Cherenkov plasmons emission by primordial neutrinos

Abstract

We study the emission of Cherenkov plasmons by the gas of neutrinos with nonzero temperature and chemical potential. The background plasma, consisting of charged leptons, is taken to be nonrelativistic. The energy emission rate is obtained for longitudinal plasmons. To get the neutrino emissivity we average quantum field theory matrix element over the distribution functions of incoming and outgoing particles. Our results are applied for the description of the cooling down of a neutrino cluster formed in the early universe. Such clusters can exist owing to the neutrino interaction with a hypothetical light scalar boson. Using particular cluster parameters, we demonstrate that the proposed cooling mechanism is efficient for some clusters. We find the temperature range where the proposed cooling channel is valid. Some useful calculations of the polarization tensor, as well as the plasmon form factors and their dispersion relations are also provided.

Figures (4)

• Figure 1: The Feynman diagram for the neutrino Cherenkov emission $\nu\to\nu+\gamma$ which results in the matrix element in Eq. (\ref{['eq:matreldef']}).
• Figure 2: The distribution of the Fermi momentum inside neutrino clusters. In this plot, $m\equiv m_{\nu}=0.1\,\text{eV}$ is the neutrino mass and $M\equiv m_{s}$ is the scalar particle mass. The solid line corresponds to $\mu_{\nu}^{(\mathrm{now})}=0.6m_{\nu}$, $R_{\mathrm{now}}\approx5m_{s}^{-1}$ and $p_{\mathrm{F}}^{(\mathrm{max})}\approx0.6m_{\nu}$; the dashed line corresponds to $\mu_{\nu}^{(\mathrm{now})}=0.3m_{\nu}$, $R_{\mathrm{now}}\approx2.1m_{s}^{-1}$ and $p_{\mathrm{F}}^{(\mathrm{max})}\approx0.3m_{\nu}$; and dash-dotted line corresponds to $\mu_{\nu}^{(\mathrm{now})}=0.15m_{\nu}$, $R_{\mathrm{now}}\approx1.3m_{s}^{-1}$ and $p_{\mathrm{F}}^{(\mathrm{max})}\approx0.15m_{\nu}$. All cluster parameters are given in the present time universe. The figure is taken from Ref. Dvo24.
• Figure 3: The cooling parameter $\Xi$ in Eq. (\ref{['eq:Fdef']}) versus $T$ for various asymmetry parameters, $\xi=\pm3.9\times10^{-3}$ (red and blue lines) and $\xi=0$ (black line). The curves for different $\xi$ almost overlap. This cooling corresponds to the cluster shown in Fig. \ref{['fig:clust']} by the solid line. It has $\mu_{\nu}^{(\mathrm{now})}=0.6m_{\nu}$, $R_{\mathrm{now}}\approx5m_{s}^{-1}$ and $p_{\mathrm{F}}^{(\mathrm{max})}\approx0.6m_{\nu}$.
• Figure 4: The contour $C$ for the integration over the complex variable $p_{0}$ in Eq. (\ref{['eq:sumMatsfer']}).