The associated production of a Z boson or an off-shell photon gamma* with a bottom quark in the forward region is studied using proton-proton collisions at a centre-of-mass energy of 7TeV. The Z bosons are reconstructed in the Z/gamma* -> mu(+)mu(-) final state from muons with a transverse momentum larger than 20 GeV, while two transverse momentum thresholds are considered for jets (10 GeV and 20 GeV). Both muons and jets are reconstructed in the pseudorapidity range 2.0 < eta < 4.5. The results are based on data corresponding to 1.0 fb(-1) recorded in 2011 with the LHCb detector. The measurement of the Z+b-jet cross-section is normalized to the Z+jet cross-section. The measured cross-sections are (Z/ (mu+ mu-) + b-jet) = 295 60 (stat) 51 (syst) 10 (lumi) fb (0.1) for p T(jet) > 10 GeV, and (Z/ (mu+ mu-) + b-jet) = 128 36 (stat) 22 (syst) 5 (lumi) fb (0.2) for p T(jet) > 20 GeV.
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