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

Measurements of the cross-section for producing $b$ quarks in the reaction $pp \to b\overline{b}X$ 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 $72.0\pm0.3\pm6.8~ \mu b$ and $154.3\pm1.5\pm 14.3~ \mu b$ for $7$ and $13 TeV$. The ratio is $2.14\pm 0.02 \pm0.13$, 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.