Abstract
We review the methods developed for combining the parton shower approximation to quantum chromodynamics with fixed-order perturbation theory so as to achieve next-to-leading-order (NLO) accuracy for inclusive observables. These developments have made it possible to generate fully simulated hadronic final states with the precision and stability of NLO calculations. We explain the underlying theory of the existing methods, MC@NLO and POWHEG, together with their similarities, differences, achievements, and limitations. For illustration, we mainly compare results on Higgs boson production at the LHC, with particular emphasis on the residual uncertainties arising from the different treatment of effects beyond NLO. We also briefly summarize the difference between these NLO plus parton shower methods and matrix-element plus parton shower matching, along with current efforts to combine the two approaches.
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