Enhanced scope of a Phase 2 CMS detector for the study of exotic physics signatures at the HL-LHC

The high luminosity LHC (HL-LHC) run, which is due to start in 2025, is expected to collect an integrated luminosity of approximately $3000~\mathrm{fb}^{-1}$ at $\sqrt{s}=14~\mathrm{TeV}$. The discovery and study of physics beyond the standard model will remain one of the major goals of the CMS collaboration during this period. Such physics can yield exotic signatures, whose observation places unusual demands on the performance and capabilities of the detector. For a few selected exotic physics models, we present studies of what can be achieved using CMS data during the HL-LHC run. We look at how this potential is influenced by the design of the upgraded CMS detector, as documented in the $\mathrm{phase~2}$ technical proposal. This document provides supplementary material for a deeper level of understanding of these studies. In the case of a high mass resonance decaying to leptons, we explore the hypothesis that this is discovered prior to 2025, and examine what would be learned about the resonance's properties using the HL-LHC data. In the case of searches for long-lived exotic particles, we show that the discovery potential is influenced by the availability of dE/dx measurements from the tracker, the precision of time of flight measurements from the electromagnetic calorimeter, and the ability to trigger on displaced leptons.