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NLO QCD corrections to same-sign $T$-odd quark pair production in the littlest Higgs model with $T$-parity at the LHC

We present the calculations for the same-sign $T$-odd mirror quark pair production of the first two generations in the littlest Higgs model with $T$-parity (LHT) at the $\sqrt{s}=14~{\rm TeV}$ LHC up to the QCD next-to-leading order (NLO) including the subsequent decays of the $T$-odd mirror quarks. The uncertainties from the factorization/renormalization scale and parton distribution functions (PDFs) are discussed. Our numerical results show that the PDF uncertainty of the NLO QCD corrected cross section for the same-sign $T$-odd mirror quark pair production of the first two generations is comparable with the scale uncertainty, and the combined uncertainty at the QCD NLO is much smaller than that at the LO with the factorization/renormalization scale $μ$ in the range of $[μ_0/4,~4μ_0]$. We also study the dependence of the total cross section on the LHT parameters, and provide the transverse momentum, rapidity, invariant mass and $H_T$ distributions of final products.