What is the Wbbar irreducible background to the Higgs searches at LHC? Matrix Element versus Parton Shower with Pythia 6.1

The W(->l nu) b bbar production at LHC is an irreducible background for the possible observability of the Standard Model (SM) and Minimal Standard Model (MSSM) Higgs boson in the associated WH production with H->b bbar decay. Here we present comparison of the background estimates as obtained with (a) complete massive matrix element for the q qbar -> W(->l nu) g*(->b bbar) process; with PYTHIA implementation of the (b) q qbar --> W process and (c) q qbar->Wg and qg->Wq processes; followed by the parton shower. All of them: (a), (b) and (c) are leading to the production of the W-boson accompanied by the b-quarks in the final event but differ in the used approximation. We concentrated on the discussion of the predictive power of these approaches on the quantities relevant for the background estimates to the Higgs boson searches at LHC.