arXiv:1912.09486 |
Its difficult to make a simple DM that annihilates to only neutrinos (when $m_{\chi} > m_e$ ) because neutrinos live in the $SU(2)$ doublet $L$.
C El Aisati et. al. arXiv:1706.06600 catalogued simple models (1 DM candidate and 1 portal particles).
Generically you have a charged lepton channel, so $\gamma$-ray telescopes will be competing.
M. Blennow et. al. arXiv:1903.00006 explored this, via a sterile neutrino portal.
Constraints on the heavy-active neutrino mixing make it difficult to go above DM masses $\sim 100\,\textrm{GeV}$ which is what we were interested in.
With interaction term $\mathcal{L}^{\varphi} = y_{\alpha} \bar{\chi} L_{\alpha} \varphi^{\dagger} + \rm h.c.\,,$ leads to $\langle \sigma v \rangle\propto \frac{m_{\chi}^2}{\left(m_{\chi}^2 + m_{\varphi}^2\right)^2}$.
Since $m_{\varphi}>m_{\chi}$ is required for DM stability, its difficult to reach higher masses.