# Almost-Entirely Empirical Estimation for Chemical Potential

## TL;DR

This paper develops an empirical method to estimate the chemical potential's dependence on rapidity in high-energy particle collisions, fitting experimental data across various energies and particle types to validate the approach.

## Contribution

It introduces a new empirical expression for the rapidity dependence of chemical potential based on statistical thermal models, validated with experimental data.

## Key findings

- Accurately fits rapidity spectra at multiple energies
- Proposes a generic energy dependence formula for chemical potential
- Reproduces experimental data with high precision

## 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 $d^2 N/2 \pi p_{\bot} dp_{\bot} dy$, 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.