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The first full angular analysis and an updated measurement of the decay-rate$CP$ asymmetry of the $D^0 \to \pi^+\pi^-\mu^+\mu^-$ and $D^0 \toK^+K^-\mu^+\mu^-$ decays are reported. The analysis uses proton-protoncollision data collected with the LHCb detector at centre-of-mass energies of7, 8 and 13 TeV. The data set corresponds to an integrated luminosity of 9fb$^{-1}$. The full set of $CP$-averaged angular observables and their $CP$asymmetries are measured as a function of the dimuon invariant mass. Theresults are consistent with expectations from the standard model and with $CP$symmetry.

Angular analysis of $D^0 \to \pi^+\pi^-\mu^+\mu^-$ and $D^0 \to K^+K^-\mu^+\mu^-$ decays and search for $CP$ violation