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Dark matter pair associated with a $W$ boson production at the LHC in next-to-leading order QCD

We investigate the QCD next-to-leading order (NLO) corrections to the production of a pair of fermionic dark matter particles associated with a W boson production through a mediator which couples to standard model particles via either a vector or axial-vector coupling at the LHC. We find that the QCD NLO corrections reduce the dependence of the total cross sections on the factorization and renormalization scales, and the $K$-factors increase with the increment of the dark matter mass. We also provide the LO and QCD NLO corrected distributions of the transverse momenta $p_T^μ$ of final muon and transverse mass $M_T$. We find that the LO cross section is significantly changed by the QCD NLO corrections.