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 $7{mathrm{,Tekern -0.1em V}}$. The Z bosons are reconstructed in the ${text{Z}/gamma^*}!rightarrow{mu^{+}mu^{-}}$ final state from muons with a transverse momentum larger than $20{mathrm{,Gekern -0.1em V}}$, while two transverse momentum thresholds are considered for jets ($10{mathrm{,Gekern -0.1em V}}$ and $20{mathrm{,Gekern -0.1em V}}$). Both muons and jets are reconstructed in the pseudorapidity range $2.0 < eta < 4.5$. The results are based on data corresponding to $1.0{,mbox{fb}^{-1}}$ 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 begin{equation*} sigma(text{$text{Z}/gamma^*(mu^{+}mu^{-})$+b-jet}) = 295 pm 60~(text{stat}) pm 51~(text{syst}) pm 10~(text{lumi}) {,mbox{fb}} end{equation*} for ${p_{rm T}}$(jet)$>10{mathrm{,Gekern -0.1em V}}$, and begin{equation*} sigma(text{$text{Z}/gamma^*(mu^{+}mu^{-})$+b-jet}) = 128 pm 36~(text{stat}) pm 22~(text{syst}) pm 5~(text{lumi}) {,mbox{fb}} end{equation*} for ${p_{rm T}}$(jet)$>20{mathrm{,Gekern -0.1em V}}$.
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