# Charmonium ground and excited states at finite temperature from complex Borel sum rules

## TL;DR

This paper uses complex Borel sum rules and maximum entropy methods to analyze charmonium spectral functions at finite temperature, successfully identifying both ground and excited states and their thermal modifications near the critical temperature.

## Contribution

It introduces a novel approach combining complex Borel sum rules with maximum entropy to extract excited charmonia states, surpassing previous QCD sum rule limitations.

## Key findings

- Successfully identified excited and ground charmonium states.
- Observed near-simultaneous melting of all states at critical temperature.
- Provided detailed spectral function modifications at finite temperature.

## Abstract

Charmonium spectral functions in vector and pseudoscalar channels at finite temperature are investigated through the complex Borel sum rules and the maximum entropy method. Our approach enables us to extract the peaks corresponding to the excited charmonia, $\psi^\prime$ and $\eta_c^\prime$, as well as those of the ground states, $J/\psi$ and $\eta_c$, which has never been achieved in usual QCD sum rule analyses. We show the spectral functions in vacuum and their thermal modification around the critical temperature, which leads to the almost simultaneous melting (or peak disappearance) of the ground and excited states.