Description
This document summarizes proposed searches for new physics accessible in the heavy-ion mode at the LHC, both through hadronic and ultraperipheral $\gamma\gamma$ interactions, and that have a competitive or, even, unique discovery potential compared to standard proton-proton collision studies. Illustrative examples include searches of new particles --- such as axion-like pseudoscalars, radions, magnetic monopoles, new long-lived particles, dark photons, and sexaquarks as dark matter candidates --- as well as new interactions, such as non-linear or non-commutative QED extensions. We argue that such interesting possibilities constitute a well-justified scientific motivation, complementing standard quark-gluon-plasma physics studies, to continue running with ions at the LHC after the Run-4, i.e. beyond 2030, including light and intermediate-mass species, accumulating nucleon-nucleon integrated luminosities in the accessible fb$^{-1}$ range per month.
