresponding transition rate using Hankel/Bessel representations, and regularizes divergent momentum integrals via dimensional regularization with minimal subtraction. In the large-expansion limit, the authors extract finite total rates, yielding explicit expressions for and its antiparticle counterpart, and they define the density number of bosons as production minus decay per unit time and volume, showing explicit momentum and renormalization-parameter dependence. The results demonstrate that such production channels are viable only when the expansion rate is large (Early Universe) and vanish in the Minkowski limit, providing a quantitative framework for non-equilibrium gauge-boson production in an expanding background and laying groundwork for further exploration of temperature dependence and quark decay channels.

Abstract

In this paper we study, via perturbative methods, the rates of production of bosons emitted in neutrino decays during the early stages of the Universe. We compute the transition amplitude corresponding to the first order of de Sitter electroweak perturbation theory and study its various limiting cases. The transition rates are derived using minimal subtraction and dimensional regularization. In the end we attempt to obtain the density number of bosons produced in perturbative transitions in de Sitter spacetime, using the rates obtained in this paper and in previous ones, and analyze the density number with respect to the particle momenta and renormalisation mass .
Paper Structure (6 sections, 72 equations, 12 figures)

This paper contains 6 sections, 72 equations, 12 figures.

Table of Contents

  1. Introduction
  2. The transition amplitude for transversal Proca modes
  3. The transition rate
  4. The transition rate in the limit of large expansion
  5. Density number of particles
  6. Conclusions

Figures (12)

  • Figure 1: Transition rate $\mathcal{R}$\ref{['Rgraff']} as a function of $M_W/\omega$, for given values of the momenta and a fixed value of $m_e/\omega$.
  • Figure 2: Transition rate $\mathcal{R}$\ref{['Rgraff']} as a function of $m_e/\omega$, for given values of the momenta and a fixed value of $M_W/\omega$.
  • Figure 3: The vacuum transition rate \ref{['rvac']}, computed in 44, as a function of the renormalisation mass $\mu$.
  • Figure 4: The $W$ decay rate \ref{['decayW']}, obtained in PTEP, with respect to the $W$ boson momentum $P$, for different values of the renormalisation mass parameter $\mu$.
  • Figure 5: The $W$ boson emission from electron rate \ref{['reltoW']}, obtained in PTEP, with respect to the electron momentum $p$, for different values of the renormalisation mass parameter $\mu$.
  • ...and 7 more figures