"Additional Figure 8" of "Search for long-lived particles decaying in the CMS endcap muon detectors in proton-proton collisions at $\sqrt{s} = $ 13 TeV"

The efficiency of $N_{station} > 1$ requirement in bins of hadronic energy in region B. Region B is defined as 671 cm $< |z| <$ 1100 cm, $r <$ 695.5 cm, and $|\eta| <$ 2. The cluster efficiency is estimated with LLPs decaying to $\tau^{+} \tau^{-}$. The sample contains equal fractions of events with LLP mass of 7, 15, 40, and 55 GeV and LLP lifetime of 0.1, 1, 10, and 100m. The first hadronic energy bin corresponds to LLPs that decayed leptonically with 0 hadronic energy. The efficiency is calculated with respect to clusters that pass all cluster-level cuts described in the paper, except for the jet veto, time cut, and $\Delta\phi$ cut. The full simulation signal yield prediction for samples with various LLP mass between 7 - 55 GeV, lifetime between 0.1 - 100 m, and decay mode to $d\bar{d}$ and $\tau^{+} \tau^{-}$ can be reproduced using this parameterization to within 10%.