Measurement of the inclusive jet cross section at the Fermilab Tevatron $p\overline{p}$ collider using a cone-based jet algorithm

We present a measurement of the inclusive jet cross section in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ based on data collected by the CDF II detector with an integrated luminosity of $1.13{\mathrm{fb}}^{-1}$. The measurement was made using the cone-based midpoint jet clustering algorithm in the rapidity region of $|y|<2.1$. The results are consistent with next-to-leading-order perturbative QCD predictions based on recent parton distribution functions (PDFs), and are expected to provide increased precision in PDFs at high parton momentum fraction $x$. The results are also compared to the recent inclusive jet cross section measurement using the $k_T$ jet clustering algorithm, and we find that the ratio of the cross sections measured with the two algorithms is in agreement with theoretical expectations over a large range of jet transverse momentum and rapidity.

Figure 1

Elevation view of half of the CDF Run II detector.

Figure 2

Jet trigger efficiencies as functions of jet $p_T$ for four trigger paths in the rapidity region $0.1<|y|<0.7$. The jet $p_T$ measured by the calorimeters is corrected as described in Sec. 5 in these distributions.

Figure 3

Jet yield distributions as functions of jet $p_T$ for four trigger paths in the rapidity region $0.1<|y|<0.7$ with no correction for trigger prescales.

Figure 4

The bisector variables described in the text are labeled in the diagram of the transverse plane shown above. $\Delta p_{T_{\perp }}$ ($\Delta p_{T_{\Vert }}$) is defined to be the component along (perpendicular to) the bisector axis of the sum of the jet $p_T$s.

Figure 5

The ${\sigma }_{\perp }$, ${\sigma }_{\Vert }$, and ${\sigma }_D$ distributions as functions of jet $p_T$ in data and pythia MC events in the region of $0.1<|y|<0.7$. The data/pythia ratio of ${\sigma }_D$ is also shown.

Figure 6

The data/MC ratio in ${\sigma }_D$ in four rapidity regions, $|y|<0.1$, $0.7<|y|<1.1$, $1.1<|y|<1.6$, and $1.6<|y|<2.1$ (solid squares). The same distribution in the region of $0.1<|y|<0.7$ is shown in Fig. 5. In the two regions where the simulation slightly underestimates the detector resolution, the MC is smeared by an additional amount to bring simulation and data into agreement (open squares).

Figure 7

The dijet $p_T$ balance ($\beta$), as defined in Sec. 5b1, for data and pythia MC events as a function of jet $\eta$.

Figure 8

The data/MC ratio in dijet $p_T$ balance ($\beta$) in five rapidity regions after the $p_T$-independent relative corrections have been applied. An additional correction is applied to the MC events to bring them into agreement with data in the regions of $|y|<0.1$, $1.1<|y|<1.6$, and $1.6<|y|<2.1$. In the most forward regions ($1.1<|y|<1.6$ and $1.6<|y|<2.1$), an additional systematic uncertainty is quoted due to the limited statistics at large $p_T$ which is shown by the dashed lines.

Figure 9

The average hadron-level jet $p_T$ as a function of the average calorimeter jet $p_T$ in five rapidity regions. The dashed lines correspond to $⟨p_T^{\mathrm{CAL}}⟩=⟨p_T^{\mathrm{HAD}}⟩$.

Figure 10

The unfolding correction factors as functions of jet $p_T$ in five rapidity regions.

Figure 11

The systematic uncertainty on the cross section in the rapidity region $0.1<|y|<0.7$ for each source considered in the measurement.

Figure 12

The relative uncertainty on the jet cross section in the rapidity region $0.1<|y|<0.7$ due to different components of the jet energy scale systematic uncertainties. The decomposition includes contributions due to the description of the calorimeter response to hadrons for three different ranges of hadron momentum and a $p_T$-independent component as discussed in Sec. 6.

Figure 13

The total systematic uncertainty on the cross section in five rapidity regions.

Figure 14

The parton-to-hadron-level correction for five rapidity regions. The correction is derived from pythia (solid line) and the difference between the herwig and pythia prediction for the correction is conservatively taken as the systematic uncertainty (shaded bands).

Figure 15

Inclusive jet cross sections measured at the hadron level using the midpoint algorithm in five rapidity regions compared to NLO pQCD predictions based on the CTEQ6.1M PDF. The cross sections for the five rapidity regions are scaled by a factor of ${10}^3$ from each other for presentation purposes.

Figure 16

The ratios of the measured inclusive jet cross sections at the hadron level with the midpoint jet clustering algorithm to the NLO pQCD predictions (corrected to the hadron level) in five rapidity regions. Also shown are the experimental systematic uncertainties on the measured cross section, the uncertainties in the hadronization and underlying event corrections added in quadrature with the experimental systematic uncertainties, and the PDF uncertainties on the theoretical predictions. The ratios of the theoretical predictions based on the MRST2004 and CTEQ6.1M are shown by the dotted lines.

Figure 17

The ratios of the inclusive jet cross sections measured using the $k_T$ algorithm with $D=0.7$ [8] to those measured using the midpoint jet-finding algorithm with $R_{\mathrm{cone}}=0.7$ in this paper (points). The systematic uncertainty on the ratio is given as the yellow band. The predictions from NLO pQCD (solid lines) and pythia (dashed lines) for this ratio are also shown.