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In the framework of the littlest Higgs model with $T$ parity, we presentcomplete calculations for the $A_H q_-$ $(q_-=u_-, \bar{u}_-,d_-,\bar{d}_-,c_-, \bar{c}_-,s_-, \bar{s}_-)$ associated production up to the QCDnext-to-leading order (NLO) at the CERN Large Hadron Collider with subsequentpure weak decay of $T$-odd mirror quark. We apply the PROSPINO scheme to avoidthe double counting problem and to keep the convergence of the perturbative QCDdescription. The theoretical correlations between the integrated cross sectionand the factorization and renormalization scale, the global symmetry-breakingscale and the Yukawa coupling parameter are studied separately. We also providethe kinematic distributions of the final decay products. Our numerical resultsshow that the NLO QCD correction reduces the scale uncertainty and enhances theleading-order integrated cross section remarkably, with the $K$ factor varyingin the range of $1.41 \sim 1.68$ ($1.58 \sim 1.89$) as the increment of theglobal symmetry-breaking scale $f$ from $500~{\rm GeV}$ to $1.5~{\rm TeV}$($1.1~{\rm TeV}$) at the $\sqrt{s} = 14~{\rm TeV}$ ($8~{\rm TeV}$) LHC. We findthat it is possible to select the signal events of the $A_Hq_-$ production fromits background by putting proper cuts on the final leading jet and missingenergy.

Precise predictions for $A_H q_-$ associated production in the littlest Higgs model with $T$ parity at the LHC