Fire streaks, electromagnetic effects, directed flow and lifetime of the plasma at SPS energies

TL;DR

This paper models electromagnetic effects on pion distributions in peripheral Pb+Pb collisions at CERN SPS energies, using a fire-streak approach to match experimental data and estimate the lifetime of the produced plasma.

Contribution

It introduces a fire-streak model incorporating realistic initial conditions and isospin effects to accurately describe electromagnetic influences on pion ratios at SPS energies.

Findings

Good agreement with NA49 data on $ ext{π}^+/ ext{π}^-$ ratios.

Short pion creation times ($0.5-2$ fm/c) are favored by data.

The model accounts for spectator expansion and flow effects.

Abstract

We present our calculation of electromagnetic effects, induced by the spectator charge on Feynman-$x_F$ distributions of charged pions in peripheral $Pb+Pb$ collisions at CERN SPS energies, including realistic initial space-time-momentum conditions for pion emission. The calculation is performed in the framework of a specific implementation of the fire-streak model, adopted to the production of both $\pi^-$ and $\pi^+$ mesons. Isospin effects are included to take into account the asymmetry in production of $\pi^+$ and $\pi^-$ at high rapidity. A comparison to a simplified model from the literature is made. We obtain a good description of the NA49 data on the $x_F$- and $p_T$-dependence of the ratio of cross sections $\pi^+/\pi^-$. The experimental data favors short times ($0.5<\tau<2$~fm/$c$) for fast pion creation in the local fire-streak rest frame. The possibility of the expansion of the spectators is considered in our calculation, and its influence on the electromagnetic effect observed for the $\pi^+/\pi^-$ ratio is discussed. The influence of directed and elliptic flow, and vorticity on the observed effect is also estimated. We conclude that the fire-streak model, which properly describes the centrality dependence of $\pi^-$ rapidity spectra at CERN SPS energies, also provides realistic initial conditions for pion production. Consequently, it provides a quantitative description of the electromagnetic effect on the $\pi^+/\pi^-$ ratio as a function of $x_F$.