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

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 $x_F$.

Comments: 6 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1910.04544