CERN Accelerating science

Feynman diagrams for $\eta$ decay to SM fermions through virtual dark photon exchange.

{\it Left panel:} Boltzmann evolution for the leading-order spectrum of Eq.~\eqref{eq:LO_spectrum} satisfying $2 m_{\pi_+} > m_{\pi_0} + m_\eta$. Solid curves assume kinetic coupling between the SM and hidden sectors throughout, whereas dotted curves correspond to decoupling at $x_{\rm dec} = 25$. Note that each curve denotes the abundance of a single real degree of freedom; in particular, the total DM abundance is given by $3 Y_{\pi_0}$ and matches the observed value (indicated by the black dotted line). {\it Right panel:} Illustration of an alternative scenario with a relatively larger $m_\eta$, satisfying $2 m_{\pi_+} < m_{\pi_0} + m_\eta$, resulting in strong further depletion of the $\eta$ abundance.

{\it Left panel:} Boltzmann evolution for the leading-order spectrum of Eq.~\eqref{eq:LO_spectrum} satisfying $2 m_{\pi_+} > m_{\pi_0} + m_\eta$. Solid curves assume kinetic coupling between the SM and hidden sectors throughout, whereas dotted curves correspond to decoupling at $x_{\rm dec} = 25$. Note that each curve denotes the abundance of a single real degree of freedom; in particular, the total DM abundance is given by $3 Y_{\pi_0}$ and matches the observed value (indicated by the black dotted line). {\it Right panel:} Illustration of an alternative scenario with a relatively larger $m_\eta$, satisfying $2 m_{\pi_+} < m_{\pi_0} + m_\eta$, resulting in strong further depletion of the $\eta$ abundance.

Boltzmann evolution for the spectrum in Eq.~\eqref{eq:LO_spectrum2}, characterized by meson mass splittings larger than the $3\to 2$ freezeout temperature. Solid curves assume kinetic coupling between the SM and hidden sector, whereas dotted curves correspond to decoupling at $x_{\rm dec} = 25$.

Exclusion regions from $\eta$ decay. We have chosen parameters so that only the $\eta\to 4e$ decay channel is relevant in setting the bounds. In this case both the $\eta$ lifetime and the kinetic decoupling depend on the combination $\hat{y} = \varepsilon \hat{e} (m_{\pi_0} /m_{A'})^2$, shown on the vertical axis. The variable $\Delta_\eta$ on the horizontal axis mainly controls the freezeout abundance of $\eta$, under the assumption of leading-order masses for the mesons.

Summary of existing and projected constraints. See the text in Section~\ref{sec:summary} for details.

Summary of existing and projected constraints. See the text in Section~\ref{sec:summary} for details.

Summary of existing and projected constraints. See the text in Section~\ref{sec:summary} for details.

Summary of existing and projected constraints. See the text in Section~\ref{sec:summary} for details.

Summary of existing and projected constraints. See the text in Section~\ref{sec:summary} for details.

Summary of existing and projected constraints. See the text in Section~\ref{sec:summary} for details.