The domain of soft hadrons in transverse momentum space in high energy collisions

Abstract

By studying experimental data for invariant transverse momentum distribution $f(p_T)$ of hadrons in high energy $pp$, $p$A and AA collisions, we find two characteristic $p_T$ points relating to the behavior of ${\left[\ln f(p_T)\right]}^{{}^{\prime \prime }}$, 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 ${\left[\ln f(p_T)\right]}^{{}^{\prime \prime }}$ is zero and another point is $p_1$ at which ${\left[\ln f(p_T)\right]}^{{}^{\prime \prime }}$ reaches maximum. \bz{The hadronic distribution can be classified into three kinetic regions, i.e., soft region $0<p_T<p_0$ dominated by hadrons from soft parton system, hard region $p_T>p_1$ dominated by hadrons from high energy partonic jet, 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, $K^{\ast }$, $\ddot{I}•$ and baryons such as $p$, $\hat{I}›$, $\hat{I}ž$, $\hat{I}\text{c◯}$ 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 $p_0$-$⟨p_T⟩$ correlation of baryons and that of mesons which can be understood by quark combination mechanism at hadronization. The systematic comparison for $p_0$-$⟨p_T⟩$ correlation of kaon, $\ddot{I}•$, $p$ and $\hat{I}›$ in $pp$, $p$-Pb, Pb-Pb and Au+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.

22 pages, 14 figures