Measuring Forward-Backward Asymmetry of $t\bar t$ and $b\bar b$ at Electron-Positron Colliders

Motivated by the measurement on the asymmetry at TEVATRON and relevant theoretical interpretations, in this work we calculate the forward-backward asymmetry ($A_{FB}$) in processes $e^+e^-\rightarrow t\bar t$ and $b\bar{b}$ up to the next-to-leading order (NLO) in both the Standard Model (SM) and the little Higgs model (LHM) which is one of the models beyond the SM (BSM). We carefully analyze the contributions of the SM and LHM to the $A_{FB}$ for $t\bar t$ and $b\bar b$ and find that to reconcile the theoretical predictions on $A_{FB}$ and the data of LEP I and II, the model parameter $a$ (see the text to find its definition) is constrained in a rather narrow region. The $A_{FB}$ will be more precisely measured at the proposed ILC and Z-factory. By a comparison with data, we can testify the validity degree of LHM and the theoretical results may be useful for designing future experiments.