The signature of charge dependent directed flow observables by electromagnetic fields in heavy ion collisions

TL;DR

This paper explores how electromagnetic fields influence charge-dependent directed flow in heavy ion collisions, providing a formula linking magnetic field features to observable flow splittings, and confirming it through numerical simulations.

Contribution

It introduces a new analytical formula relating magnetic field characteristics to charge-dependent flow splitting, validated by numerical simulations, enhancing understanding of electromagnetic effects in collisions.

Findings

Charge-dependent v1 splitting correlates with magnetic field at formation and freeze-out.

Derived formula for the slope of v1 splitting as a function of p_T and magnetic field parameters.

Numerical simulations confirm the analytical formula's validity.

Abstract

We discuss the generation of the directed flow $v_1(p_T,y_z)$ induced by the electromagnetic field as a function of $p_T$ and $y_z$. Despite the complex dynamics of charged particles due to strong interactions generating several anisotropies in the azimuthal angle, it is possible at $p_T > m$ to directly correlate the splitting in $v_1$ of heavy quarks with different charges to some main features of the magnetic field, and in particular its values at formation and freeze-out time. We further found that the slope of the splitting $d\Delta v_1/dy_z|_{y_z=0}$ of positively and negatively charged particles at high $p_T$ can be formulated as $d\Delta v_1/dy_z|_{y_z=0}=-\alpha \frac{\partial \ln f}{\partial p_T}+\frac{2\alpha-\beta}{p_T}$, where the constants $\alpha$ and $\beta$ are constrained by the $y$ component of magnetic fields and the sign of $\alpha$ is simply determined by the difference $\Delta[tB_y(t)]$ in the center of colliding systems at the formation time of particles and at the time when particles leave the effective range of electromagnetic fields or freeze out. The formula is derived from general considerations and is confirmed by several related numerical simulations; it supplies a useful guide to quantify the effect of different magnetic field configurations and provides an evidence of why the measurement of $\Delta v_1$ of charm, bottom and leptons from $Z^0$ decay and their correlations are a powerful probe of the initial e.m. fields in ultra-relativistic collisions.