Domain of soft hadrons in transverse momentum space in high energy collisions

By studying experimental data for invariant transverse momentum distribution $f({p}_{T})$ of hadrons in high energy $pp$, $p\mathrm{A}$, and AA collisions, we find two characteristic ${p}_{T}$ points relating to the behavior of ${[\mathrm{ln}f({p}_{T})]}^{\ensuremath{'}\ensuremath{'}}$, i.e., the second derivative of the logarithm of hadronic ${p}_{T}$ spectrum with respect to ${p}_{T}$. One point is ${p}_{0}$ at which ${[\mathrm{ln}f({p}_{T})]}^{\ensuremath{'}\ensuremath{'}}$ is zero and another point is ${p}_{1}$ at which ${[\mathrm{ln}f({p}_{T})]}^{\ensuremath{'}\ensuremath{'}}$ reaches maximum. The hadronic distribution can be classified into three kinetic regions, i.e., soft region $0<{p}_{T}<{p}_{0}$ dominated by hadrons from the soft parton system, hard region ${p}_{T}>{p}_{1}$ dominated by hadrons from high energy partonic jets, and the transition region ${p}_{0}<{p}_{T}<{p}_{1}$ of above two sources of hadron production. Using rich data of hadronic ${p}_{T}$ spectra at RHIC and LHC, we carry out a systematical analysis for ${p}_{0}$ and ${p}_{1}$ of kaon, ${K}^{*}$, $\ensuremath{\phi}$, and baryons such as $p$, $\mathrm{\ensuremath{\Lambda}}$, $\mathrm{\ensuremath{\Xi}}$, $\mathrm{\ensuremath{\Omega}}$ in $pp$, $p$-Pb, and heavy-ion collisions, and show their dependence on hadron species, collision energy, collision centrality, and/or charged-particle multiplicity. We also study the correlation between ${p}_{0}$ of hadrons and their average transverse momentum $⟨{p}_{T}⟩$, and find a difference between ${p}_{0}\ensuremath{-}⟨{p}_{T}⟩$ correlation of baryons and that of mesons, which can be understood by the quark combination mechanism at hadronization. The systematic comparison for ${p}_{0}\ensuremath{-}⟨{p}_{T}⟩$ correlation of kaon, $\ensuremath{\phi}$, $p$, and $\mathrm{\ensuremath{\Lambda}}$ in $pp$, $p$-Pb, Pb-Pb, and $\mathrm{Au}+\mathrm{Au}$ collisions at RHIC and LHC energies indicates that ${p}_{0}$ is a sensitive physical quantity of reflecting the production property of soft hadrons in high energy collisions.