Measurement of the $eta$ and $omega$ Dalitz decays transition form factors in p-A collisions at 400 GeV/$c$ with the NA60 apparatus

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.