An almost-entirely precise empirical estimation for various chemical potentials

Abstract

The transverse momentum spectra of the well-identified produced particles, π+, π−, K+, K−, p, p̄, Ks0, Λ, Λ̄, Ξ−, and Ξ+ are analyzed in a statistical approach. From the partition function of grand-canonical ensemble, we propose a generic expression for the dependence of the generic chemical potential μ on the rapidity y. Then, by fitting this expression to the experimental results on the most central p⊥ and d2N/2πp⊥dp⊥dy, at energies ranging from 7.7 to 200GeV, we have introduced a generic expression for the rapidity dependence of μ, at different energies, namely μ=a+by2, where a and b are constants. We find that the resulting energy dependence sNN=c[(μ−a)/b]d/2 agrees well with the statistical thermal models, where c and d are constants. We also present precise estimations of various types of chemical potentials, μB, μS, and μQ, the baryon, the strangeness, and the charge chemical potential, respectively.