Measurement of the Differential Production Cross Section of $J/\Psi\rightarrow\mu^+\mu^-$ in Proton-Proton Collisions at $\sqrt{s}=$~10~TeV with Simulated Data

We present several methods for measuring the differential production cross section of $J/\Psi \rightarrow\ mu^+\mu^-$ in proton-proton collisions at $\sqrt{s}=$~10~TeV, using simulated samples of $J/\Psi$ corresponding to data to be collected in the first LHC run by the CMS detector. We show the reconstruction and trigger performance of the CMS detector for single muons and $J/\Psi \rightarrow \mu^+ \mu^-$, discussing reconstruction efficiencies and trigger efficiencies. We also separate prompt $J/\Psi$ from those produced in the decay of B-hadrons by exploiting the long lifetime of beauty particles. About thirteen thousand reconstructed prompt $J/\Psi$ events pass the dedicated $J/\Psi$ trigger in a simulated data sample corresponding to an integrated luminosity of 1~pb$^{-1}$.