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We present a new method of solving the probability distribution for baryons, antibaryons and mesons at the hadronization of constituent quark and antiquark system. The hadronization is governed by the quark combination rule in the quark combination model developed by the Shandong Group. We use the method of the generating function to derive the outcome of the quark combination rule, which is much simpler and easier to be generalized than the original method. Furthermore, we use the formula of the quark combination rule and its generalization to study the property of multiplicity distribution of net-protons. Taking a naive case of quark number fluctuations and correlations at hadronization, we calculate ratios of multiplicity cumulants of final-state net-protons and discuss the potential applicability of quark combination model in studying hadronic multiplicity fluctuations and the underlying phase transition property in relativistic heavy-ion collisions., 17 pages, 3 figures. To be published in Chinese Physics C

We show that the spectra of and at midrapidity in the inelastic events in collisions at 13 TeV exhibit a constituent quark number scaling property, which is a clear signal of quark combination mechanism at hadronization. We use a quark combination model with equal velocity combination approximation to systematically study the production of identified hadrons in collisions at = 13 TeV. The midrapidity spectra for protons, , , , and in the inelastic events are simultaneously fitted by the model. The multiplicity dependence of the yields of these hadrons are also well understood. The strong dependence of the ratio is well explained by the model, which further suggests that the production of two hadrons with similar masses is determined by their quark content at hadronization. The spectra of strange hadrons at midrapidity in different multiplicity classes in collisions at 13 TeV are predicted for further tests of the model. The midrapidity spectra of soft ( GeV/c) strange quarks and up/down quarks at hadronization in collisions at 13 TeV are extracted.

The rapidity and transverse momentum spectra for identified hadrons in central Au+Au collisions at $\sqrt{s_{NN}}= 200$ GeV are computed in a quark combination model. The data of rapidity distributions for $\pi^{\pm}$, $K^{\pm}$, $p(\bar{p})$ and net protons $(p-\bar{p})$ are well described. We also predict rapidity distributions for $K^{0}_{s}$, $\Lambda(\bar{\Lambda})$, $\mathrm{\Xi^{-}}$ ($\mathrm{\bar{\Xi}^{_+}}$) and $\mathrm{\Omega^{-}}+\mathrm{\bar{\Omega}}^{_+}$. The multiplicity ratios of charged antihadrons to hadrons as a function of rapidity are reproduced. The results for ${p}_{T}$ spectra of $\pi^{\pm}$, $K^{\pm}$, $p(\bar{p})$ and for the $p/\pi$ ratios in a broader ${p}_{T}$ range agree well with the data. Finally the rapidity dependence of transverse momentum distributions for hadrons are given.