In a recent work from the ALICE collaboration an excess of relatively soft dilepton pairs was reported in p+p collisions at $13$ TeV. In the report no satisfactory explanation was found via standard bremsstrahlung computations. In this letter, textit{anomalous} dilepton pairs are produced non-perturbatively from the back-reaction of the vacuum to a $qbar{q}$ pair, travelling back-to-back. The dilepton spectrum is computed by folding this rate with the cross-section for the process p+p$rightarrow qbar{q}$, which was computed using the framework of the Color Glass Condensate Effective Field Theory (CGC EFT) in the $k_perp$-factorized limit. The resulting spectra is compatible within uncertainties with the data, and moreover, provides exciting insight into the non-perturbative phenomena that ultra-soft electromagnetic radiation can probe.
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