  The CMS Collaboration intends to pursue the study of central exclusive
production (CEP) events, pp $\to$ pXp, at the High-Luminosity LHC (HL-LHC) by
means of a new near-beam proton spectrometer. In CEP events, the state X is
produced at central rapidities, and the scattered protons do not leave the beam
pipe. The kinematics of X can be fully reconstructed from that of the protons,
which gives access to final states otherwise not visible. CEP allows unique
sensitivity to physics beyond the standard model, e.g. in the search for
anomalous quartic gauge couplings, axion-like particles, and in general new
resonances. CMS has been successfully operating the Precision Proton
Spectrometer (PPS), initially a joint CMS and TOTEM project, since 2016. The
present document outlines the physics interest of a new PPS at the HL-LHC, and
explores its feasibility and expected performance. Discussions with the machine
groups led to the identification of four locations suitable for the
installation of movable proton detectors: at 196, 220, 234, and 420 m from the
interaction point, on both sides. Acceptance studies indicate that having the
beams cross in the vertical plane at the interaction point, as implemented
after Long Shutdown 3, is preferable over the present horizontal crossing. This
gives access to states X in the mass range 133 GeV$-$2.7 TeV with the stations
at 196, 220, and 234 m. The lower mass limit becomes 43 GeV if the 420 m
station is included, which makes it possible to study central exclusive
production of the 125 GeV Higgs boson. This is a major improvement with respect
to the current mass range of 350 GeV$-$2 TeV. The project and its costs can
easily be staged; the 420 m station can be addressed in a second step. In
summary, a new near-beam proton spectrometer for operation at the HL-LHC
appears feasible. It would greatly extend the CMS physics reach with a limited
investment.
