The dilepton transverse momentum spectra and invariant mass spectra for low $p_T <0.15$~GeV/c in Au+Au collisions of different centralities at $sqrt{s_{NN}}$ = 200 GeV are studied within the parton-hadron-string dynamics (PHSD) transport approach. The PHSD describes the whole evolution of the system on a microscopic basis, incorporates hadronic and partonic degrees-of-freedom, the dynamical hadronization of partons and hadronic rescattering. For dilepton production in p+p, p+A and A+A reactions the PHSD incorporates the leading hadronic and partonic channels (also for heavy flavors) and includes in-medium effects such as a broadening of the vector meson spectral functions in hadronic matter and a modification of initial heavy-flavor correlations by interactions with the partonic and hadronic medium. The transport calculations reproduce well the momentum integrated invariant mass spectra from the STAR Collaboration for minimum bias Au+Au collisions at $sqrt{s_{NN}}$ = 200 GeV, while the description of the STAR data - when gating on low $p_T < 0.15$ GeV/c - is getting worse when going from central to peripheral collisions. An analysis of the transverse momentum spectra shows that the data for peripheral (60-80%) collisions are well reproduced for $p_T>0.2$ GeV/c while the strong peak at low $p_T < 0.15$ GeV/c, that shows up in the experimental data for the mass bins ($0.4 < M < 0.7$ GeV and $1.2 < M < 2.6$ GeV), is fully missed by the PHSD and cannot be explained by the standard in-medium effects. This provides a new puzzle for microscopic descriptions of low $p_T$ dilepton data from the STAR Collaboration.
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