This paper describes the measuremet of J/ψ inclusive, prompt
and non-prompt cross section using the dimuon channel in the CMS experiment with the first 314 nb−1 of LHC data. An important contribution to the systematic uncertainty is given by the unknown polarization of the prompt J/ψ, in particular for what concerns the measurement of the detector acceptance. A complex framework for a measure of the prompt J/ψ polarization has been developed by the CMS
collaboration and a measure of the angular parameters is foreseen in the close future. A brief description of the main issues of the polarization measurement is also given
