$\eta$ distributions of fake tracks in minimum-bias collision events and chargino tracks in 3 TeV wino signal events. The normalization is arbitrary. The details of fake track reconstruction is described in Sect. 5.2. The fake-track distribution is shown only within the range $|\eta|<2$.

Probability of finding a fake track in an event as a function of the average number of $pp$ interactions per bunch crossing ($\left<\mu\right>$). The probabilities for the tracks reconstructed with $N_{\mathrm{layer}}^{\mathrm{hit}}=4$ (5) are shown by the open (filled) markers, and they are presented separately for the three tracker layouts, the default layout ($\#$1) in black circles, the alternative layouts of $\#$2 in magenta squares and $\#$3 in red upward triangles. The probabilities for the layout $\#$2 are shown only at $\left<\mu\right>=200$. The estimate from the mixed sample of non-diffractive and diffractive events for the default layout is shown by the blue diamond for comparison purpose.

Expected discovery significance for the wino model with 30 ab$^{-1}$ with the requirement of $N_{\mathrm{layer}}^{\mathrm{hit}}=5$. The grey (red) bands show the significance using the default (alternative) layout $\#$1 ($\#$3). The difference between the solid and hatched bands corresponds to the different pileup conditions of $\left<\mu\right>=200$ and 500. The band width corresponds to the significance variation due to the two models assumed for soft QCD processes.

Expected discovery significance for the higgsino model with 30 ab$^{-1}$ with the requirement of $N_{\mathrm{layer}}^{\mathrm{hit}}=5$. The grey (red) bands show the significance using the default (alternative) layout $\#$1 ($\#$3). The difference between the solid and hatched bands corresponds to the different pileup conditions of $\left<\mu\right>=200$ and 500. The band width corresponds to the significance variation due to the two models assumed for soft QCD processes.

Expected discovery significance for the wino model with 30 ab$^{-1}$ with the requirements of $N_{\mathrm{layer}}^{\mathrm{hit}}=5$ and a good time-fit quality. The background reduction rate with the time information is assumed to be the same for both pileup conditions. The grey (red) bands show the significance using the default (alternative) layout $\#$1 ($\#$3). The difference between the solid and hatched bands corresponds to the different pileup conditions of $\left<\mu\right>=200$ and 500. The band width corresponds to the significance variation due to the two models assumed for soft QCD processes.

Expected discovery significance for the higgsino model with 30 ab$^{-1}$ with the requirements of $N_{\mathrm{layer}}^{\mathrm{hit}}=5$ and a good time-fit quality. The background reduction rate with the time information is assumed to be the same for both pileup conditions. The grey (red) bands show the significance using the default (alternative) layout $\#$1 ($\#$3). The difference between the solid and hatched bands corresponds to the different pileup conditions of $\left<\mu\right>=200$ and 500. The band width corresponds to the significance variation due to the two models assumed for soft QCD processes.

Summary of reach for charginos using a disappearing-track signature. The FCC-hh 5$\sigma$-discovery reach assuming the alternative layout, the average number of $pp$ interactions per bunch crossing of 500, only non-diffractive soft-QCD processes and a use of the time information of the pixel detector is shown in blue. The reach for the wino scenario is obtained by extrapolating the sensitivity curve in Fig. 6. The 5$\sigma$-discovery reach and the 95% CL exclusion sensitivity are taken from [46]. The observed exclusion in the ATLAS search with 36 fb$^{-1}$ of Run 2 data [39, 47] are shown as well.

Radial distances (in mm) of the first five layers from the beam line for the three inner-tracker layouts considered in this study.

Signal acceptance for the 3 TeV wino and 1 TeV higgsino with $|\eta|<1$ for the three inner-tracker layouts. The acceptances are provided separately for the requirements of $N_{\mathrm{layer}}^{\mathrm{hit}}=4$ and 5. The alternative layout $\#$3 has significantly higher acceptance than the others because the relevant layers are located closer to the beam line, particularly for the higgsino case with $N_{\mathrm{layer}}^{\mathrm{hit}}=5$.

Signal and background yields as well as the discovery significance for the 3 TeV wino and 1 TeV higgsino with 30 ab$^{-1}$ with the requirements of $N_{\mathrm{layer}}^{\mathrm{hit}}=5$ under the pileup condition of $\left<\mu\right>=200$. The fake-track background rate is assumed to be same for both alternative layouts. The kinematic selection requirements on the leading jet $p_{T}$ and $E_{\text{T}}^{\text{miss}}$ are also given.

Signal and background yields as well as the discovery significance for the 3 TeV wino and 1 TeV higgsino with 30 ab$^{-1}$ with the requirements of $N_{\mathrm{layer}}^{\mathrm{hit}}=5$ under the pileup condition of $\left<\mu\right>=500$. The fake-track background rate is assumed to be same for both alternative layouts. The kinematic selection requirements on the leading jet $p_{T}$ and $E_{\text{T}}^{\text{miss}}$ are also given.