  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\bar{Q}$ pair) is aligned in the direction parallel as well as perpendicular
to the relative velocity of the $ Q\bar{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\bar{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.
