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We describe the transverse momentum spectra of $\pi^\pm$, $K^\pm$, $p$, and$\bar{p}$ produced in different centralities gold-gold (Au-Au) collisions atdifferent collision energies range from 7.7 to 62.4 GeV by a two-componentErlang distribution. The fitting results are consistent with the experimentaldata, and the centrality- and energy-dependent yield ratios of negative topositive particles are obtained from the normalization constants. Based on theyield ratios, the energy- and centrality-dependent chemical potentials of lighthadrons and quarks are extracted. The study shows that the dependences of thethree types of particle yield ratios on centrality are not significant,especially for $\pi$. The logarithms of the three yield ratios show obviouslinear dependence on $1/\sqrt{s_{NN}}$ over a range from 7.7 to 62.4 GeV. Theextracted chemical potentials show obvious dependence on energy, and decreasewith the increase of energy. The dependences of the energy-dependent chemicalpotentials of light hadrons and quarks on centrality are relatively moreobvious in low energy region. The derived curves of chemical potentials for allcentralities, from the linear fits of the logarithms of yield ratios vs energy,have the extremum at the same energy of 3.526 GeV, which possibly is thecritical energy of phase transition from a liquid-like hadron state to agas-like quark state in the collision system. With the increase of energy, alltypes of chemical potentials become small and tend to zero at very high energy,which indicates that with the increase of energy, the hadronic interactionsgradually fade and the partonic interactions gradually become greater.

Centrality-dependent chemical potentials of light hadrons and quarks  based on transverse momentum spectra and particle yield ratios in Au-Au  collisions