A search is presented for long-lived charged particles that decay within the silicon tracker of the CMS detector. Such particles can produce a "disappearing track" signature, identified as an isolated track with no associated hits in the muon detectors, little calorimeter energy deposits, and missing hits in the outermost layers of the silicon tracker. The search is performed in proton-proton collision data recorded by the CMS experiment at a center-of-mass energy of 13 TeV during 2017 and 2018, corresponding to an integrated luminosity of $101~\mathrm{fb}^{-1}$. The observation of $48$ events is consistent with the estimated background of $47.8 \, _{-2.3}^{+2.7} (\mathrm{stat.}) \pm 8.1 (\mathrm{syst.})$ events. Upper limits are set on chargino production in the context of an anomaly-mediated supersymmetry breaking model for purely wino- and higgsino-like neutralino mixing scenarios. At $95\%$ confidence level, chargino masses in the higgsino case are excluded below $750~\mathrm{GeV}$ ($175~\mathrm{GeV}$) for a lifetime of $3$ ($0.05$) ns. In the wino case, the results of the search in the 2017 and 2018 data-taking periods are combined with the previous CMS result in the 2015 and 2016 periods, forming the full Run 2 results. At $95\%$ confidence level, chargino masses in the wino case are excluded below $884~\mathrm{GeV}$ ($474~\mathrm{GeV}$) for a lifetime of $3$ ($0.2$) ns.
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