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

TL;DR

This study identifies characteristic transverse momentum points in high energy collisions, classifies hadron production into three regions, and analyzes their dependence on collision parameters, revealing insights into soft and hard hadron production mechanisms.

Contribution

The paper introduces a systematic analysis of characteristic $p_{T}$ points in hadron spectra, linking them to production mechanisms and collision properties, based on extensive experimental data.

Findings

Identification of two characteristic $p_{T}$ points, $p_{0}$ and $p_{1}$.

Classification of hadron spectra into soft, transition, and hard regions.

Correlation between $p_{0}$ and average transverse momentum, differing for baryons and mesons.

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 $\left[\ln f(p_{T})\right]^{''}$, 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, $K^{*}$, $\phi$ and baryons such as $p$, $\Lambda$, $\Xi$, $\Omega$ 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 $\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, $\phi$, $p$ and $\Lambda$ 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.