NLO QCD predictions for W+1 jet and W+2 jet production with at least one b jet at the 7 TeV LHC

We calculate the production of a W boson in association with up to two jets including at least one b-jet to next-to-leading order (NLO) in QCD at the CERN Large Hadron Collider with 7 TeV center-of-mass energy. Both exclusive and inclusive event cross section and b-jet cross sections are presented. The calculation is performed consistently in the five-flavor-number scheme where both q anti-q' and bq (q =\= b) initiated parton level processes are included at NLO QCD. We study the residual theoretical uncertainties of the NLO predictions due to the renormalization and factorization scale dependence, to the uncertainty from the parton distribution functions, and to the values of alpha_s and the bottom-quark mass.