Dielectron production at midrapidity at low transverse momentum in peripheral and semi-peripheral Pb$-$Pb collisions at $\sqrt{s_{\mathrm{N}\mathrm{N}}}=5.02$ TeV

The first measurement of the ${\mathrm{e}}^{+}{\mathrm{e}}^{-}$ pair production at low lepton pair transverse momentum ($p_{\mathrm{T},\mathrm{e}\mathrm{e}}$) and low invariant mass ($m_{\mathrm{e}\mathrm{e}}$) in non-central Pb$-$Pb collisions at $\sqrt{s_{\mathrm{N}\mathrm{N}}}=5.02$ TeV at the LHC is presented. The dielectron production is studied with the ALICE detector at midrapidity ($\mathrm{\mid }{\eta }_{\mathrm{e}}\mathrm{\mid }<0.8$) as a function of invariant mass ($0.4\le m_{\mathrm{e}\mathrm{e}}<2.7$ GeV/$c^2$) in the 50$-$70% and 70$-$90% centrality classes for $p_{\mathrm{T},\mathrm{e}\mathrm{e}}<0.1$ GeV/$c$, and as a function of $p_{\mathrm{T},\mathrm{e}\mathrm{e}}$ in three $m_{\mathrm{e}\mathrm{e}}$ intervals in the most peripheral Pb$-$Pb collisions. Below a $p_{\mathrm{T},\mathrm{e}\mathrm{e}}$ of 0.1 GeV/$c$, a clear excess of ${\mathrm{e}}^{+}{\mathrm{e}}^{-}$ pairs is found compared to the expectations from known hadronic sources and predictions of thermal radiation from the medium. The $m_{\mathrm{e}\mathrm{e}}$ excess spectra are reproduced, within uncertainties, by different predictions of the photon$-$photon production of dielectrons, where the photons originate from the extremely strong electromagnetic fields generated by the highly Lorentz-contracted Pb nuclei. Lowest-order quantum electrodynamic (QED) calculations, as well as a model that takes into account the impact-parameter dependence of the average transverse momentum of the photons, also provide a good description of the $p_{\mathrm{T},\mathrm{e}\mathrm{e}}$ spectra. The measured $\sqrt{\langle p_{\rm T,ee}^{2} \rangle}$oftheexcess$p_{\rm T,ee}$ spectrum in peripheral Pb$-$Pb collisions is found to be comparable to the values observed previously at RHIC in a similar phase-space region.