String percolation threshold for elliptically bounded systems

TL;DR

This paper extends the string percolation model to include eccentricity effects in small systems, revealing how initial geometry influences the percolation threshold, with implications for understanding phase transitions in nuclear collisions.

Contribution

It introduces an eccentricity-dependent extension of the string percolation threshold for small systems, highlighting geometry effects on phase transition conditions.

Findings

Percolation threshold depends on eccentricity in small systems.

Uniform density profiles show consistency with thermodynamic limit.

Eccentricity effects are significant in low-string-number systems.

Abstract

It has been shown that a hot and dense deconfined nuclear matter state produced in ultra-relativistic heavy-ion collisions, can be quantitatively described by the String Percolation phenomenological model. The model address the phase transition in terms of the two-dimensional continuum percolation theory over strings, which are schematic representations of the fundamental interactions among the partons of the colliding nuclei in the initial state. In this work, we present an extension of the critical string density results including the eccentricity dependence on the initial state geometry focus on small string number with different density profile, small deviations from the different profile densities are found. The percolation threshold shows consistency with the thermodynamic limit for the uniform density profile with a large number of strings in the case of circular boundary system. A significant dependence on the eccentricity for a small number of strings compared to high occupancy systems is exhibited, the implications may become relevant in hadron-hadron or hadron-nucleus collision systems.