Directed Flow of Charm Quarks as a Witness of the Initial Strong Magnetic Field in Ultra-Relativistic Heavy Ion Collisions

Ultra-relativistic Heavy-Ion Collision (HIC) generates very strong initial magnetic field ($\vec B$) inducing a vorticity in the reaction plane. The high $\vec{B}$ influences the evolution dynamics that is opposed by the large Faraday current due to electric field generated by the time varying $\vec{B}$. We show that the resultant effects entail a significantly large directed flow ($v_1$) of charm quarks (CQs) compared to light quarks due to a combination of several favorable conditions for CQs, mainly: (i) unlike light quarks formation time scale of CQs, $\tau_f \simeq \, 0.1 \rm fm/c$ is comparable to the time scale when $\vec B$ attains its maximum value and (ii) the kinetic relaxation time of CQs is similar to the QGP lifetime, this helps the CQ to retain the initial kick picked up from the electromagnetic field in the transverse direction. The effect is also odd under charge exchange allowing to distinguish it from the vorticity of the bulk matter due to the initial angular momentum conservation; conjointly thanks to its mass, $M_c >>\Lambda_{QCD}$, there should be no mixing with the chiral magnetic dynamics. Hence CQs provide very crucial and independent information on the strength of the magnetic field produced in HIC.