  The ALICE experiment at the LHC has studied J/psi production at mid-rapidity
in pp collisions at sqrt{s}=7 TeV through its electron pair decay on a data
sample corresponding to an integrated luminosity L_int = 5.6nb-1. The fraction
of J/psi from the decay of long-lived beauty hadrons was determined for J/psi
candidates with transverse momentum p_t>1.3 GeV/c and rapidity |y|<0.9. The
cross section for prompt J/psi mesons, i.e. directly produced J/psi and prompt
decays of heavier charmonium states such as the Psi(2S) and Csi_c resonances,
is sigma_prompt-J/psi(pt > 1.3 GeV/c, |y| < 0.9) = 8.3 +- 0.8(stat.) +-
1.1(syst.) + 1.5 - 1.4(syst. pol.) micro barn. The cross section for the
production of b-hadrons decaying to J/psi with p_t>1.3 GeV/c and |y|<0.9 is
sigma_{J/psi<-h_B} = 1.46 +- 0.38(stat.) + 0.26 -0.32(syst.) micro barn. The
results are compared to QCD model predictions. The shape of the p_t and y
distributions of b-quarks predicted by perturbative QCD model calculations are
used to extrapolate the measured cross section to derive the b-bbar pair total
cross section and dsigma/dy at mid-rapidity.
