https://doi.org/10.1140/epjp/s13360-021-01694-4
Regular Article
The signature of charge dependent directed flow observables by electromagnetic fields in heavy ion collisions
1
Laboratori Nazionali del Sud, INFN-LNS, Via S. Sofia 62, I-95123, Catania, Italy
2
Department of Physics and Astronomy, University of Catania, Via S. Sofia 64, 1-95125, Catania, Italy
Received:
18
March
2021
Accepted:
22
June
2021
Published online:
6
July
2021
We discuss the generation of the directed flow 
induced by the electromagnetic field as a function of 
and 
. Despite the complex dynamics of charged particles due to strong interactions generating several anisotropies in the azimuthal angle, it is possible at 
to directly correlate the splitting in 
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 
of positively and negatively charged particles at high can be formulated as 
, where f is the spectra of the charged particles and the constants 
and 
(order of MeV) are constrained by the y component of magnetic fields and the sign of is simply determined by the difference ![$$\Delta [tB_y(t)]$$](/articles/epjplus/abs/2021/07/13360_2021_Article_1694/13360_2021_Article_1694_tex_eq13.png)
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 
of charm, bottom and leptons from 
decay and their correlations are a powerful probe of the initial e.m. fields in ultra-relativistic collisions.
© The Author(s) 2021
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