An almost-entirely precise empirical estimation for various chemical potentials

Abstract

The transverse momentum spectra of the well-identified produced particles, ${\pi }^{+}$, ${\pi }^{-}$, $K^{+}$, $K^{-}$, $p$, $\bar{p}$, $K_s^0$, $\Lambda$, $\bar{\Lambda }$, ${\Xi }^{-}$, and ${\Xi }^{+}$ 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 $\mu$ on the rapidity $y$. Then, by fitting this expression to the experimental results on the most central $p_{\perp }$ and $d^{2}N/2\pi p_{\perp }d{p}_{\perp }dy$, at energies ranging from $7.7$ to $200$GeV, we have introduced a generic expression for the rapidity dependence of $\mu$, at different energies, namely $\mu =a+b{y}^2$, where $a$ and $b$ is constants. We find that the resulting energy dependence $\sqrt{s_{\mathtt{NN}}}=c[(\mu -a)/b{]}^{d/2}$ agrees well with the statistical thermal models. We also present precise estimations of various types of chemical potentials, ${\mu }_B$, ${\mu }_S$, and ${\mu }_Q$, the baryon, the strangeness, and the charge chemical potential, respectively.

Comments: 15 pages, 3 eps figures, 13 tables, submitted to INJP