Precision calculations for the $T$-odd quark pair production at the CLIC   $e^+e^-$ linear collider
  We perform the precision calculations for the \eeqq ($q_-\bar{q}_-=u_-\bar u_-, ~c_-\bar c_-,~ d_-\bar d_-,~s_-\bar s_-$) processes up to the QCD next-to-leading order (NLO) including full weak decays for the final $T$-odd mirror quarks in the littlest Higgs model with $T$-parity (LHT) at the Compact Linear Collider (CLIC). We show the dependence of the leading order (LO) and NLO QCD corrected cross sections on the colliding energy $\sqrt{s}$, and provide the LO and QCD NLO kinematic distributions of final particles. The results show that the LO cross section can be enhanced by the NLO QCD correction and the $K$-factor increases obviously when the threshold of the on-shell $q_-\bar{q}_-$-pair production approaches the colliding energy $\sqrt{s}$. The $K$-factor value varies in the range of $1.04 \sim 1.41$ in our chosen parameter space. We find that a simple approximation of multiplying the LO kinematic distribution with the integrated $K$-factor is not appropriate for precision study of the \eeqq ($q_-\bar{q}_-=u_-\bar u_-,~c_-\bar c_-,~d_-\bar d_-,~s_-\bar s_-$) processes, since the NLO QCD corrections are phase space dependent. It is necessary to calculate the differential cross sections including full NLO QCD corrections to get reliable results. 
A. B. Mahfoudh, Guo Lei, Liu Wen, Ma Wen-Gan, Zhang Ren-You and Zhang   Wen-Juan
hep-ph