The first measurements of the forward-backward asymmetry of the dimuon pair ($A_{\mathrm{FB}}$), the triple-product asymmetry ($A_{2\varphi }$), and the charge-parity-conjugation asymmetry ($A_{CP}$), in $D^0\to {\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-}$ and $D^0\to K^{+}{K}^{-}{\mu }^{+}{\mu }^{-}$ 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 $5{\mathrm{fb}}^{-1}$. The asymmetries are measured to be $A_{\mathrm{FB}}(D^0\to {\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-})=(3.3\pm 3.7\pm 0.6)\%$, $A_{2\varphi }(D^0\to {\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-})=(-0.6\pm 3.7\pm 0.6)\%$, $A_{CP}(D^0\to {\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-})=(4.9\pm 3.8\pm 0.7)\%$, $A_{\mathrm{FB}}(D^0\to K^{+}{K}^{-}{\mu }^{+}{\mu }^{-})=(0\pm 11\pm 2)\%$, $A_{2\varphi }(D^0\to K^{+}{K}^{-}{\mu }^{+}{\mu }^{-})=(9\pm 11\pm 1)\%$, $A_{CP}(D^0\to K^{+}{K}^{-}{\mu }^{+}{\mu }^{-})=(0\pm 11\pm 2)\%$, 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.

• Received 28 June 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.091801

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