Ensemble-mean ${\mathbf{p}}_{\mathbf{t}}$ and hadron production in high-energy nuclear collisions

A two-component (soft + hard) model (TCM) of hadron production in high-energy nuclear collisions is applied to ensemble-mean $p_t$ (denoted by ${\bar{p}}_t$) data for $p$-$p$, $p$-Pb and Pb-Pb collisions from the relativistic heavy ion collider (RHIC) and large hadron collider (LHC). This ${\bar{p}}_t$ TCM is directly related to a recently-published TCM for the charge-multiplicity $n_{ch}$ and collision-energy dependence of $p_t$ spectrum data from $p$-$p$ collisions. Multiplicity dependence of the $p$-$p$ spectrum hard component observed in the previous study is consistent with similar behavior for $\bar p_t$hardcomponent$\bar p_{th}$\mathrm{.}$p$-$p$ ${\bar{p}}_t$ $n_{ch}$ dependence is observed to follow a noneikonal trend for the TCM hard component (dijet production $\propto n_{ch}^2$), whereas the trend for Pb-Pb collisions is consistent with the eikonal approximation assumed for the Glauber A-A centrality model. The $p$-Pb trend is intermediate, transitioning from the noneikonal $p$-$p$ trend for more-peripheral collisions to an eikonal trend for more-central collisions. The multiplicity dependence of participant number $N_{part}$ and binary-collision number $N_{bin}$ inferred from $p$-Pb $\bar p_t$ data differs strongly from a Glauber Monte Carlo model of that system. The rapid increase with $n_{ch}$ and large magnitude of ${\bar{p}}_t$ for the $p$-$p$ and $p$-Pb systems suggests that minimum-bias jets (TCM hard component) dominate ${\bar{p}}_t$ variation. The trend for ${\bar{p}}_{th}$ in Pb-Pb collisions is consistent with quantitative modification of jet formation in more-central A-A collisions.