Measurement of particle production and inclusive differential cross sections in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$

We report a set of measurements of particle production in inelastic $p\overline{p}$ collisions collected with a minimum-bias trigger at the Tevatron Collider with the CDF II experiment. The inclusive charged particle transverse momentum differential cross section is measured, with improved precision, over a range about ten times wider than in previous measurements. The former modeling of the spectrum appears to be incompatible with the high particle momenta observed. The dependence of the charged particle transverse momentum on the event particle multiplicity is analyzed to study the various components of hadron interactions. This is one of the observable variables most poorly reproduced by the available Monte Carlo generators. A first measurement of the event transverse energy sum differential cross section is also reported. A comparison with a pythia prediction at the hadron level is performed. The inclusive charged-particle differential production cross section is fairly well reproduced only in the transverse momentum range available from previous measurements. At higher momentum the agreement is poor. The transverse energy sum is poorly reproduced over the whole spectrum. The dependence of the charged particle transverse momentum on the particle multiplicity needs the introduction of more sophisticated particle production mechanisms, such as multiple parton interactions, in order to be better explained.

Figure 1

Ratio of the corrected to uncorrected $p_T$ distributions. The correction is roughly flat for $p_T>10\mathrm{GeV}/c$.

Figure 2

Calorimeter response as a function of the event $\sum _{}^{}{E}_T$. The systematic uncertainty is shown as a band.

Figure 3

The unfolding factor of the $\sum _{}^{}{E}_T$ distribution. The uncertainty is taken as one half of the maximum variation obtained when adding and subtracting the statistical uncertainty to the MC distributions from which the unfolding is computed.

Figure 4

The raw event average charged particle multiplicity as a function of the instantaneous luminosity. The line represents a linear fit (with slope equal to $0.0022\pm 0.0003$). The uncertainty is statistical only.

Figure 5

Left upper plot: the track $p_T$ differential cross section is shown. The error bars describe the uncertainty on the data points. This uncertainty includes the statistical uncertainty on the data and the statistical uncertainty on the total correction. A fit to the functional form in Eq. (8) in the region of $0.4<p_T<10\mathrm{GeV}/c$ is also shown for the data used in the 1988 analysis [5] at the center of mass energy of 1800 GeV (dashed line). A fit with a more complicated function [Eq. (9)] is shown as a continuous line. The fit to the 1800 GeV data is scaled by a factor 2 to account for the different normalization. In the plot at the bottom, the systematic and the total uncertainties are shown. The total uncertainty is the quadratic sum of the uncertainty reported on the data points and the systematic uncertainty. The right-hand side plots show the same distributions but with a logarithmic horizontal scale.

Figure 6

Left upper plot: comparison of the track $p_T$ differential cross section with pythia prediction at hadron level (Tune A with ${\widehat{p}}_{T^0}=1.5\mathrm{GeV}/c$). The data error bars describe the uncertainty on the data points. This uncertainty includes the statistical uncertainty on the data and the statistical uncertainty on the total correction. The error bars on MC represent its statistical uncertainty. The ratio of data over prediction is shown in the lower plot. The right-hand-side plots show the same distributions but with a logarithmic horizontal scale. Note that these distributions are cut off at $50\mathrm{GeV}/c$ since pythia does not produce particles at all beyond that value.

Figure 7

The dependence of the average track $p_T$ on the event multiplicity. A comparison with the Run I measurement is shown. The error bars in the upper plot describe the uncertainty on the data points. This uncertainty includes the statistical uncertainty on the data and the statistical uncertainty on the total correction. In the lower plot the systematic uncertainty (solid yellow band) and the total uncertainty are shown. The total uncertainty is the quadratic sum of the uncertainty reported on the data points and the systematic uncertainty.

Figure 8

For tracks with $|\eta |<1$, the dependence of the average track $p_T$ on the event multiplicity is shown. The error bars on data describe the uncertainty on the data points. This uncertainty includes the statistical uncertainty on the data and the statistical uncertainty on the total correction. A comparison with various pythia tunes at hadron level is shown. Tune A with ${\widehat{p}}_{T^0}=1.5\mathrm{GeV}/c$ was used to compute the MC corrections in this analysis (the statistical uncertainty is shown only for the highest multiplicities where it is significant). Tune A with ${\widehat{p}}_{T^0}=0\mathrm{GeV}/c$ is very similar to ${\widehat{p}}_{T^0}=1.5\mathrm{GeV}/c$. The same tuning with no multiple parton interactions allowed (“no MPI”) yields an average $p_T$ much higher than data for multiplicities greater than about 5. The ATLAS tune yields too low an average $p_T$ over the whole multiplicity range.

Figure 9

Left upper plot: the differential $\sum _{}^{}{E}_T$ cross section in $|\eta |\le 1$. The error bars describe the uncertainty on the data points. This uncertainty includes the statistical uncertainty on the data and the statistical uncertainty on the total correction. In the bottom plot the systematic (solid band) and the total (continuous line) uncertainties are shown. The total uncertainty is the quadratic sum of the uncertainty reported on the data points and the systematic uncertainty. The right-hand-side plots show the same distributions but with a logarithmic horizontal scale.

Figure 10

The left upper plot shows the same data as Fig. 9 compared to a pythia prediction at hadron level. The data error bars describe the uncertainty on the data points. This uncertainty includes the statistical uncertainty on the data and the statistical uncertainty on the total correction. The error bars on MC represent its statistical uncertainty. The ratio of data to pythia Tune A using ${\widehat{p}}_{T^0}=1.5\mathrm{GeV}/c$ is shown in the lower plot. The right-hand-side plots show the same distributions but with a logarithmic horizontal scale.