Measurements of charge and $CP$ asymmetries in $b$-hadron decays using top-quark events collected by the ATLAS detector in $pp$ collisions at $\sqrt{s}=8$ TeV

Same- and opposite-sign charge asymmetries are measured in lepton+jets $t\bar{t}$ events in which a $b$-hadron decays semileptonically to a soft muon, using data corresponding to an integrated luminosity of 20.3 fb$^{-1}$ from proton-proton collisions at a centre-of-mass energy of $\sqrt{s}=8$ TeV collected with the ATLAS detector at the Large Hadron Collider at CERN. The charge asymmetries are based on the charge of the lepton from the top-quark decay and the charge of the soft muon from the semileptonic decay of a $b$-hadron and are measured in a fiducial region corresponding to the experimental acceptance. Four $CP$ asymmetries (one mixing and three direct) are measured and are found to be compatible with zero and consistent with the Standard Model.