Hard processes in multi-TeV ion collisions

Motivated by the ion-collision program at the Large Hadron Collider, plans for its high-luminosity upgrade, and on-going discussions for multi-TeV future hadron colliders, we systematically investigate hard-scattering, Standard Model processes in many-TeV ion-ion collisions. We focus on the symmetric beam configurations $^{208}$Pb-$^{208}$Pb, $^{131}$Xe-$^{131}$Xe, $^{12}$C-$^{12}$C, and $pp$, and we catalog total and fiducial cross sections for dozens of processes, ranging from associated-Higgs and multiboson production to associated-top pair production, at next-to-leading order in QCD for nucleon-nucleon collision energies from $\sqrt{s_{NN}}=1$ to $100$ TeV. We report the residual scale uncertainties at this order as well as the uncertainties originating from fits of nuclear parton densities. We also discuss the propagation of nuclear dynamics (as encoded in nuclear parton densities) into parton luminosities, and ultimately into predictions for cross sections. Finally, we report on the emergence of trends and the reliability of extrapolating cross sections across different nuclei. For Pb-Pb collisions at a hypothetical Future Circular Collider with $\sqrt{s_{NN}}=39$ TeV, $\mathcal{O}(10^{8})$ weak bosons, $\mathcal{O}(10^5)$ diboson pairs, $\mathcal{O}(10^4)$ $WH$ and $ZH$ pairs, $\mathcal{O}(10^3)$ triboson events, $\mathcal{O}(10^5)$ high-$p_T$ photons events, and $\mathcal{O}(10^7)$ $t\overline{t}$ pairs can be produced with $\mathcal{L}=33$~nb$^{-1}$ of data. At $\sqrt{s_{NN}}=5.52$ TeV, one can expect $\mathcal{O}(10-10^6)$ single, multiboson, and top events per $1$ nb$^{-1}$. Decay rates and experimental selection/acceptance rates will impact final event yields, and merits further study; as an illustrative example, we focus on select diboson and triboson channels in lead-lead collisions and discuss their observability at the high-luminosity phase of the LHC and the FCC.