Measurement of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi></mml:math>meson and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>b</mml:mi></mml:math>-hadron production cross sections in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi><mml:mover accent="true"><mml:mi>p</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math>collisions at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msqrt><mml:mi>s</mml:mi></mml:msqrt><mml:mo>=</mml:mo><mml:mn>1960</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi mathvariant="normal">G</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">V</mml:mi></mml:math>

We present a new measurement of the inclusive and differential production cross sections of $J/\ensuremath{\psi}$ mesons and $b$ hadrons in proton-antiproton collisions at $\sqrt{s}=1960\text{ }\text{ }\mathrm{G}\mathrm{e}\mathrm{V}$. The data correspond to an integrated luminosity of $39.7\text{ }\text{ }{\mathrm{p}\mathrm{b}}^{\ensuremath{-}1}$ collected by the CDF run II detector. We find the integrated cross section for inclusive $J/\ensuremath{\psi}$ production for all transverse momenta from 0 to $20\text{ }\text{ }\mathrm{G}\mathrm{e}\mathrm{V}/c$ in the rapidity range $|y|&lt;0.6$ to be $4.08\ifmmode\pm\else\textpm\fi{}0.02(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}{)}_{\ensuremath{-}0.33}^{+0.36}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})\text{ }\text{ }\ensuremath{\mu}\mathrm{b}$. We separate the fraction of $J/\ensuremath{\psi}$ events from the decay of the long-lived $b$ hadrons using the lifetime distribution in all events with ${p}_{T}(J/\ensuremath{\psi})&gt;1.25\text{ }\text{ }\mathrm{G}\mathrm{e}\mathrm{V}/c$. We find the total cross section for $b$ hadrons, including both hadrons and antihadrons, decaying to $J/\ensuremath{\psi}$ with transverse momenta greater than $1.25\text{ }\text{ }\mathrm{G}\mathrm{e}\mathrm{V}/c$ in the rapidity range $|y(J/\ensuremath{\psi})|&lt;0.6$ is $0.330\ifmmode\pm\else\textpm\fi{}0.005(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}{)}_{\ensuremath{-}0.033}^{+0.036}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})\text{ }\text{ }\ensuremath{\mu}\mathrm{b}$. Using a Monte Carlo simulation of the decay kinematics of $b$ hadrons to all final states containing a $J/\ensuremath{\psi}$, we extract the first measurement of the total single $b$-hadron cross section down to zero transverse momentum at $\sqrt{s}=1960\text{ }\text{ }\mathrm{G}\mathrm{e}\mathrm{V}$. We find the total single $b$-hadron cross section integrated over all transverse momenta for $b$ hadrons in the rapidity range $|y|&lt;0.6$ to be $17.6\ifmmode\pm\else\textpm\fi{}0.4(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}{)}_{\ensuremath{-}2.3}^{+2.5}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})\text{ }\text{ }\ensuremath{\mu}\mathrm{b}$.