Charmonium transition in electromagnetic and rotational fields

Abstract

We study heavy quarkonia in the frame of potential model in electromagnetic and rotational fields. The rotation itself cannot induce charmonium dissociation, but its coupling to the magnetic field can largely enhance or reduce the Lorentz potential and therefore affects the charmonium properties strongly. The charmonium wave function is significantly broadened in the direction of the Lorentz force, which leads to the charmonium transition from strongly interacting bound state to magnetic and rotational interaction controlled bound state. The condition for the transition seems possible to be realized in high energy nuclear collisions.

Theory progress at Strange Quark Matter 2021

“…These lattice results were also used as input in a deep learning analysis to extract the heavy quark potential in the quark gluon plasma [31], and the imaginary part turned out to be quite different from that of the hard thermal loop potential used in [29]. As for heavy quarks, also for charmonium states effects of strong electromagnetic fields, as well as vorticity fields, were considered and studied via the two-body Schroedinger equation [32]. Both mass and shape of the charmonium were significantly affected by the fields.…”

Charmonium in electromagnetic and vortical fields

“…mass and shape, of open/hidden heavy flavor states will be changed in electromagnetic fields [20][21][22][23]. Following these studies, we investigate charmonia in both electromagnetic and vortical fields [24].…”

“…We can clearly see that there are no coupling terms between electromagnetic and vortical fields, which means that the rotation does not induce any electromagnetic effect. It is necessary to emphasize that the coupling term emerges if the electromagnetic fields are defined directly in the rotating frame [24]. We construct a two-body Schrödinger equation to describe a charmonium system in a rotational medium and under the impact of electromagnetic fields,…”

“…3, we first transform the single particle coordinates and momenta to the center-of-mass and relative ones, R = (x a +x b )/2, r = x a −x b , P = p a +p b , and p = (p a −p b )/2. Different from the case with only electromagnetic fields where the total wave function can always be separated into a center-of-mass and a relative part with the help of the conserved pseudo-momentum [21,24], it is no longer possible to find a conserved quantity to separated the two parts in a rotational field. However, considering the fact that the strength of the magnetic field in relativistic heavy-ion collisions can reach eB ≈ 70m 2 π , which is much larger than the vortical field m Q ω ≈ m 2 π for charm quarks, we can choose the electromagnetic related parts as the main part and take the rotational related terms as perturbations.…”

“…That's the nature of particles in a vortical field and we can use the average value R in our calculation. Details about the numerical calculation and results are shown in [24].…”