Feasibility study of a J/$\psi$ cross section measurement with early CMS data

We report on the methods and plans for measuring the differential $p_T$~ \jpsi$\rightarrow\mu^+\mu^-$ production cross section, using data to be collected in the first LHC run by the CMS detector. Making use of the large B-hadron lifetime, we show how to separate the promptly produced \jpsi's from those coming from B-hadron decays. Since the \jpsi~production cross section is expected to be large, the analysis should be viable with relatively small data sets, that will become available early in the startup of the LHC. We also address effects of a non-perfect detector alignment, as well as systematic uncertainties. About 70 thousand \jpsi~decays are reconstructed for an integrated luminosity of 3~pb$^{-1}$ in 14 TeV collisions, in the range of \ptjpsi~between 5 and 40 GeV/c. The precision of the result is limited by systematic uncertainties, and is at the 15~\% level.