Thermal Static Potential and Pseudo-Scalar Quarkonium Spectral Functions from 2+1 Flavor Lattice QCD

Abstract

Quarkonia, which are bound states of a heavy quark and antiquark, play a key role in probing the quark-gluon plasma (QGP). The dynamics of quarkonia in the QGP are encoded in their finite-temperature spectral functions. In this work, we estimate the quarkonium spectral functions in the pseudo-scalar channel using 2+1 flavor lattice QCD with a pion mass of $320\,\text{MeV}$, at temperatures of $220\,\text{MeV}\,(1.2\,T_{pc}),\,251\,\text{MeV}\,(1.4\,T_{pc})\,\text{and}\,293\,\text{MeV}\,(1.6\,T_{pc})$. Reconstructing the spectral function from the Euclidean lattice correlator is a well-known ill-posed problem, requiring additional physics-motivated input. We address this by smoothly matching contributions from different frequency regions of the spectral function, using appropriate physics valid for each region. The spectral function around $\omega \sim 2\,M_q$ is obtained using a non-perturbative complex potential, while for $\omega \gg 2\,M_q$ it is modeled using results from vacuum perturbation theory. Since the pseudoscalar channel does not receive a transport contribution near $\omega \sim 0$, we find that the combination of these two regions already provides a good description of the relativistic lattice pseudoscalar correlator. We observe a substantial thermal width in the $\eta_c(1S)$ state, indicating that pseudoscalar charmonium ($\eta_c$) is nearing dissolution at the studied temperatures. In comparison, the $\eta_b$ ground state exhibits little change and remains well-defined.