We present a new measurement of the inclusive and differential production cross sections of $J/\psi$ mesons and $b$-hadrons in proton-antiproton collisions at $\sqrt{s}=1960$ GeV. The data correspond to an integrated luminosity of 39.7 pb$^{-1}$ collected by the CDF Run II detector. We find the integrated cross section for inclusive $J/\psi$ production for all transverse momenta from 0 to 20 GeV/$c$ in the rapidity range $|y|<0.6$ to be $4.08 \pm 0.02 (stat)^{+0.36}_{-0.33} (syst) \mu {\rm b}$. We separate the fraction of $J/\psi$ events from the decay of the long-lived $b$-hadrons using the lifetime distribution in all events with $p_T(J/\psi) > 1.25$ GeV/$c$. We find the total cross section for $b$-hadrons, including both hadrons and anti-hadrons, decaying to $J/\psi$ with transverse momenta greater than 1.25 GeV/$c$ in the rapidity range $|y(J/\psi)|<0.6$, is $ 0.330 \pm 0.005 (stat) ^{+0.036}_{-0.033} (syst) ~\mu{\rm b}$. Using a Monte Carlo simulation of the decay kinematics of $b$-hadrons to all final states containing a $J/\psi$, we extract the first measurement of the total single $b$-hadron cross section down to zero transverse momentum at $\sqrt{s}=1960$ GeV. We find the total single $b$-hadron cross section integrated over all transverse momenta for $b$-hadrons in the rapidity range $|y|<0.6$ to be $ 17.6 \pm 0.4 (stat)^{+2.5}_{-2.3} (syst) \mu{\rm b}$.
We report a high statistics measurement of Upsilon production with an 800 GeV/c proton beam on hydrogen and deuterium targets. The dominance of the gluon-gluon fusion process for Upsilon production at this energy implies that the cross section ratio, $\sigma (p + d \to \Upsilon) / 2\sigma (p + p\to \Upsilon)$, is sensitive to the gluon content in the neutron relative to that in the proton. Over the kinematic region 0 < x_F < 0.6, this ratio is found to be consistent with unity, in striking contrast to the behavior of the Drell-Yan cross section ratio $\sigma(p+d)_{DY}/2\sigma(p+p)_{DY}$. This result shows that the gluon distributions in the proton and neutron are very similar. The Upsilon production cross sections are also compared with the p+d and p+Cu cross sections from earlier measurements.