Feasibility Study of the Measurement of the Differential Production Cross Section of $\Upsilon\rightarrow\mu^+\mu^-$ with the CMS detector in Early LHC Data

We present a feasibility study of the measurement of the differential production cross-section of $\Upsilon\rightarrow\mu^+\mu^-$ in early proton-proton collision data produced by the LHC accelerator at $\sqrt{s}=$~10~TeV and collected by the CMS detector. About two thousand reconstructed $\Upsilon\rightarrow\mu^+\mu^-$ decays are expected to pass the di-muon trigger per 1~pb$^{-1}$ of data, providing a statistically significant signal sample. The $\Upsilon$ resonance also provides the set of muons used to measure the reconstruction and trigger efficiencies in the low transverse momentum range.