Heavy quarkonium moving in hot and dense deconfined nuclear matter

We study the behavior of the complex potential between a heavy quark and its antiquark, which are in relative motion with respect to a hot and dense medium. The heavy quark-antiquark complex potential is obtained by correcting both the Coulombic and the linear terms in the Cornell potential through a dielectric function estimated within the real-time formalism using the hard thermal loop approximation. We show the variation of both the real and the imaginary parts of the potential for different values of velocities when the bound state ($Q\overline{Q}$ pair) is aligned in the direction parallel as well as perpendicular to the relative velocity of the $Q\overline{Q}$ pair with the thermal medium. With an increase of the relative velocity the screening of the real part of the potential becomes weaker at short distances and stronger at large distances for the parallel case. However, for the perpendicular case the potential decreases with an increase of the velocity at all distances, which results in the larger screening of the potential. In addition, the inclusion of the string term makes the screening of the potential weaker as compared to the Coulombic term alone for both cases. Therefore, by combining all these effects we expect a stronger binding of a $Q\overline{Q}$ pair in a moving medium in the presence of the string term as compared to the Coulombic term alone. The imaginary part decreases (in magnitude) with an increase of the relative velocity, leading to a decrease of the width of the quarkonium state at higher velocities. The inclusion of the string term increases the magnitude of the imaginary part, which results in an increase of the width of the quarkonium states. All of these effects lead to the modification in the dissolution of quarkonium states.

Figure 1

Variation of the real part of the potential with the separation distance $r$ between $Q$ and $\overline{Q}$ for various values of velocity at $T=250\mathrm{MeV}$, when the dipole axis is along (left) and perpendicular to (right) the direction of the velocity of the thermal medium.

Figure 2

Variation of the real part of the potential with the separation distance $r$ between $Q$ and $\overline{Q}$ for various values of temperature at $v=0$ (dotted line) and $v=0.9$ (solid line), when the dipole axis is along (left) and perpendicular to (right) the direction of the velocity of the thermal medium, along with the $T=0$ (solid black line) potential.

Figure 3

Variation of the real part of the potential with the separation distance $r$ between $Q$ and $\overline{Q}$ for various values of chemical potential at $v=0$ (dotted line) and $v=0.9$ (solid line), when the dipole axis is along (left) and perpendicular to (right) the direction of the velocity of the thermal medium.

Figure 4

Real part of the potential for various values of velocity at $T=200\mathrm{MeV}$ (left) and $T=400\mathrm{MeV}$ (right) with the angle ${\theta }_{vr}$ between the dipole orientation and the velocity direction.

Figure 5

Variation of the imaginary part of the potential with the separation distance $r$ between $Q$ and $\overline{Q}$ for various values of velocity at $T=250\mathrm{MeV}$ when the dipole axis is along (left) and perpendicular to (right) the velocity direction.

Figure 6

Variation of the imaginary part of the potential with the separation distance $r$ between $Q$ and $\overline{Q}$ for various values of temperature when the dipole axis is along (left) and perpendicular to (right) the velocity direction.

Figure 7

Variation of the decay width with temperature $T$ for $J/\psi$ and $\mathrm{\Upsilon }$ for $v=0$ (left) and $v=0.9$ (right).

Figure 8

Variation of the decay width for $J/\psi (1S)$ (left) and $\mathrm{\Upsilon }(1S)$ (right) states with velocity $\mathbf{v}$ for different values of temperature $T$.

Figure 9

Variation of the scaled decay width [$\mathrm{\Gamma }(v)/\mathrm{\Gamma }(0)$] for $J/\psi (1S)$ (left) and $\mathrm{\Upsilon }(1S)$ (right) states with velocity $\mathbf{v}$ for different values of temperature $T$.

Figure 10

Variation of the scaled decay width [$\mathrm{\Gamma }(v)/\mathrm{\Gamma }(0)$] for $J/\psi (1S)$ (left) and $\mathrm{\Upsilon }(1S)$ (right) states with velocity $\mathbf{v}$ for different values of chemical potential $\mu$.