Soft dilepton production in relativistic heavy-ion collisions

The production of electron-positron pairs with invariant masses less than 300 MeV from thermalized hadronic matter in relativistic heavy-ion collisions is calculated using a soft virtual photon approximation. The general theoretical framework is reviewed and extended to include arbitrarily massed and charged reaction partners, which we apply to pions and quarks. This result, exact within the soft photon approximation, is compared with a widely used approximate result which uses an electromagnetic amplitude limited in validity to momentum transfers less than 4${\mathit{m}}_{\mathrm{\pi }\left(\mathit{q}\right)}^2$. This momemtum-restricted method works very well for pions, constituent quarks, and medium quarks, whereas it fails when applied to current quarks. A field-theory calculation is performed for the ππ elastic cross section which gives excellent agreement with data. Quark-antiquark annihilation diagrams in the Born approximation are estimated and compared with ${\mathrm{\pi }}^0$ and η Dalitz decay contributions to the ${\mathit{e}}^{+}$ ${\mathit{e}}^{\mathrm{-}}$ invariant-mass spectra. A comparison is made between the rate of production of zero total momentum soft dileptons obtained using resummation techniques in QCD perturbation theory and that which we calculate using this soft photon approximation. Then a Bjorken picture for the evolution is adopted allowing an integration over the history of the colliding nuclei. Using initial conditions likely to be found at the BNL Relativistic Heavy Ion Collider or CERN Large Hadron Collider we conclude even if Dalitz decays can be identified and subtracted from the experimental data it will be difficult to distinguish quark from pion degrees of freedom in the low-mass ${\mathit{e}}^{+}$ ${\mathit{e}}^{\mathrm{-}}$ spectra.