  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.
