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Probing the gauge bosons $Z'$ and $B'$ from the Littlest Higgs model in the high-energy linear $e^{+}e^{-}$ colliders

The littlest Higgs (LH) model predicts the existence of the new gauge bosons $Z'$ and $B'$. We calculate the contributions of these new particles to the processes $e^{+}e^{-}\to\bar{f}f$ with $f=τ, μ, b,$ or $c$ and study the possibility of detecting these new particles via these processes in the future high-energy linear $e^{+}e^{-}$ collider (LC) experiments with $\sqrt{s}=500GeV$ and $£_{int}=340fb^{-1}$. We find that, with reasonable values of the parameter preferred by the electroweak precision data, the possible signals of these new particles might be detected. The $Z'$ mass $M_{Z'}$ can be explored up to $2.8TeV$ via the process $e^{+}e^{-}\to\bar{b}b $ for $0.3\leq c \leq 0.5 $ and the $B'$ mass $M_{B'}$ can be explored up to $1.26TeV$ via the process $e^{+}e^{-}\to\bar{l}l $ for $0.64\leq c' \leq 0.73 $.