Nonperturbative effect on the melting of Quarkonium states Binoy Krishna Patra, Lata Thakur and Uttam Kakade Department of Physics, Indian Institute of Technology Roorkee, India We have studied the quasi-free dissociation of quarkonia through a complex potential by correcting both the perturbative and nonperturbative terms of the Q ¯ Q potential at T=0 through the dielectric function in real-time formalism. The remnants of the non- perturbative confining force makes the real-part of the potential more stronger and the (magnitude) imaginary-part too becomes larger and thus contribute more to the thermal width. Thereafter we explore how does the presence of a not necessarily isotropic QCD medium modify both the real and imaginary part of potential, by calculating the leading anisotropic corrections to the propagators. We found that the presence of the anisotropy makes the real-part of the potential stronger but weakens the imaginary- part slightly, overall the anisotropy enhances the dissociation points higher, compared to isotropic medium. Potential in hot QCD medium (m Q >> Λ QCD , T << m Q ) The central theme of our work is how the theoretical predictions based on high temperature methods, such as HTL perturbation theory might be modified by the remnants of the non-perturbative confining force, just above the crossover or transition tempera- ture [1]? The medium-modification to the Q ¯ Q potential at T=0 can be obtained by correcting its both short and long-distance part with a dielectric function, ǫ(p), through its Fourier transform, V (p) [2, 3]: V (r, T ) =  d 3 p (2π) 3/2 (e ip·r − 1) V (p) ǫ(p) ,V (p)= −  (2/π) α p 2 − 4σ √ 2πp 4 . The dielectric permittivity: ǫ -1 (p)= − lim ω→0 p 2 D 00 11 (ω,p) will be obtained from the resummed propagators in HTl perturbation theory. HTL Self-energies and Propagators  Retarded self-energy [4] Π ij (P )= −g 2  d 3 k v i ∂f (k) ∂k l  δ jl + v j p l P ·V +iǫ  which can be evaluated by the anisotropic phase-space distribution (ξ ≪ 1) [5]: f aniso (k)= f iso   k 2 + ξ (k.n) 2  .  The retarded/advanced and symmetric self-energies contribute to the real-part and the imaginary-part of the self-energies, re- spectively. In Keldysh representation, the propagators and self-energies are: D 0 R = D 0 11 − D 0 12 , D 0 A = D 0 11 − D 0 21 ,D 0 F = D 0 11 + D 0 22 Π R =Π 11 +Π 12 , Π A =Π 11 +Π 21 , Π F =Π 11 +Π 22 . 1