A study of early data $B$-physics at CMS

We present plans for the reconstruction of three $b$-hadron decay modes: $B^{0} \rightarrow K^0_S J/\psi$, $B^+ \rightarrow K^{*+}(K^0_S \pi^+) J/\psi$, and $\Lambda^0_b\rightarrow \Lambda^0 J/\psi$ with dimuon final states in early data from the CMS detector at the LHC. Our analysis will include measurements of lifetimes and transverse momentum differential cross sections. Techniques used in analysis of these decay modes will eventually be used for reconstruction of rare $b$ decay modes with similar topology once the LHC reaches higher integrated luminosity.