The ALICE collaboration at the LHC reports measurement of the inclusive production cross section of electrons from semi-leptonic decays of beauty hadrons with rapidity $|y|<0.8$ and transverse momentum $1<p_{\mathrm{T}}<10$ GeV/$c$, in pp collisions at $\sqrt{s} = $ 2.76 TeV. Electrons not originating from semi-electronic decay of beauty hadrons are suppressed using the impact parameter of the corresponding tracks. The production cross section of beauty decay electrons is compared to the result obtained with an alternative method which uses the distribution of the azimuthal angle between heavy-flavour decay electrons and charged hadrons. Perturbative QCD calculations agree with the measured cross section within the experimental and theoretical uncertainties. The integrated visible cross section, $\sigma_{\mathrm{b} \rightarrow \mathrm{e}} = 3.47\pm0.40(\mathrm{stat})^{+1.12}_{-1.33}(\mathrm{sys})\pm0.07(\mathrm{norm}) \mu$b, was extrapolated to full phase space using Fixed Order plus Next-to-Leading Log (FONLL) predictions to obtain the total b$\bar{\mathrm{b}}$ production cross section, $\sigma_{\mathrm{b\bar{b}}} = 130\pm15.1(\mathrm{stat})^{+42.1}_{-49.8}(\mathrm{sys})^{+3.4}_{-3.1}(\mathrm{extr})\pm2.5(\mathrm{norm})\pm4.4(\mathrm{BR}) \mu$b.
The first measurements of the invariant differential cross sections of inclusive $\pi^0$ and $\eta$ meson production at mid-rapidity in proton-proton collisions at $\sqrt{s}=0.9$ TeV and $\sqrt{s}=7$ TeV are reported. The $\pi^0$ measurement covers the ranges $0.4<p_T<7$ GeV/$c$ and $0.3<p_T<25$ GeV/$c$ for these two energies, respectively. The production of $\eta$ mesons was measured at $\sqrt{s}=7$ TeV in the range $0.4<p_T<15$ GeV/$c$. Next-to-Leading Order perturbative QCD calculations, which are consistent with the $\pi^0$ spectrum at $\sqrt{s}=0.9$ TeV, overestimate those of $\pi^0$ and $\eta$ mesons at $\sqrt{s}=7$ TeV, but agree with the measured $\eta/\pi^0$ ratio at $\sqrt{s}=7$ TeV.
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