Measurement of indirect $CP$ asymmetries in $D^0rightarrow K^-K^+$ and $D^0rightarrow pi^-pi^+$ decays using semileptonic $B$ decays

Time-dependent $CP$ asymmetries in the decay rates of the singly Cabibbo-suppressed decays $D^0rightarrow K^-K^+$ and $D^0rightarrow pi^-pi^+$ are measured in $pp$ collision data corresponding to an integrated luminosity of 3.0 fb$^{-1}$ collected by the LHCb experiment. The $D^0$ mesons are produced in semileptonic $b$-hadron decays, where the charge of the accompanying muon is used to determine the initial state as $D^0$ or $bar{D}^0$. The asymmetries in effective lifetimes between $D^0$ and $bar{D}^0$ decays, which are sensitive to indirect $CP$ violation, are determined to be begin{align*} A_{Gamma}(K^-K^+) = (-0.134 pm 0.077 ; {}^{+0.026}_{-0.034})% , A_{Gamma}(pi^-pi^+) = (-0.092pm 0.145 ; {}^{+0.025}_{-0.033})% , end{align*} where the first uncertainties are statistical and the second systematic. This result is in agreement with previous measurements and with the hypothesis of no indirect $CP$ violation in $D^0$ decays.