Measurement of Angular and CP Asymmetries in $D^0\to\pi^+\pi^-\mu^+\mu^-$ and $D^0\to K^+K^-\mu^+\mu^-$ decays

The first measurements of the forward-backward asymmetry of the dimuon pair $(A_{FB})$, the triple-product asymmetry $(A_{2ϕ})$, and the charge-parity-conjugation asymmetry $(A_{CP})$, in $D^0 → π^+ π^- μ^+ μ^-$ and $D^0 → K^+ K^- μ^+ μ^-$ decays are reported. They are performed using data from proton-proton collisions collected with the LHCb experiment from 2011 to 2016, corresponding to a total integrated luminosity of 5 fb$^{-1}$. The asymmetries are measured to be $A_{FB}(D^0 → π^+ π^- μ^+ μ^-)=(3.3±3.7±0.6)\%$, $A_{2ϕ}(D^0 → π^+ π^- μ^+ μ^- )=(-0.6±3.7±0.6)\%$, $A_{CP}(D^0 → π^+ π^- μ^+ μ^-)=(4.9±3.8±0.7)\%, A_{FB}(D^0 → K^+ K^- μ^+ μ^- )=(0±11±2)\%, A_{2ϕ}(D^0 → K^+ K^- μ^+ μ^-)=(9±11±1)\%, A_{CP}(D^0 → K^+ K^- μ^+ μ^- )=(0±11±2)\%$, where the first uncertainty is statistical and the second systematic. The asymmetries are also measured as a function of the dimuon invariant mass. The results are consistent with the standard model predictions