$ 1\,TeV; \item $\slashed{E}_T>$ 1\,TeV; \item $\Delta\phi_{\rm min}^{j,\slashed{E}_T}>$1.5 to reduce the contribution from hard jets faking MET. \end{itemize} In addition, ATLAS selects isolated charged tracks that give at least 5 hits in the inner tracker layers, of which 3 are in the pixel tracker and 2 in the (double-sided) SCT, to facilitate a good track reconstruction. In order to satisfy this criterion a track must reach a transverse distance $r$ of 30 cm, severely compromising the sensitivity to intermediate-lifetime particles. Instead, we will allow the radius at which 100\% efficiency is reached for a disappearing charged track to vary, and show how this affects the sensitivity for different masses and lifetimes of the charged state. The pseudorapidity range of the ATLAS analysis is limited by the extent of the Transition Radiation Tracker (TRT), which is used to veto long-lived tracks, but as we shall show later increasing the $\eta$ range has little effect on the sensitivity of this analysis. We will also comment on the variation of the sensitivity with changes in the leading jet $p_T$ and MET cuts. Our charged track selection is as follows: \begin{itemize} \begin{samepage} \item $p_{T,{\rm track}}>1$\,TeV; \end{samepage} \item transverse track length $r_\textrm{min}\le r_\textrm{track}\le 65$ cm, with $r_\textrm{min}$ the minimum length necessary for a reliable track reconstruction;\footnote{We also assume the presence of a tracker at 65 cm that fulfils the role of the TRT.} \item 0 $<|\eta_{\rm track}|<$ 2, \end{itemize} for tracks which are assumed to satisfy isolation criteria similar to those used in the ATLAS analysis, rescaled to the busier 100\,TeV environment~\cite{Aad-ml-2013yna}, possibly supplemented with a veto on large calorimeter deposits close to the extrapolated path of the charged particle leaving the track. We show in figure~\ref{fig:EtaDistrib} the charged track distribution with transverse distance from the beamline $r$. In the left panel (a), we bin the distribution in $\eta$ for $m_\chi=1.1$\,TeV and $p_T(j_1),\slashed{E}_T\ge 1$\,TeV, while in the right panel (b) we integrate the total number of charged tracks over $|\eta|\le2$ , for three different masses, and two different $p_T,\slashed{E}_T,p_{T,\text{tr}}$ cuts. We take a nominal decay length of 6.6 mm, which corresponds to the proper lifetime of the charged component of 1.1\,TeV pure-Higgsino state, for illustration. The sensitivity to charged tracks in the current ATLAS search begins at $r=30$ cm, shaded in cyan in the left panel. It is evident from the plots that TeV-scale charged states with sub-cm $c\tau$ cannot make it out to large enough transverse distances in order to be covered by existing searches. Were it instead possible to achieve 100\% track reconstruction efficiency within 10 cm of the beamline, one could have $\mathcal{O}$(10) events for weak-doublet masses comfortably up to 1\,TeV. \begin{figure} \centering \subfloat[] {\includegraphics[width=0.49\textwidth]{EtaR1100Pt1000}} ~\subfloat[] {\includegraphics[width=0.49\textwidth]{TReach}} ]]>

1$\,TeV to decay to a charged state with momentum below the detection threshold is already vanishingly small, the neutral decay products would still leave large energy deposits in the calorimeters so even those events could be removed efficiently with suitable isolation cuts. What remains are events where the hadron decays to a charged state and missing energy (i.e.\ neutrinos), which is suppressed in the SM due to the absence of flavour-changing neutral currents.} Fake backgrounds consist of interacting hadron tracks, leptons failing identification criteria at low track $p_{T}$, and tracks with mismeasured $p_T$ due to ``a high density of silicon hits, hadronic interactions and scattering''~\cite{Aad-ml-2013yna} at large track $p_{T}$. These fakes are not well-described by Monte Carlo simulations at the LHC at 8\,TeV centre-of-mass. Instead, their $p_T$ spectra are fit to data in specific `control' regions and subtracted, rendering their extrapolation to 100\,TeV rather difficult. In addition their composition and spectra are characteristic of the particular detector in which they are measured (ATLAS in this instance), and a naive extrapolation to a hypothetical detector for a 100\,TeV hadron machine, with unknown properties, would be crude at best. Nevertheless we will make some attempt to do this. First, we assume that the fake backgrounds at FCC-hh have a similar composition and are again dominated at high track $p_T$ by the mismeasured hadronic tracks satisfying the ATLAS 8\,TeV disappearing track selection, which is fitted using a control region consisting of disappearing tracks with large impact parameter, see~\cite{Aad-ml-2013yna} for details. Since these likely originate in high-$p_T$ collisional backgrounds, which scale like the falling PDFs, we assume the hadronic fakes satisfying our {\it modified} selection criteria retain the same scaling with track $p_T$ as the original ($p_{T,{\rm track}}^{-a}$ with $a=1.78\pm 0.5$), with a floating overall normalization that parametrizes our uncertainty. This normalization constant can be estimated using the scaling of some chosen process with centre-of-mass energy. Previous works~\cite{Low-ml-2014cba,Cirelli-ml-2014dsa} used Standard Model $(Z\rightarrow\nu\nu)$ plus jets, the rate for this process scales with the product of the quark and gluon PDFs. In order to be maximally conservative, we will also show the outcome using the scaling of SM multijets, with large fake MET. This is glue-glue-initiated, and hence grows faster with energy. We estimate the significance using the usual gaussian expression, \begin{equation} {\rm Significance}=\frac{S}{\sqrt{B+\lambda^2 B^2}} \end{equation} for $S$ signal events and $B$ background events, and background systematic uncertainty $\lambda=50\%$, using the difference between the two methods of scaling the backgrounds as a measure of our total background uncertainty. We superimpose the resulting discovery ($5\sigma$) and exclusion ($2\sigma$) bands on to the event count contours in figure~\ref{fig:XSNumber}(b). The grey shaded region shows the extent of the FCC sensitivity, with the width of the coloured bands representing our estimated uncertainty in the significance contours. We see that the FCC with modified tracking can comfortably cover $c\tau$ down to about 7 mm for $m_\chi\sim 1$\,TeV\@. The extent of the sensitivity at larger masses depends on which estimate of the backgrounds is closer to reality, with our optimistic projection extending discovery reach to $m_\chi=1.4$\,TeV. ]]>