Measurement of the $B^{\pm }$ production cross-section in pp collisions at $\sqrt{s}=$ 7 and 13 TeV

The production of $B^{\pm }$ mesons is studied in $pp$ collisions at centre-of-mass energies of 7 and 13 TeV, using $B^{\pm}\rightarrow J/\psi K^{\pm}$decaysanddatasamplescorrespondingto1.0fb$^{-1}$ and 0.3 fb${}^{-1}$, respectively. The production cross-sections summed over both charges and integrated over the transverse momentum range $0<p_{\text{T}}<40$ GeV/$c$ and the rapidity range $2.0<y<4.5$ are measured to be $\sigma(pp \rightarrow B^{\pm} X, \sqrt{s} = $\text{7 TeV}$) = 43.0 \pm 0.2 \pm 2.5 \pm 1.7\mu b,$ $\sigma(pp \rightarrow B^{\pm} X, \sqrt{s} = $\text{13 TeV}$) = 86.6 \pm 0.5 \pm 5.4 \pm 3.4\mu b,$ where the first uncertainties are statistical, the second are systematic, and the third are due to the limited knowledge of the $B^{\pm }\to J\mathrm{/}\psi K^{\pm }$ branching fraction. The ratio of the cross-section at 13 TeV to that at 7 TeV is determined to be $2.02\pm 0.02\text{(stat)}\pm 0.12\text{(syst)}$. Differential cross-sections are also reported as functions of $p_{\text{T}}$ and $y$. All results are in agreement with theoretical calculations based on the state-of-art fixed next-to-leading order quantum chromodynamics.