Precision study of the $\eta\to\mu^+\mu^-\gamma$ and $\omega\to\mu^+\mu^-\pi^0$ electromagnetic transition form-factors and of the $\rho\to\mu^+\mu^-$ line shape in NA60

The NA60 experiment studied low-mass muon pair production in proton-nucleus (p-A) collisions using a 400~GeV proton beam at the CERN SPS. The low-mass dimuon spectrum is well described by the superposition of the two-body and Dalitz decays of the light neutral mesons $\eta$, $\rho$, $\omega$, $\eta'$ and $\phi$, and no evidence of in-medium effects is found. A new high-precision measurement of the electromagnetic transition form factors of the $\eta$ and $\omega$ was performed, profiting from a 10~times larger data sample than the peripheral In-In sample previously collected by NA60. Using the pole-parameterisation $|F(M)|^2 = (1 -M^2/\mathrm{\Lambda}^2)^{-2}$ we find $\mathrm{\Lambda}_\eta^{-2} = 1.934\ \pm\ 0.067$~(stat.) $\pm\ 0.050$~(syst.)~(GeV/$c^2$)$^{-2}$ and $\mathrm{\Lambda}_\omega^{-2} = 2.223\ \pm\ 0.026$~(stat.) $\pm\ 0.037$~(syst.)~(GeV/$c^2$)$^{-2}$. An improved value of the branching ratio of the Dalitz decay $\omega \to \mu^+\mu^-\pi^0$ is also obtained, with $BR(\omega \to \mu^+\mu^-\pi^0) = [1.41~\pm~0.09~\mathrm{(stat.)}$ $\pm~0.15~\mathrm{(syst.)}] \times 10^{-4}$. Further results refer to the $\rho$ line shape and a new limit on $\rho/\omega$ interference in hadron interactions.