  The NA60 experiment has studied low-mass muon pairs production in
proton-nucleus collisions at 400 GeV/$c$ at the CERN SPS. The mass spectrum is
well described by the superposition of the two-body and Dalitz decays of the
light neutral mesons $\eta$, $\rho$, $\omega$, $\eta'$ and $\phi$. The large
collected statistics allows to isolate the contributions due to the Dalitz
decays of the $\eta$ and $\omega$ mesons, from which the electromagnetic
transition form factors of the two mesons have been extracted. The found values
agree with the previous available measurements, improving their uncertainty
thanks to the higher statistics. The results thus confirm the discrepancy with
the prediction of the Vector Meson Dominance model in the case of the
electromagnetic form factor of the $\omega$ meson.
