Measurement of the $J/\psi$ meson and $b$-hadron production cross sections in $p\overline{p}$ collisions at $\sqrt{s}=1960\mathrm{G}\mathrm{e}\mathrm{V}$

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 $\sqrt{s}=1960\mathrm{G}\mathrm{e}\mathrm{V}$. The data correspond to an integrated luminosity of $39.7{\mathrm{p}\mathrm{b}}^{-1}$ 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 $20\mathrm{G}\mathrm{e}\mathrm{V}/c$ in the rapidity range $|y|<0.6$ to be $4.08\pm 0.02(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}{)}_{-0.33}^{+0.36}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})\mu \mathrm{b}$. 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 $p_T(J/\psi )>1.25\mathrm{G}\mathrm{e}\mathrm{V}/c$. We find the total cross section for $b$ hadrons, including both hadrons and antihadrons, decaying to $J/\psi$ with transverse momenta greater than $1.25\mathrm{G}\mathrm{e}\mathrm{V}/c$ in the rapidity range $|y(J/\psi )|<0.6$ is $0.330\pm 0.005(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}{)}_{-0.033}^{+0.036}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})\mu \mathrm{b}$. 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 $\sqrt{s}=1960\mathrm{G}\mathrm{e}\mathrm{V}$. 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 $17.6\pm 0.4(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}{)}_{-2.3}^{+2.5}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})\mu \mathrm{b}$.