Finite Temperature Quarkonia Spectral Functions in the Pseudoscalar Channel

Quarkonia, the bound states of heavy quark-antiquark pairs, are important tools for studying the quark-gluon plasma (QGP). In this study, we examine the behavior of in-medium quarkonium bound states in the QGP by analyzing their spectral functions at two temperatures, $T = 220\,\textrm{MeV}$ and $T = 293\,\textrm{MeV}$. We use physics-motivated information to reconstruct the spectral function from the Euclidean lattice correlator. Near the threshold, the spectral function is estimated through a complex potential, determined non-perturbatively from Wilson line correlators. Our results show that the real part of the potential undergoes color screening above $T_{pc}$, while the imaginary part grows rapidly with increasing distance and temperature. For the ultraviolet (UV) part of the spectral function, we use the perturbative vacuum spectral function, as the temperature effects are suppressed in this region. In the absence of a transport peak in the pseudoscalar channel, we find that this combination effectively describes the pseudoscalar correlator on the lattice, calculated using relativistic quark fields. Our results show that pseudoscalar charmonium ($\eta_c$) experiences significant thermal effects, as indicated by the broadening of the $\eta_c(1S)$ state. In contrast, the $\eta_b(1S)$ state remains intact, with a sharp bound state peak.