# Mid-rapidity dependence of hadron production in $p-p$ and $A-A$ collisions

## TL;DR

This paper models the rapidity dependence of pion production in proton-proton and heavy-ion collisions using a self-similarity approach, providing analytical formulas that fit experimental data at small rapidities and revealing universal energy patterns.

## Contribution

It introduces an analytical self-similarity function for rapidity spectra in $pp$ and $AA$ collisions, accurately describing data at small rapidities.

## Key findings

- Analytical form of the self-similarity function $\Pi(y,p_t)$ derived.
- Good agreement with experimental rapidity spectra at $|y| extless 0.3$.
- Universal energy dependence of the spectra demonstrated.

## Abstract

The calculation of inclusive spectra of pions produced in $pp$ and $AA$ collisions as a function of rapidity $y$ is presented within the self-similarity approach. It is shown that at not large rapidities $y$ one can obtain the analytical form of the self-similarity function $\Pi(y,p_t)$ dependent of $y$ and hadron transverse momentum $p_t$. A satisfactory description of data on the rapidity spectra at $|y|\leq$ 0.3 is illustrated within a good agreement. The universal energy dependence of these spectra is also shown.