Almost-Entirely Empirical Estimation for Chemical Potential

Abstract

Based on statistical thermal approaches, the transverse momentum distribution of the well-identified produced particles, ${\pi }^{+}$, ${\pi }^{-}$, $K^{+}$, $K^{-}$, $p$, $\bar{p}$, is studied. From the partition function of grand-canonical ensemble, we propose a generic expression for the dependence of the full chemical potential $\mu$ on rapidity $y$. Then, by fitting this expression with the experimental results of most central $p_{\perp }$ and $d^{2}N/2\pi p_{\perp }d{p}_{\perp }dy$, at $7.7$, $11.5$, $19.6$, $27$, $39$, $130$, $200$GeV, we introduce a generic expression for the rapidity dependence of $\mu$, at different energies and particle types, $\mu =a+b{y}^2$. The resulting energy dependence reads $\sqrt{s_{\mathtt{NN}}}=c[(\mu -a)/b{]}^{d/2}$. As a validation check, the proposed approach reproduces, excellently, the rapidity spectra measured at different energies.

Comments: 11 pages, 5 figures, VI tables, submitted to JETP