Detector acceptance and signal reconstruction efficiency for K$^{\ast0}$ and $\phi$ mesons, which includes reconstruction, track selection and particle identification efficiency. For K$^{\ast0}$ and $\phi$ production below $\pt$ $< $ 3 GeV/$c$, the PID efficiency is relative to the TPC-TOF approach, whereas for $\phi$ production with $\pt$ $>$ 3 GeV/$c$ no PID contribution is included, as no particle identification is applied in the analysis.