Almost Entirely Empirical Estimation for Chemical Potential

Based on statistical thermal approaches, the transverse momentum distribution of the well-identified produced particles, π⁺, π^–, K⁺, K^–, p, and $\overline{p}$, is studied. We aim at introducing a novel almost entirely empirical estimation for the inclusive chemical potential μ. From the partition function of a grand-canonical ensemble, we propose a generic expression for the dependence of μ on the rapidity y. Then, by fitting this expression with the experimental results of the most central p_⊥ and d²N/2πp_⊥dp_⊥dy, at 7.7, 11.5, 19.6, 27, 39, 130, 200 GeV, we introduce a generic expression for the rapidity dependence of for all particle yields, at different energies, μ = a + by². The resulting energy dependence reads $\sqrt{s_{\text{NN}}}$ = c[(μ – a)/b]^d/2. As a validation test, we show that the proposed approach reproduces excellently the rapidity spectra of various particle yields measured, at different energies.