Precision study of the $\hat{I}\cdot \to \hat{I}{¼}^{+}\hat{I}{¼}^{-}{\hat{I}}^3$ and $\ddot{I}‰\to \hat{I}{¼}^{+}\hat{I}{¼}^{-}\ddot{I}{€}^0$ electromagnetic transition form-factors and of the $\ddot{I}\to \hat{I}{¼}^{+}\hat{I}{¼}^{-}$ line shape in NA60

Abstract

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 $\hat{I}\cdot$, $\ddot{I}$, $\ddot{I}‰$, $\hat{I}{\cdot }^{\prime }$ and $\ddot{I}•$, and no evidence of in-medium effects is found. A new high-precision measurement of the electromagnetic transition form factors of the $\hat{I}\cdot$ and $\ddot{I}‰$ was performed, profiting from a 10~times larger data sample than the peripheral In-In sample previously collected by NA60. Using the pole-parameterisation $|F(M){|}^2=(1-M^2/\hat{\mathrm{I}}{›}^2{)}^{-2}$ we find $\hat{\mathrm{I}}{›}_{\hat{I}}{\cdot }^{-2}=1.934\pm 0.067$~(stat.) $\pm 0.050$~(syst.)~(GeV/$c^2$)${}^{-2}$ and $\hat{\mathrm{I}}{›}_{\ddot{I}}{‰}^{-2}=2.223\pm 0.026$~(stat.) $\pm 0.037$~(syst.)~(GeV/$c^2$)${}^{-2}$. An improved value of the branching ratio of the Dalitz decay $\ddot{I}‰\to \hat{I}{¼}^{+}\hat{I}{¼}^{-}\ddot{I}{€}^0$ is also obtained, with $BR(\ddot{I}‰\to \hat{I}{¼}^{+}\hat{I}{¼}^{-}\ddot{I}{€}^0)=[1.41\pm 0.09(stat.)$ $\pm 0.15(syst.)]\times 10^{-4}$. Further results refer to the $\ddot{I}$ line shape and a new limit on $\ddot{I}/\ddot{I}‰$ interference in hadron interactions.