Midrapidity average transverse momentum of identified charged particles in high-energy heavy-ion collisions

Abstract

The average transverse momentum <inline-formula><tex-math id="M8">\begin{document}$\left\langle p_{\mathrm{T}} \right\rangle$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M8.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M8.png"/></alternatives></inline-formula> of final particles is an important observable in high-energy heavy-ion collision experiments. It reflects the properties of soft hadrons and thermonuclear matter, and it can also be used to deduce the information about the evolution of collision systems. By using the phenomenological linear and power-law functions, we study the dependency of the average transverse momentum <inline-formula><tex-math id="M9">\begin{document}$\langle p_{\mathrm{T}}\rangle$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M9.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M9.png"/></alternatives></inline-formula> at midrapidity in Au + Au and Pb + Pb collisions from the STAR, PHENIX and ALICE Collaborations on four normalized physical quantities, i.e. the collision centrality, the average number of binary collisions per participant pair <inline-formula><tex-math id="M10">\begin{document}$\dfrac{2N_{{\mathrm{coll}}}}{N_{{\mathrm{part}}}}$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M10.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M10.png"/></alternatives></inline-formula>, the average pseudorapidity density of charged particles per participant pair <inline-formula><tex-math id="M11">\begin{document}$\dfrac{2}{N_{{\mathrm{part}}}}\dfrac{{\mathrm{d}}N_{{\mathrm{ch}}}}{{\mathrm{d}}\eta}$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M11.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M11.png"/></alternatives></inline-formula> and the average pseudorapidity density of charged particles per binary collision <inline-formula><tex-math id="M12">\begin{document}$\dfrac{1}{N_{{\mathrm{coll}}}}\dfrac{{\mathrm{d}}N_{{\mathrm{ch}}}}{{\mathrm{d}}\eta} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M12.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M12.png"/></alternatives></inline-formula>. The results show that the average transverse momentum <inline-formula><tex-math id="M13">\begin{document}$\langle p_{\mathrm{T}} \rangle$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M13.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M13.png"/></alternatives></inline-formula> of identified particles exhibits a good linear relationship with collision centrality, and it follows a nice power-law relationship with the average number of binary collisions per participant pair <inline-formula><tex-math id="M14">\begin{document}$\dfrac{2N_{{\mathrm{coll}}}}{N_{{\mathrm{part}}}}$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M14.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M14.png"/></alternatives></inline-formula>, the average pseudorapidity density of charged particles per participant pair <inline-formula><tex-math id="M15">\begin{document}$\dfrac{2}{N_{{\mathrm{part}}}}\dfrac{{\mathrm{d}}N_{{\mathrm{ch}}}}{{\mathrm{d}}\eta}$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M15.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M15.png"/></alternatives></inline-formula>, and the average pseudorapidity density of charged particles per binary collision <inline-formula><tex-math id="M16">\begin{document}$\dfrac{1}{N_{{\mathrm{coll}}}}\dfrac{{\mathrm{d}}N_{{\mathrm{ch}}}}{{\mathrm{d}}\eta}$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M16.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M16.png"/></alternatives></inline-formula>. It is also found that the fitting parameters in the proposed phenomenological functions for the average transverse momentum <inline-formula><tex-math id="M17">\begin{document}$\langle p_{\mathrm{T}} \rangle$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M17.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M17.png"/></alternatives></inline-formula> with collision centrality and the average number of binary collisions per participant pair follow a power-law function with collision energy, which endows the phenomenological approach with predictive ability. Therefore, the collision centrality and the average number of binary collisions per participant pair are good physical quantities for studying the average transverse momentum of identified particles in high-energy heavy-ion collisions. The results in this study can be used to predict the average transverse momentum of identified particles at other collision energy of which the experimental data are not available so far. The mass ordering of the average transverse momentum of identified particles, i.e. <inline-formula><tex-math id="M18">\begin{document}$\text{π}^{-}$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M18.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M18.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M19">\begin{document}${\mathrm{K}}^{-} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M19.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M19.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M20">\begin{document}$\bar{{\mathrm{p}}}$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M20.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20240905_M20.png"/></alternatives></inline-formula>, is also discussed and explained by the particle production time related to energy conservation, at a given collision centrality and energy.