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We compute the $O(\alpha_s \alpha^2)$ and $O(\alpha_s^2 \alpha)$contributions to the production cross section of a $Z$ boson with one $b$ jetat the Large Hadron Collider (LHC), and study their phenomenological relevancefor LHC physics. The accurate prediction of hadronic $Z+b$-jet production isneeded to control a background that greatly affects both the measurement ofHiggs-boson properties and searches of new physics at the LHC. At the same timeit could enable the first precise measurement of the $b$-quark partondistribution function. In this context $b$-quark mass effects become relevantand need to be studied with care, both at the level of the hard process and atthe level of the initial- and final-state parton evolution. It is the aim ofthis paper to explore some of these issues in the framework of a massive 5Flavor Scheme and to assess the need for both the inclusion of electroweakcorrections, in addition to QCD corrections, and $b$-quark mass effects in theprediction of total and differential cross sections for hadronic $Z+b$-jetproduction.

Electroweak and QCD corrections to $Z$-boson production with one $b$ jet in a massive 5 Flavor Scheme