  We study the invariant-mass distributions of dileptons produced in
ultrarelativistic heavy-ion collisions at very low pair transverse momenta,
$P_T\leq 0.15$ GeV. Specifically, we investigate the interplay of thermal
radiation with initial photon annihilation processes, $\gamma \gamma \to l^+
l^-$, triggered by the coherent electromagnetic fields of the incoming nuclei.
For the thermal radiation, we employ the emission from the QGP and hadronic
phases with in-medium vector spectral functions which describes the inclusive
excess radiation observed over a wide range of collision energies. For the
coherent photon fusion processes, whose spectrum is much softer than for
thermal radiation, we employ initial fluxes from the Fourier transform of
charge distributions of the colliding nuclei in the equivalent-photon
approximation. We first verify that the combination of photon fusion, thermal
radiation and final-state hadron decays gives a fair description of the
low-$P_T$ dilepton mass spectra as recently measured by the STAR collaboration
in $\sqrt{s_{NN}}$=200 GeV Au+Au collisions for different centrality classes,
including experimental acceptance cuts. The coherent contribution dominates in
peripheral collisions, while thermal radiation shows a markedly stronger
increase with centrality. We perform similar calculations at lower collision
energies ($\sqrt{s_{NN}}$=17.3 GeV) and compare to the acceptance-corrected
dimuon excess spectra measured by the NA60 experiment at the CERN SPS; here,
the contribution from photoproduction is subleading. We also provide
predictions for the ALICE experiment at the LHC; the pertinent excitation
function from SPS to LHC energies reveals a nontrivial interplay of
photoproduction and thermal radiation.
