Improved Monte Carlo Glauber predictions at present and future nuclear colliders

We present the results of an improved Monte Carlo Glauber (MCG) model of relevance for collisions involving nuclei at center-of-mass energies of BNL RHIC ($\sqrt{s_{\rm NN}}=0.2$ TeV), CERN LHC ($\sqrt{s_{\rm NN}}=2.76$-$8.8$ TeV), and proposed future hadron colliders ($\sqrt{s_{\rm NN}}\approx 10$-$63$ TeV). The inelastic pp cross sections as a function of $\sqrt{s_{\rm NN}}$ are obtained from a precise data-driven parametrization that exploits the many available measurements at LHC collision energies. We describe the nuclear transverse profile with two separated 2-parameter Fermi distributions for protons and neutrons to account for their different densities close to the nuclear periphery. Furthermore, we model the nucleon degrees of freedom inside the nucleus through a lattice with a minimum nodal separation, combined with a "recentering and reweighting" procedure, that overcomes some limitations of previous MCG approaches. The nuclear overlap function, number of participant nucleons and binary nucleon-nucleon collisions, participant eccentricity and triangularity, overlap area and average path length are presented in intervals of percentile centrality for lead-lead (PbPb) and proton-lead (pPb) collisions at all collision energies. We demonstrate for collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV that the central values of the Glauber quantities change by up to 7%, in a few bins of reaction centrality, due to the improvements implemented, though typically remain within the previously assigned systematic uncertainties, while their associated uncertainties are generally smaller (mostly below 5%) at all centralities than for earlier calculations. Tables for all quantities versus centrality at present and foreseen collision energies involving Pb nuclei, as well as for collisions of XeXe at $\sqrt{s_{\rm NN}}=5.44$, and AuAu and CuCu at $\sqrt{s_{\rm NN}}=0.2$ TeV, are provided.