The 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 $pp$, $p$A and AA collisions, we find two characteristic $p_{T}$ points relating to the behavior of $\left[\ln f(p_{T})\right]^{’’}$, 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 $\left[\ln f(p_{T})\right]^{’’}$ is zero and another point is $p_{1}$ at which $\left[\ln f(p_{T})\right]^{’’}$ 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, $K^{*}$, $ϕ$ and baryons such as $p$, $Λ$, $Ξ$, $Ω$ 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 $\left\langle p_{T}\right\rangle $, and find a difference between $p_{0}$-$\left\langle p_{T}\right\rangle $ correlation of baryons and that of mesons which can be understood by quark combination mechanism at hadronization. The systematic comparison for $p_{0}$-$\left\langle p_{T}\right\rangle $ correlation of kaon, $ϕ$, $p$ and $Λ$ 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.

💡 Research Summary

The authors address a long‑standing ambiguity in high‑energy hadron production: where does the “soft” regime, governed by low‑momentum partons, end and the “hard” regime, dominated by high‑energy jets, begin? By examining the invariant transverse‑momentum spectra f(p_T) measured in proton‑proton (pp), proton‑nucleus (pA) and nucleus‑nucleus (AA) collisions at RHIC and LHC, they propose a model‑independent method based on the curvature of the logarithmic spectrum, i.e. the second derivative