Measurement of the $b$-quark production cross-section in 7 and 13 TeV $pp$ collisions

Measurements of the cross-section for producing \bquark quarks in the reaction $pp\to b\bar{b}X$ are reported in 7 and 13 TeV collisions at the LHC as a function of the pseudorapidity $\eta$ in the range $2<\eta <5$ covered by the acceptance of the LHCb experiment. The measurements are done using semileptonic decays of $b$-flavored hadrons decaying into a ground-state charmed hadron in association with a muon. The cross-sections in the covered $\eta$ range are $72.0\pm 0.3\pm 6.8\mu$b and $144\pm 1\pm 21\mu$b for 7 and 13 TeV. The ratio is $2.00\pm 0.02\pm 0.26$, where the quoted uncertainties are statistical and systematic, respectively. The agreement with theoretical expectation is good at 7 TeV, but differs somewhat at 13 TeV. The measured ratio of cross-sections is larger at lower $\eta$ than the model prediction.