Energy correlation of bottom quarks from decays of top quarks in electron$-$positron annihilation

Abstract

Joint energy distribution of the bottom quark and antiquark from decays of the top quark and antiquark produced in the reaction $e^+ e^- \to t \bar{t}$ is studied. Main emphasis is put on $CP$-violation effects in the interaction of the photon and $Z$ boson with the top quarks. Energy asymmetries of $b$ and $\bar{b}$ quarks, which give access to the $CP$-violating terms, are considered. To estimate the magnitude of these asymmetries, the $CP$-violating $\gamma t t $ and $Z t t$ couplings are calculated in one-loop model with exchange of the Higgs boson with the mass of $125$ GeV. Interaction of this boson with the top quarks is assumed to include scalar and pseudoscalar couplings. Values of these couplings are constrained from the recent CMS analysis. Energy dependence of the asymmetries of $b$ and $\bar{b}$ quarks is calculated up to $\sqrt{s}=1.2$ TeV and some interesting features of their behavior are observed. These observables can be of interest for future studies at electron$-$positron colliders CLIC and ILC.