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Effects of strong magnetic field on the formation of wakes in thermal QCD

We have investigated how the wakes in the induced charge density and in the potential due to the passage of highly energetic partons through a thermal QCD medium get affected by the presence of strong magnetic field. For that purpose, we wish to analyze first the dielectric responses of the medium both in presence and absence of strong magnetic field. We found that for slow moving partons, the real part of dielectric function is not affected by the magnetic field whereas for fast moving partons, for small $|\textbf{k}|$, it becomes very large and approaches towards its counterpart at $B=0$, for large $|\textbf{k}|$. On the other hand the imaginary part is decreased for both slow and fast moving partons, due to the fact that the imaginary contribution due to quark-loop vanishes. With these ingredients, we found that the oscillation in the (scaled) induced charge density, due to the very fast partons becomes less pronounced in the presence of strong magnetic field whereas for smaller parton velocity, no significant change is observed. For the (scaled) wake potential along the motion of fast moving partons (which is of Lennard-Jones (LJ) type), the depth of negative minimum in the backward region gets reduced drastically, resulting in the reduction of the amplitude of oscillation. On the other hand in the forward region, it remains as the screened Coulomb one, except the screening now becomes much stronger for higher parton velocity. Similarly for the wake potential transverse to the motion of partons in both forward and backward regions, the depth of LJ potential for fast moving partons gets decreased severely, but still retains the forward-backward symmetry. However, for lower parton velocity, the magnetic field does not affect it significantly.