  Ultrarelativistic heavy ion collisions are expected to generate a huge
electromagnetic field, $eB \approx 10^{18}\, Gauss$, that induces a splitting
of the directed flow, $v_1=\left\langle p_x/p_T \right\rangle $, of charged
particles and anti-particles. Such a splitting for charmed meson manifests even
for neutral particle/anti-particles pairs ($D^0, \overline{D}^0$), hence being
also a unique probe of the formation of the quark-gluon plasma phase. For the
first time here we show that electromagnetic field may generate a $v_1(D^0) -
v_1( \overline{D}^0)$ as huge as the one recently observed at LHC against early
expectations.
  Within this new research topic we point out a novel measurement: $v_1$ of
leptons from $Z^0$ decay and its correlation to that of $D$ and $B$ mesons. The
correlation for $\Delta v_1$ of $l^{+} - l^{-}$, $D^0-\overline{D}^0$ and
$B^0-\overline{B}^0$ would provide a strong probe of the electromagnetic origin
of the splitting and hence of the formation of a quark-gluon plasma phase with
heavy quarks as degrees of freedom. The case of the $v_1({l^{\pm}})$ presents
features due to the peculiar form of the $p_T$ spectrum never appreciated
before in the study of heavy ion collisions. We specifically predict a sudden
change of the $\Delta v_1(p_T)$ of leptons at $p_T=45$ GeV$/c$, that can be
traced back to a universal relation of $\Delta v_1$ with the slope of the $p_T$
particle distribution and the integrated effect of the Lorentz force.
