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$HZ$ associated production at the LHC within the littlest Higgs model at NLO+NLL accuracy

We consider the $HZ$ associated production at the $14~{\rm TeV}$ LHC in the littlest Higgs model (LHM) and study the corrections of the transverse momentum resummation and threshold resummation at the next-to-leading logarithmic (NLL) accuracy and the fixed-order prediction at the QCD next-to-leading order (NLO) including the contribution from the one-loop-induced $gg$-fusion channel. The QCD NLO+NLL effects on the integrated cross section and the distributions of transverse momentum and invariant mass of the $HZ$ system for the $HZ$ production in the LHM are discussed. The distributions of transverse momentum and invariant mass of the $HZ$ system are evaluated by means of the transverse momentum resummation and threshold resummation, respectively. We estimate their scale uncertainties and find that the predictions obtained at the QCD NLO+NLL accuracy are much more reliable than those using the pure NLO approach. We see also that the relative deviation between the results in the LHM and the standard model is considerably reduced by the resummation effects, but still observable.