A new measurement of the inclusive and differential production cross sections of \jpsi mesons and $b$-hadrons in proton-antiproton collisions at $\sqrt{s} = 1960$ GeV is presented. The data correspond to an integrated luminosity of 39.7 pb$^{-1}$ collected by the CDF Run II detector. The integrated cross section for inclusive \jpsi production for all transverse momenta from 0 to 20 GeV/$c$ in the rapidity range $|y| < 0.6$ is found to be $4.08 \pm 0.02(stat) ^{+0.36}_{-0.33}(syst)$ $\mu$b. The fraction of \jpsi events from the decay of the long-lived $b$-hadrons is sperated by using the lifetime distribution in all events with $p_{T}(J/\psi) > 1.25$ GeV/$c$. The total cross section for $b$-hadrons, including both hadrons and anti-hadrons, decaying to \jpsi with transverse momenta greater than 1.25 GeV/$c$ in the rapidity range $|y(J/\psi)| < 0.6$, is found to be $0.330 \pm 0.005(stat) ^{+0.036}_{-0.033}(syst)$ $\mu$b. Using a Monte Carlo simulation of the decay kinematics of $b$-hadrons to all final states containing a \jpsi, the first measurement of the total single $b$-hadron cross section down to zero transverse momentum is extracted at $sqrt{s} = $1960 GeV. The total single $b$-hadron cross section integrated over all transverse momenta for $b$-hadrons in the rapidity range $|y| < 0.6$ is found to be $17.6 \pm 0.4(stat) ^{+2.5}_{-2.3}(syst)$ $\mu$b. Posted to /cdf/pub/thesis/cdf8750_Jpsi_bhadronXsection.pdf http://www-cdf.fnal.gov/thesis/cdf8750_Jpsi_bhadronXsection.pdf Posted by tomohiro