Heavy quarkonium in vector and scalar channels

We study quarkonium in hot QCD, emphasizing its nature as a short-lived transient with an exponentially decaying wave function. The heavy quark mass allows for a nonrelativistic expansion around the two-quark threshold, and the static potential is then seen to contain a temperature-dependent imaginary part, which leads to an unstable quark-antiquark state. We solve the corresponding Schrödinger equation and estimate the spectral functions in different channels. In particular, through careful evaluation we find a peak also in the scalar channel, although it is strongly suppressed with respect to the vector channel peak. We also plot the dilepton production rate, which shows a peak-like structure even at temperatures so high that the peak in the spectral function has disappeared.