Averaged transverse momentum correlations of hadrons in relativistic heavy-ion collisions

We compile experimental data for the averaged transverse momentum ($⟨p_T⟩$) of proton, $\mathrm{\Lambda }$, ${\mathrm{\Xi }}^{-}$, ${\mathrm{\Omega }}^{-}$ and $\varphi$ at mid-rapidity in Au+Au collisions at $\sqrt{s_{NN}}=$ 200, 39, 27, 19.6, 11.5, 7.7 GeV and in Pb+Pb collisions at $\sqrt{s_{NN}}=$ 2.76 TeV, and find that experimental data of these hadrons exhibit systematic correlations. We apply a quark combination model with equal-velocity combination approximation to derive analytic formulas of hadronic $\left\langle p_{T}\right\rangle $inthecaseofexponentialformofquark$p_{T}$ spectra at hadronization. We use them to successfully explain the systematic correlations exhibited in $⟨p_T⟩$ data of $p\mathrm{\Lambda }$, $\mathrm{\Lambda }{\mathrm{\Xi }}^{-}$, ${\mathrm{\Xi }}^{-}{\mathrm{\Omega }}^{-}$ and ${\mathrm{\Xi }}^{-}\varphi$ pairs. We also use them to successfully explain the regularity observed in $\left\langle p_{T}\right\rangle $ofthesehadronsasthefunctionof$(dN_{ch}/dy)/(N_{part}/2)$ at mid-rapidity in central heavy-ion collisions at both RHIC and LHC energies. Our results suggest that the constituent quark degrees of freedom and the equal-velocity combination of these constituent quarks at hadronization play important role in understanding the production of baryons and $\varphi$ meson at these RHIC and LHC energies.