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 $17.6\pm 0.4(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}{)}_{-2.3}^{+2.5}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})\mu \mathrm{b}$.

Figure 1

Mass distribution of reconstructed di-muon $J/\psi$ candidates. The points are data. The solid line is the fit to the signal approximated as a double Gaussian and a linear fit for the background. The hatched region is the fitted background. The fit gives a signal of $299800\pm 800$ $J/\psi$ events with an averaged mass of $3.09391\pm 0.00008\mathrm{G}\mathrm{e}\mathrm{V}/c^2$ obtained and an average width of $0.020\pm 0.001\mathrm{G}\mathrm{e}\mathrm{V}/c^2$ mainly due to detector resolution. The uncertainties here are statistical only.

Figure 2

Invariant mass distributions of reconstructed $J/\psi \to \mu \mu$ events in the ranges of $p_T(\mu \mu )<0.25\mathrm{G}\mathrm{e}\mathrm{V}/c$ (top left panel), $1.25<p_T(\mu \mu )<1.5\mathrm{G}\mathrm{e}\mathrm{V}/c$ (top right panel), $5.0<p_T(\mu \mu )<5.5\mathrm{G}\mathrm{e}\mathrm{V}/c$ (bottom left panel), and $12.0<p_T(\mu \mu )<14.0\mathrm{G}\mathrm{e}\mathrm{V}/c$ (bottom right panel). The points with error bars are data. The solid lines are the fits to the signal shape from the simulation and a polynomial shape for the background. The shaded histograms are the fitted background shapes. The number of signal events and the fit probability of the binned ${\chi }^2$ fitting are also provided.

Figure 3

Acceptance of $J/\psi \to \mu \mu$ events determined from a GEANT simulation of the CDF detector. The acceptance is shown as a function of $p_T(J/\psi )$ and $y(J/\psi )$. The acceptance as a function of $p_T(J/\psi )$ is measured integrated over $|y|<0.6$ and the acceptance as a function of $y$ is shown integrated over all $p_T$.

Figure 4

The level 1 CMU trigger efficiency as a function of muon $p_T$. Points with error bars are measurement points. The solid line is the fitting result using the function described in the text. The dashed lines indicate the range used to determine the uncertainty.

Figure 5

Inclusive $J/\psi$ cross section, $d\sigma /d{p}_T·\mathrm{B}\mathrm{r}(J/\psi \to \mu \mu )$, as a function of $J/\psi$ $p_T$ integrated over the rapidity range $|y|<0.6$. The differential cross section with systematic and statistical uncertainties added is plotted. This includes correlated uncertainties.

Figure 6

The invariant $J/\psi$ cross section, $d\sigma /d{p}_T^2·\mathrm{B}\mathrm{r}(J/\psi \to \mu \mu )$, as a function of $p_T^2(J/\psi )$. The differential cross section is plotted. This includes correlated uncertainties.

Figure 7

Fits to the $J/\psi$ pseudoproper decay time in the ranges of $1.25<p_T(\mu \mu )<1.5\mathrm{G}\mathrm{e}\mathrm{V}/c$ (top panel), $5.0<p_T(\mu \mu )<5.5\mathrm{G}\mathrm{e}\mathrm{V}/c$ (bottom left panel), and $12.0<p_T(\mu \mu )<14.0\mathrm{G}\mathrm{e}\mathrm{V}/c$ (bottom right panel). The solid lines are the fits to all the events in the mass window of 2.85 to $3.35\mathrm{G}\mathrm{e}\mathrm{V}/c^2$, the dashed lines are the fit to all signal events, the solid histograms are the fits to the portion of the signal events that are from $b$-hadron decays, and the dot-dashed lines are the fits to background events including events in the invariant mass sidebands.

Figure 8

Fraction of $J/\psi$ from $b$-hadron decays in the inclusive $J/\psi$ events of run II data as a function of $J/\psi$ transverse momentum. Error bars include both statistical and systematic errors.

Figure 9

Differential cross-section distribution of $J/\psi$ events from the decays of $b$ hadrons as a function of $J/\psi$ transverse momentum integrated over the rapidity range $|y|<0.6$. The crosses with error bars are the data with systematic and statistical uncertainties added including correlated uncertainties. The solid line is the central theoretical values using the FONLL calculations outlined in [41]; the dashed line is the theoretical uncertainty.

Figure 10

The inclusive $J/\psi$ cross section as a function of $J/\psi$ $p_T$ integrated over the rapidity range $|y|<0.6$ is plotted as points with error bars where all uncertainties have been added. The hatched histogram indicates the contribution to the cross section from prompt charmonium production. The cross-hatched histogram is the contribution from decays of $b$ hadrons.

Figure 11

Differential cross-section distribution of $b$-hadron production as a function of $b$-hadron transverse momenta. The crosses with error bars are the data with systematic and statistical uncertainties added, including correlated uncertainties. The solid line is the central theoretical values using the FONLL calculations outlined in [41]; the dashed line is the theoretical uncertainty.

Figure 12

Ratio of the differential cross-section distributions of $J/\psi$ events from the decays of $b$ hadrons as a function of $J/\psi$ transverse momentum from CDF run I and run II.

Figure 13

The differential cross-section distributions of $b$ hadrons as a function of $b$-hadron momentum from the measurement of the $B^{+}$ meson cross section in CDF run I [9] and $b$-hadron inclusive cross section extracted in this analysis (run II). The differential cross sections showed are integrated over the rapidity range $|y(H_b)|<1.0$.