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 ${[\ln f(p_T)]}^{\prime \prime }$, 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 ${[\ln f(p_T)]}^{\prime \prime }$ is zero and another point is $p_1$ at which ${[\ln f(p_T)]}^{\prime \prime }$ 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, $K^{*}$, $\varphi$, and baryons such as $p$, $\mathrm{\Lambda }$, $\mathrm{\Xi }$, $\mathrm{\Omega }$ 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 $p_0-⟨p_T⟩$ correlation of baryons and that of mesons, which can be understood by the quark combination mechanism at hadronization. The systematic comparison for $p_0-⟨p_T⟩$ correlation of kaon, $\varphi$, $p$, and $\mathrm{\Lambda }$ 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.

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• Particle production
• Relativistic heavy-ion collisions