Underlying event in hard interactions at the Fermilab Tevatron $\overline{p}p$ collider

For comparison of inclusive jet cross sections measured at hadron-hadron colliders to next-to-leading order (NLO) parton-level calculations, the energy deposited in the jet cone by spectator parton interactions must first be subtracted. The assumption made at the Tevatron is that the spectator parton interaction energy is similar to the ambient level measured in minimum bias events. In this paper, we test this assumption by measuring the ambient charged track momentum in events containing large transverse energy jets at $\sqrt{s}=1800\mathrm{G}\mathrm{e}\mathrm{V}$ and $\sqrt{s}=630\mathrm{G}\mathrm{e}\mathrm{V}$ and comparing this ambient momentum with that observed both in minimum bias events and with that predicted by two Monte Carlo models. Two cones in $\eta -\varphi$ space are defined, at the same pseudorapidity, $\eta$, as the jet with the highest transverse energy ($E_T^{(1)}$), and at $\pm {90}^o$ in the azimuthal direction, $\varphi$. The total charged track momentum inside each of the two cones is measured. The minimum momentum in the two cones is almost independent of $E_T^{(1)}$ and is similar to the momentum observed in minimum bias events, whereas the maximum momentum increases roughly linearly with the jet $E_T^{(1)}$ over most of the measured range. This study was carried out using data from the CDF detector taken during Run 1 (1994-1995). The study will help improve the precision of comparisons of jet cross section data and NLO perturbative QCD predictions. The distribution of the sum of the track momenta in the two cones is also examined for five different $E_T^{(1)}$ bins. The HERWIG and PYTHIA Monte Carlo generators are reasonably successful in describing the data, but neither can describe completely all of the event properties.

Figure 1

An example of a 2-jet event in the detector region under study. The cones used for the determination of the underlying event contribution are at $\eta ={\eta }^{(1)}$ and $\varphi ={\varphi }^{(1)}\pm 90°$ where (${\eta }^{(1)},{\varphi }^{(1)}$) is the centroid of the highest $E_T$ jet in the event.

Figure 2

$P_T^{90,\mathrm{m}\mathrm{a}\mathrm{x}}$, $P_T^{90,\mathrm{m}\mathrm{i}\mathrm{n}}$ and their difference $\Delta P_T^{90}$ as a function of the $E_T$ of the highest energy jet at $\sqrt{s}=1800\mathrm{G}\mathrm{e}\mathrm{V}$. The default parameters for PYTHIA (version 6.115) and HERWIG (version 5.6) have been used.

Figure 3

$P_T^{90,\mathrm{m}\mathrm{a}\mathrm{x}}$, $P_T^{90,\mathrm{m}\mathrm{i}\mathrm{n}}$ and their difference $\Delta P_T^{90}$ as a function of the $E_T$ of the highest energy jet at $\sqrt{s}=1800\mathrm{G}\mathrm{e}\mathrm{V}$. PYTHIA (version 6.115) has been tuned to reproduce the data. The default parameters for HERWIG (version 5.6) have been used.

Figure 4

The distributions for the total $p_T$ in the sum of the $\mathrm{m}\mathrm{a}\mathrm{x}$ and $\mathrm{m}\mathrm{i}\mathrm{n}$ cones is plotted for five different bins of the $E_T$ of the highest energy jet. Data, HERWIG (version 5.6) and PYTHIA (version 6.115) distributions are shown at $\sqrt{s}=1800\mathrm{G}\mathrm{e}\mathrm{V}$.

Figure 5

Number of tracks in the $\mathrm{m}\mathrm{a}\mathrm{x}$ and $\mathrm{m}\mathrm{i}\mathrm{n}$ cone as a function of the $E_T$ of the leading jet. Data, HERWIG (version 5.6) and PYTHIA (version 6.115) distributions are plotted at $\sqrt{s}=1800\mathrm{G}\mathrm{e}\mathrm{V}$.

Figure 6

Distribution of track multiplicity (left) and transverse momentum (right) in the $\sqrt{s}=1800\mathrm{G}\mathrm{e}\mathrm{V}$ minimum bias sample. The inset in the right plot shows the low $P_T$ portion of the spectrum on a linear scale.

Figure 7

$P_T^{sum}$ (Swiss cheese). The two and three most energetic jets in each event are subtracted from the total transverse momentum in the central detector region. Data, HERWIG (version 5.6) and PYTHIA (version 6.115) results are shown at $\sqrt{s}=1800\mathrm{G}\mathrm{e}\mathrm{V}$.

Figure 8

$P_T^{90,\mathrm{m}\mathrm{i}\mathrm{n}}$, $P_T^{90,\mathrm{m}\mathrm{a}\mathrm{x}}$ and their difference $\Delta P_T^{90}$ at $\sqrt{s}=630\mathrm{G}\mathrm{e}\mathrm{V}$ as a function of the $E_T$ of the leading jet.

Figure 9

$P_t^{\mathrm{s}\mathrm{u}\mathrm{m}}$ (Swiss cheese). The two and three most energetic jets in the events are subtracted from the total transverse momentum in the central detector region. Data, HERWIG (version 5.6) and PYTHIA (version 6.115) results are shown at $\sqrt{s}=630\mathrm{G}\mathrm{e}\mathrm{V}$.

Figure 10

Distribution of track multiplicity (left) and transverse momentum (right) in the $\sqrt{s}=630\mathrm{G}\mathrm{e}\mathrm{V}$ minimum bias sample. The inset in the right plot shows the low $P_T$ portion of the spectrum on a linear scale.