B-physics: new states, rare decays and branching ratios in CDF

We present results and prospects for searches for rare B and D meson decays with final state dimuons, including B_s\to\mu\mu, B_d\to\mu\mu, and D\to\mu\mu. Upper limits on the branching fractions are compared to previous CDF measurements, recent results from the B factories and theoretical expectations. We also report on new measurements of production and decay properties of the X(3872) particle, discovered in 2003 by the Belle Collaboration. New results on the measurement of the relative branching fraction for the Cabibbo suppressed decay B^+\to J/\psi\pi^+ Br(B^+\to J/\psi\pi^+)/Br(B^+\to J/\psi K^+) are presented too. The presented results are based on the analyses of 70 to 220 pb^-1 of data collected by the CDF II detector in p\bar p collisions at \sqrt{s} = 1.96 GeV at Fermilab Tevatron.