Sterile neutrino dark matter production in presence of nonstandard neutrino self-interactions: An EFT approach

Sterile neutrinos with keV-scale masses are popular candidates for warm dark matter. In the most straightforward case, they are produced via oscillations with active neutrinos. We introduce effective self-interactions of active neutrinos and investigate the effect on the parameter space of sterile neutrino mass and mixing. Our focus is on mixing with electron neutrinos, which is subject to constraints from several upcoming or running experiments like TRISTAN, ECHo, BeEST, and HUNTER. Depending on the size of the self-interaction, the parameter space moves closer to, or further away from, the one testable by those future experiments. In particular, we show that phase 3 of the HUNTER experiment would test a larger amount of parameter space in the presence of self-interactions than without them. We also investigate the effect of the self-interactions on the free-streaming length of the sterile neutrino dark matter, which is important for structure formation observables.

Figure 1

Self-energy diagrams relevant for the thermal potential, tadpole (left) and sunset (right).

Figure 2

Pseudoscalar mediator case. The oblique straight lines are constituted by the points corresponding to the values of $m_s$ and ${\sin }^2(2\theta )$ for which the condition ${\mathrm{\Omega }}_s{h}^2={\mathrm{\Omega }}_{\mathrm{DM}}{h}^2=0.12$ (left panel) and ${\mathrm{\Omega }}_s{h}^2=0.1\times {\mathrm{\Omega }}_{\mathrm{DM}}{h}^2=0.012$ (right panel) is satisfied, for different strengths of NSSI parametrized by ${\epsilon }_P$. The black line corresponds to the case of standard Dodelson-Widrow production, i.e., ${\epsilon }_P=0$, while different shades of red, green, and blue correspond to increasing values of ${\epsilon }_P$ in the range [0.1, 100]. The regions in which upcoming experiments will be sensitive are enclosed by beige (HUNTER), black and gray (TRISTAN), and blue (ECHo) lines. The purple line represents the current constraint from x-ray observations. Three values of mediator mass were chosen, $m_{\varphi }=10$, 50, 100 GeV for the upper, middle, and lower panel. Four benchmark points BP1-4 are also given, see main text. The scalar mediator case looks identical.

Figure 3

Axial-vector mediator case. The oblique straight lines are constituted by the points corresponding to the values of $m_s$ and ${\sin }^2(2\theta )$ for which the condition ${\mathrm{\Omega }}_s{h}^2={\mathrm{\Omega }}_{\mathrm{DM}}{h}^2=0.12$ (left panel) and ${\mathrm{\Omega }}_s{h}^2=0.1\times {\mathrm{\Omega }}_{\mathrm{DM}}{h}^2=0.012$ (right panel) is satisfied, for different strengths of NSSI parametrized by ${\epsilon }_A$. The black line corresponds to the case of standard Dodelson-Widrow production, i.e., ${\epsilon }_A=0$, while different shades of red, green, and blue correspond to increasing values of ${\epsilon }_A$ in the range [0.1, 100]. The regions in which upcoming experiments will be sensitive are enclosed by beige (HUNTER), black and gray (TRISTAN), and blue (ECHo) lines. The purple line represents the current constraint from x-ray observations. Three values of mediator mass were chosen, $m_{\varphi }=10$, 50, 100 GeV for the upper, middle, and lower panel.

Figure 4

Sterile neutrino momentum distribution $r^{2}f(r)$, where $r=p/T$ in the case of Dodelson-Widrow production modified by the action of pseudoscalar NSSI. The values of the sterile neutrino parameters are chosen as $m_s=10\mathrm{keV}$, ${\sin }^2(2\theta )=1.1\times {10}^{-9}$ (BP2 in Figs. 2 and 3). In different shades of red, green, and blue, we observe the result corresponding to different values of ${\epsilon }_P$. The black dashed line represents the distribution function that gives ${\mathrm{\Omega }}_s{h}^2={\mathrm{\Omega }}_{\mathrm{DM}}{h}^2=0.12$. The black solid line represents the standard Dodelson-Widrow case where the pseudoscalar NSSI is switched off.

Figure 5

Variation of the free streaming length of sterile neutrino dark matter determined by the increasing strength of NSSI for different values of $m_s$ and ${\sin }^2(2\theta )$. Each color refers to a benchmark point given in Figs. 2 and 3. Each line type corresponds to a different value of the NSSI mediator mass. Black squares pinpoint to values of ${\epsilon }_P$ for which the condition ${\mathrm{\Omega }}_s{h}^2={\mathrm{\Omega }}_{\mathrm{DM}}{h}^2=0.12$ is satisfied. Black triangles identify values of ${\epsilon }_P$ such that only the 10% of the DM abundance is constituted by sterile neutrinos in the “cocktail DM” scenario.

Figure 6

Evolution of the production rate of sterile neutrino with $m_s=10\mathrm{keV}$ and ${\sin }^2(2\theta )=1.1\times {10}^{-9}$ (BP2 in Fig. 2) with temperature. The black thick line corresponds to the standard Dodelson-Widrow production case. The black dashed line corresponds to the production assisted by pseudoscalar NSSI with ${\epsilon }_P$ such that ${\mathrm{\Omega }}_s{h}^2={\mathrm{\Omega }}_{\mathrm{DM}}{h}^2=0.12$. Different shades of red, green, and blue correspond to increasing strength of NSSI involved in the sterile neutrino production. All the lines are obtained under the hypothesis that the NSSI mediator has mass $m_{\varphi }=10\mathrm{GeV}$.