Charmonia spectral functions at finite temperature are studied using QCD sum rules in combination with the maximum entropy method. This approach enables us to directly obtain the spectral function from the sum rules, without having to introduce any specific assumption about its functional form. As a result, it is found that while J/ψ and η(c) manifest themselves as significant peaks in the spectral function below the deconfinement temperature T(c), they quickly dissolve into the continuum and almost completely disappear at temperatures between 1.0T(c) and 1.1T(c).
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