We report a measurement of the forward-backward asymmetry, A(FB), in b (b) over bar pairs produced in proton-antiproton collisions and identified by muons from semileptonic b-hadron decays. The event sample is collected at a center-of-mass energy of root s = 1.96 TeV with the CDF II detector and corresponds to 6.9 fb(-1) of integrated luminosity. We obtain an integrated asymmetry of A(FB)(b (b) over bar) = (1.2 +/- 0.7)% at the particle level for b-quark pairs with invariant mass, m(b (b) over bar), down to 40 GeV/c(2) and measure the dependence of A(FB)(b (b) over bar) on m(b (b) over bar). The results are compatible with expectations from the standard model.
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