J/Psi prompt and non-prompt cross sections in pp collisions at sqrt(s) = 7 TeV

We present a measurement of the inclusive total and differential production cross sections of $J/\psi$ mesons and b-hadrons in pp collisions at $\sqrt{s}=7$~TeV with the CMS experiment. The data correspond to an integrated luminosity of 100~nb$^{-1}$ and were collected during the first months of LHC operation. The differential production cross section of $J/\psi$ from inclusive processes has been measured as a function of the $J/\psi$ transverse momentum, up to 30 \GeVc, for two rapidity ranges: $|y|<1.4$ and $1.4<|y|<2.4$. The total cross section for inclusive \JPsi production, times the dimuon decay branching fraction, has been determined to be $289.1 \pm 16.7\mbox{(stat)}\pm 60.1\mbox{(syst)}$ nb for transverse momenta between $4$ and $30$~\GeVc and in the rapidity range $|y|<$2.4. The b-hadron component has been determined from a fit to the decay length distribution of displaced $J/\psi$ decays, and a \pt~differential cross section for b-hadron decays has been derived. The total cross section times $BR(\JPsi\to\mu^+\mu^-)$ for the \JPsi production coming from B-hadrons, decaying to \JPsi mesons with transverse momenta between $4$ and $30$~\GeVc and in the rapidity range $|y|<$2.4, is measured to be $ 56.1\pm 5.5\mbox{(stat)}\pm 7.2\mbox{(syst)}$ nb. The paper ends with some comparisons between the measurements and model calculations.