Ratios of jet and hadron spectra at LHC energies: measuring high-$p_T$ suppression without a $pp$ reference

We analyze the reliability of several techniques for computing jet and hadron spectra at different collision energies. This is relevant for discovering energy loss in the upcoming oxygen-oxygen (OO) run at the LHC, for which a reference <math display="inline"><mi>p</mi><mi>p</mi></math> run is currently not planned. For hadrons and jets we compute the ratio of spectra between different <math display="inline"><mi>p</mi><mi>p</mi></math> collision energies in perturbative QCD, which can be used to construct a reference spectrum. Alternatively, it can be interpolated from measured spectra at nearby energies. We estimate the precision of both strategies for the spectra ratio relevant to the oxygen run, and conclude that the central values agree to 4% accuracy for hadrons and 2% accuracy for jets. Finally we propose taking the ratio of OO and <math display="inline"><mi>p</mi><mi>p</mi></math> spectra at different collision energies, which cleanly separates the experimental measurement and theoretical computation.