Decays of b hadrons into final states containing a D0 meson and a muon are used to measure the b anti-b production cross-section in proton-proton collisions at a centre-of-mass energy of 7 TeV at the LHC. In the pseudorapidity interval 2 < eta < 6 and integrated over all transverse momenta we find that the average cross-section to produce b-flavoured or anti-b-flavoured hadrons is (75.3 +/- 5.4 +/- 13.0) microbarns.
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