\section{ANNEX A: Reference FM-Detector Geometry}
\label{sec:annex-a_fm-det-geometry}
The following dimensions are the direct \acs{GEANT4} simulation results and are shown here for reference.

\begin{itemize}
    \item Thickness: 0.5~mm
    \item Radius of the inner segments $r_{i1}$ / $r_{i2}$ = 11.34~mm / 10.84~mm
    \item Radius of the middle segments $r_{m1}$ / $r_{m2}$ = 30.0~mm / 29.5~mm
    \item Radius of outer anticoincidence ring $r_a$ = 58.3~mm
    \item Distance between two SSD's around BGO: 30~mm
    \item Distance between two SSD's around Aerogel: 50~mm
    \item Area of inner segments $A_{i1}$ / $A_{i2}$ = 403.9~mm$^2$ / 369.1~mm$^2$
    \item Area of middle segments $A_{m1}$ / $A_{m2}$ = 807.8~mm$^2$ / 788.3~mm$^2$
    \item Area of outer ring $A_o$ = 7862.7~mm$^2$
\end{itemize}
BGO:
\begin{itemize}
    \item Polyhedra with 6 sides
    \item Thickness : 20mm
    \item r$_{max}$ = 45mm
\end{itemize}
Aerogel:
\begin{itemize}
    \item Box
    \item Thickness: 40mm
    \item Width: 62mm
    \item Height: 62mm
\end{itemize}