Bulk QCD Thermodynamics and Sterile Neutrino Dark Matter

TL;DR

The paper investigates how the finite-temperature QCD transition influences the relic density of sterile-neutrino dark matter produced by active-sterile decoherence. It develops a nonequilibrium transport framework that couples sterile-neutrino production to the evolving QCD background, treating both first-order and crossover transitions and including entropy dilution, with key parameters $m_s$, $\sin^2 2\theta$, and lepton number $L$. The analysis shows that the expansion history during the QCD epoch can significantly modify the resulting relic density, with a first-order transition yielding a constant-temperature interval of order the Hubble time that enhances production relative to a crossover. It also discusses observational tests via radiative decay $\nu_s \rightarrow \nu_\alpha \gamma$, enabling measurements or constraints on $m_s$ and $\sin^2 2\theta$, and thus linking dark-matter phenomenology to the finite-temperature QCD transition and lepton asymmetries.

Abstract

We point out that the relic densities of singlet (sterile) neutrinos of interest in viable warm and cold dark matter scenarios, depend on the characteristics of the QCD transition in the early universe. In the most promising of these dark matter scenarios the production of the singlets occurs at or near the QCD transition. Since production of the singlets, their dilution, and the disappearance of weak scatterers occur simultaneously, we calculate these processes contemporaneously to obtain accurate predictions of relic sterile neutrino mass density. Therefore, a determination of the mass and superweak mixing of the singlet neutrino through, for example, its radiative decay, along with a determination of its contribution to the critical density, can provide insight into the finite-temperature QCD transition.

Figures (4)

• Figure 1: Evolution of temperature for a first-order transition (solid) and crossover transition (dashed) for $T_{\rm crit} = 150\rm\ MeV$.
• Figure 2: The fraction of critical density $\Omega_s$ produced above a temperature $T_{\rm prod}$. Here we have taken $T_{\rm crit} = 150\rm\ MeV$. There is significant enhancement due to thermal lingering after $T_{\rm crit}$ for a crossover transition (dashed), and there is a dramatic enhancement at $T_{\rm crit}$ in the first order case (solid). The most significant difference between the two cases stems from the delay of the radiation-dominated era in a first-order transition. Here we have taken $m_s = 3\ \rm keV$, $\sin^2 2\theta=2.6\times 10^{-8}$, and $L\sim 10^{-10}$.
• Figure 3: Fraction of critical density contributed by relic sterile neutrinos for a varying critical temperature for the QCD transition. Solid line is for a simple crossover QCD transition; dashed line is for a first-order transition. Here we have specified $m_s = 3\ \rm keV$, $\sin^2 2\theta=2.6\times 10^{-8}$, and $L\sim 10^{-10}$.
• Figure 4: Shown is the parameter space available for sterile neutrino dark matter, with varying lepton-number cosmologies. The contours (numbered by their initial lepton number) are positions in the mass and mixing angle space where sterile neutrinos produce critical densities of $\Omega_s h^2 = 0.15$. The thin (thick) lines are for first-order (crossover) QCD transitions ($T_{\rm crit} = 150\rm\ MeV$). Also shown are the excluded regions (shaded gray) from small scale structures---the Gunn-Peterson bound and Lyman-$\alpha$ forest---and halo phase space densities, the resolution of the diffuse x-ray background by Chandra, and observations of the Virgo cluster by XMM-Newton. The dashed region is that which may be probed by the proposed Constellation-X mission Abazajian:2001vt.