Abstract
Due to their large mass and early production, heavy quarks (quarkonia) can be sensitive probes to investigate the fast-decaying electromagnetic and vortical fields produced in heavy-ion collisions. The non-relativistic Schrödinger-like equation for heavy quarks under strong electromagnetic fields in the rotating frame is deduced and used to construct the two-body equation for the charmonium system. The effective potential between charm and anti-charm quarks becomes anisotropic in electromagnetic and vortical fields, especially along the direction of the Lorentz force. The vorticity will affect this asymmetry and catalyze the transition from a strong interaction dominant bound state to an electromagnetic and vortical interaction controlled anisotropic bound state.
Highlights
Many theoretical studies show that strong electromagnetic fields are generated in noncentral relativistic heavy-ion collisions [1,2,3,4,5]
There is a carried by the system of two colliding nuclei in non-central heavy-ion collisions. Most of this total angular momentum is carried away by the spectators, there is still a sizable fraction that remains in the created quark-gluon plasma (QGP) and induces a nonzero rotational motion [6,7,8]
Heavy quarks and especially quarkonia are the most sensitive and effective probes due to the following reasons: The heavy quark mass is much large than the QCD cutoff, mc, mb ΛQCD, so their production can be well described by perturbative QCD; The heavy quark mass is much larger than the typical temperature of the hot medium, their mass does not change in the hot medium, and their number is conserved during the evolution; Heavy quarks are produced at a very early stage in the collision with a formation time of τc ∼ 1/2mc ≈ 0.06 fm/c for charm quark and τb ≈ 0.02 fm/c for bottom quark, they can feel the strongest electromagnetic and vortical fields
Summary
Many theoretical studies show that strong electromagnetic fields are generated in noncentral relativistic heavy-ion collisions [1,2,3,4,5]. Heavy quarks in electromagnetic and vortical fields can generate directed flow (v1) [14, 15]. The static properties, e.g. mass and shape, of open/hidden heavy flavor states will be changed in electromagnetic fields [20,21,22,23].
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