  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 $q\bar{q}$ pair, travelling
back-to-back. The dilepton spectrum is computed by folding this rate with the
cross-section for the process p+p$\rightarrow q\bar{q}$, 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.
