Study of the energy dependence of the underlying event in proton-antiproton collisions

We study charged particle production (${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$, $|\eta |<0.8$) in proton-antiproton collisions at total center-of-mass energies $\sqrt{s}=300\mathrm{GeV}$, 900 GeV, and 1.96 TeV. We use the direction of the charged particle with the largest transverse momentum in each event to define three regions of $\eta -\varphi$ space: “toward”, “away”, and “transverse.” The average number and the average scalar ${\mathrm{p}}_T$ sum of charged particles in the transverse region are sensitive to the modeling of the “underlying event.” The transverse region is divided into a MAX and MIN transverse region, which helps separate the “hard component” (initial and final-state radiation) from the “beam-beam remnant” and multiple parton interaction components of the scattering. The center-of-mass energy dependence of the various components of the event is studied in detail. The data presented here can be used to constrain and improve QCD Monte Carlo models, resulting in more precise predictions at the LHC energies of 13 and 14 TeV.

Figure 1

Illustration of the regions of $\eta -\varphi$ space that are defined relative to the direction of a “leading object” in the event. The “leading object” can be the highest ${\mathrm{p}}_T$ charged particle (left), the highest ${\mathrm{p}}_T$ charged-particle or calorimeter jet (middle), or the lepton-pair in $Z$-boson production (right). The relative azimuthal angle $\mathrm{\Delta }\varphi =\varphi -{\varphi }_L$, where ${\varphi }_L$ is the azimuthal angle of the leading object and $\varphi$ is the azimuthal angle of a charged particle. The “toward” region is defined by $|\mathrm{\Delta }\varphi |<60°$ and $|\eta |<{\eta }_{\text{cut}}$, while the “away” region is $|\mathrm{\Delta }\varphi |>120°$ and $|\eta |<{\eta }_{\text{cut}}$. The two “transverse” regions $-120°<\mathrm{\Delta }\varphi <-60°$, $|\eta |<{\eta }_{\text{cut}}$ and $60°<\mathrm{\Delta }\varphi <120°$, $|\eta |<{\eta }_{\text{cut}}$ are referred to as “transverse 1” and “transverse 2”.

Figure 2

(a) Illustration of the regions of $\eta -\varphi$ space that are defined relative to the direction of the highest ${\mathrm{p}}_T$ charged particle (i.e., leading charged particle). The relative angle $\mathrm{\Delta }\varphi =\varphi -{\varphi }_{\mathrm{MAX}}$, where ${\varphi }_{\mathrm{MAX}}$ is the azimuthal angle of the leading charged particle and $\varphi$ is the azimuthal angle of a charged particle. On an event by event basis, we define “transMAX” (“transMIN”) to be the maximum (minimum) number or scalar ${\mathrm{p}}_T$ sum of charged particles in the two transverse regions “transverse 1” and “transverse 2” shown in Fig. 1. (b) Illustration of the topology of a hadron-hadron collision in which a hard parton-parton collision has occurred. For events with large initial or final-state radiation the transMAX region contains the third jet, while both the transMAX and transMIN regions receive contributions from the multiple parton interactions (MPI) and the beam-beam remnants (BBR).

Figure 3

(a) Data at 1.96 TeV, 900 GeV, and 300 GeV on the pseudorapidity distribution, $\mathrm{d}\mathrm{N}/\mathrm{d}\eta$, for charged particles with $|\eta |<0.8$ and ${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$ and (c) ${\mathrm{p}}_T>1.0\mathrm{GeV}/\mathrm{c}$ for events with at least one charged particle with $|\eta |<0.8$ and ${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$ and ${\mathrm{p}}_T>1.0\mathrm{GeV}/\mathrm{c}$, respectively. (b) Data on the pseudorapidity distribution, $\mathrm{d}\mathrm{N}/\mathrm{d}\eta$, at $\eta =0$ for charged particles with $|\eta |<0.8$ and ${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$ and (d) ${\mathrm{p}}_T>1.0\mathrm{GeV}/\mathrm{c}$ for events with at least one charged particle with $|\eta |<0.8$ and ${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$ and ${\mathrm{p}}_T>1.0\mathrm{GeV}/\mathrm{c}$, respectively, plotted versus the center-of-mass energy. The data are corrected to the particle level with errors that include both the statistical error and the systematic uncertainty and are compared with pythia 6.4 Tune Z1.

Figure 4

Data at 1.96 TeV (a,b), 900 GeV (c,d), and 300 GeV (e,f) on the average overall number of charged particles with $|\eta |<0.8$ and ${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$ (including the leading charged particle) for events with at least one charged particle with $|\eta |<0.8$ and ${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$ plotted versus the transverse momentum of the leading charged particle, PTmax. The horizontal dashed lines correspond to the average overall number of charged particles with $|\eta |<0.8$ and ${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$ for events with at least one charged particle with $|\eta |<0.8$ and ${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$ if one includes all PTmax values (see Table 2). The data are corrected to the particle level with errors that include both the statistical error and the systematic uncertainty, and are compared with pythia Tune Z1 and $Z{2}^{*}$ (a,c,e) and pythia Tune $Z{2}^{*}$ and $4{\mathrm{C}}^{*}$ (b,d,f).

Figure 5

Data at 1.96 TeV (a,b), 900 GeV (c,d), and 300 GeV (e,f) on the overall associated charged particle and charged PTsum density (${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$, $|\eta |<0.8$) as defined by the leading charged particle, as a function of the ${\mathrm{p}}_T$ of the leading charged particle, PTmax (where the vertical axis scale applies to both densities with appropriate units). The leading charged particle is not included in the overall associated density. The data are corrected to the particle level with errors that include both the statistical error and the systematic uncertainty, and are compared with pythia Tune Z1 and $Z{2}^{*}$ (a,c,e) and pythia Tune $Z{2}^{*}$ and $4{\mathrm{C}}^{*}$ (b,d,f).

Figure 6

Data at 1.96 TeV (a,b), 900 GeV (c,d), and 300 GeV (e,f) on the charged particle density (${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$, $|\eta |<0.8$) in the toward, away, and transverse regions as defined by the leading charged particle, as a function of the ${\mathrm{p}}_T$ of the leading charged particle, PTmax. The leading charged particle is not included in the toward density. The data are corrected to the particle level with errors that include both the statistical error and the systematic uncertainty, and are compared with pythia Tune Z1 and $Z{2}^{*}$ (a,c,e) and pythia Tune $Z{2}^{*}$ and $4{\mathrm{C}}^{*}$ (b,d,f).

Figure 7

Data at 1.96 TeV (a,b), 900 GeV (c,d), and 300 GeV (e,f) for the charged PTsum density (${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$, $|\eta |<0.8$) in the toward, away, and transverse regions as defined by the leading charged particle, as a function of the ${\mathrm{p}}_T$ of the leading charged particle, PTmax. The leading charged particle is not included in the toward density. The data are corrected to the particle level with errors that include both the statistical error and the systematic uncertainty, and are compared with pythia Tune Z1 and $Z{2}^{*}$ (a,c,e) and pythia Tune $Z{2}^{*}$ and $4{\mathrm{C}}^{*}$ (b,d,f).

Figure 8

Data at 1.96 TeV, 900 GeV, and 300 GeV on the charged particle density (${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$, $|\eta |<0.8$) in the toward (a,b) and away (c,d) regions as defined by the leading charged particle, as a function of the ${\mathrm{p}}_T$ of the leading charged particle, PTmax. The leading charged particle is not included in the toward density. The data are corrected to the particle level with errors that include both the statistical error and the systematic uncertainty, and are compared with pythia Tune Z1 and $Z{2}^{*}$ (a,c) and pythia Tune $Z{2}^{*}$ and $4{\mathrm{C}}^{*}$ (b,d).

Figure 9

Data at 1.96 TeV, 900 GeV, and 300 GeV on the charged PTsum density (${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$, $|\eta |<0.8$) in the toward (a,b) and away (c,d) regions as defined by the leading charged particle, as a function of the ${\mathrm{p}}_T$ of the leading charged particle, PTmax. The leading charged particle is not included in the toward density. The data are corrected to the particle level with errors that include both the statistical error and the systematic uncertainty, and are compared with pythia Tune Z1 and $Z{2}^{*}$ (a,c) and pythia Tune $Z{2}^{*}$ and $4{\mathrm{C}}^{*}$ (b,d).

Figure 10

Data at 1.96 TeV, 900 GeV, and 300 GeV on the charged particle density (${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$, $|\eta |<0.8$) in the transMAX (a,b) and transMIN (c,d) regions as defined by the leading charged particle, as a function of the ${\mathrm{p}}_T$ of the leading charged particle, PTmax. The data are corrected to the particle level with errors that include both the statistical error and the systematic uncertainty, and are compared with pythia Tune Z1 and $Z{2}^{*}$ (a,c) and pythia Tune $Z{2}^{*}$ and $4{\mathrm{C}}^{*}$ (b,d).

Figure 11

Data at 1.96 TeV, 900 GeV, and 300 GeV on the charged PTsum density (${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$, $|\eta |<0.8$) in the transMAX (a,b) and transMIN (c,d) regions as defined by the leading charged particle, as a function of the ${\mathrm{p}}_T$ of the leading charged particle, PTmax. The data are corrected to the particle level with errors that include both the statistical error and the systematic uncertainty, and are compared with pythia Tune Z1 and $Z{2}^{*}$ (a,c) and pythia Tune $Z{2}^{*}$ and $4{\mathrm{C}}^{*}$ (b,d).

Figure 12

Data at 1.96 TeV, 900 GeV, and 300 GeV on the charged particle density (${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$, $|\eta |<0.8$) for $\text{trans}\mathrm{AVE}=(\text{trans}\mathrm{MAX}+\text{trans}\mathrm{MIN})/2$ (a,b) and $\text{trans}\mathrm{DIF}=\text{trans}\mathrm{MAX}-\text{trans}\mathrm{MIN}$ (c,d) as defined by the leading charged particle, as a function of the ${\mathrm{p}}_T$ of the leading charged particle, PTmax. The data are corrected to the particle level with errors that include both the statistical error and the systematic uncertainty, and are compared with pythia Tune Z1 and $Z{2}^{*}$ (a,c) and pythia Tune $Z{2}^{*}$ and $4{\mathrm{C}}^{*}$ (b,d).

Figure 13

Data at 1.96 TeV, 900 GeV, and 300 GeV on the charged PTsum density (${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$, $|\eta |<0.8$) for $\text{trans}\mathrm{AVE}=(\text{trans}\mathrm{MAX}+\text{trans}\mathrm{MIN})/2$ (a,b) and $\text{trans}\mathrm{DIF}=\text{trans}\mathrm{MAX}-\text{trans}\mathrm{MIN}$ (c,d) as defined by the leading charged particle, as a function of the ${\mathrm{p}}_T$ of the leading charged particle, PTmax. The data are corrected to the particle level with errors that include both the statistical error and the systematic uncertainty, and are compared with pythia Tune Z1 and $Z{2}^{*}$ (a,c) and pythia Tune $Z{2}^{*}$ and $4{\mathrm{C}}^{*}$ (b,d).

Figure 14

(a,b) Data on the transMAX and transMIN charged particle density as defined by the leading charged particle, for $5.0<\mathrm{PT}\max <6.0\mathrm{GeV}/\mathrm{c}$ plotted versus the center-of-mass energy for charged particles with ${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$ and $|\eta |<0.8$. (c,d) Ratio of the data at 1.96 TeV, 900 GeV, and 300 GeV to the corresponding value at 300 GeV for the transMAX and transMIN charged particle density plotted versus the center-of-mass energy. The data are corrected to the particle level with errors that include both the statistical error and the systematic uncertainty, and are compared with pythia Tune Z1 and $Z{2}^{*}$ (a,c) and pythia Tune $Z{2}^{*}$ and $4{\mathrm{C}}^{*}$ (b,d). The theory curves include the predictions of the pythia tunes at 7 TeV.

Figure 15

(a,b) Data on the transMAX and transMIN charged PTsum density as defined by the leading charged particle, for $5.0<\mathrm{PT}\max <6.0\mathrm{GeV}/\mathrm{c}$ plotted versus the center-of-mass energy for charged particles with ${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$ and $|\eta |<0.8$. (c,d) Ratio of the data at 1.96 TeV, 900 GeV, and 300 GeV to the corresponding value at 300 GeV plotted versus the center-of-mass energy. The data are corrected to the particle level with errors that include both the statistical error and the systematic uncertainty, and are compared with pythia Tune Z1 and $Z{2}^{*}$ (a,c) and pythia Tune $Z{2}^{*}$ and $4{\mathrm{C}}^{*}$ (b,d). The theory curves include the predictions of the pythia tunes at 7 TeV.

Figure 16

(a,b) Data on the transAVE and transDIF charged particle density as defined by the leading charged particle, for $5.0<\mathrm{PT}\max <6.0\mathrm{GeV}/\mathrm{c}$ plotted versus the center-of-mass energy for charged particles with ${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$ and $|\eta |<0.8$. (c,d) Ratio of the data at 1.96 TeV, 900 GeV, and 300 GeV to the corresponding value at 300 GeV plotted versus the center-of-mass energy. The data are corrected to the particle level with errors that include both the statistical error and the systematic uncertainty, and are compared with pythia Tune Z1 and $Z{2}^{*}$ (a,c) and pythia Tune $Z{2}^{*}$ and $4{\mathrm{C}}^{*}$ (b,d). The theory curves include the predictions of the pythia tunes at 7 TeV.

Figure 17

(a,b) Data on the transAVE and transDIF charged PTsum density as defined by the leading charged particle, for $5.0<\mathrm{PT}\max <6.0\mathrm{GeV}/\mathrm{c}$ plotted versus the center-of-mass energy for charged particles with ${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$ and $|\eta |<0.8$. (c,d) Ratio of the data at 1.96 TeV, 900 GeV, and 300 GeV to the corresponding value at 300 GeV plotted versus the center-of-mass energy. The data are corrected to the particle level with errors that include both the statistical error and the systematic uncertainty, and are compared with pythia Tune Z1 and $Z{2}^{*}$ (a,c) and pythia Tune $Z{2}^{*}$ and $4{\mathrm{C}}^{*}$ (b,d). The theory curves include the predictions of the pythia tunes at 7 TeV.

Figure 18

Ratio of the data at 1.96 TeV, 900 GeV, and 300 GeV to the corresponding value at 300 GeV for the transMIN and transDIF charged particle density (a,b) and charged PTsum density (c,d) as defined by the leading charged particle, for $5.0<\mathrm{PT}\max <6.0\mathrm{GeV}/\mathrm{c}$ plotted versus the center-of-mass energy. The data are corrected to the particle level with errors that include both the statistical error and the systematic uncertainty, and are compared with pythia Tune Z1 and $Z{2}^{*}$ (a,c) and pythia Tune $Z{2}^{*}$ and $4{\mathrm{C}}^{*}$ (b,d). The theory curves include the predictions of the pythia tunes at 7 TeV.

Figure 19

(a,b) Data at 1.96 TeV, 900 GeV, and 300 GeV on the charged particle average ${\mathrm{p}}_T$ (${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$, $|\eta |<0.8$) in the transverse region as defined by the leading charged particle, as a function of the ${\mathrm{p}}_T$ of the leading charged particle, PTmax. (c,d) Data on the transverse charged particle average ${\mathrm{p}}_T$ as defined by the leading charged particle, for $5.0<\mathrm{PT}\max <6.0\mathrm{GeV}/\mathrm{c}$ plotted versus the center-of-mass energy for charged particles with ${\mathrm{p}}_T>0.5\mathrm{GeV}/\mathrm{c}$ and $|\eta |<0.8$. The data are corrected to the particle level with errors that include both the statistical error and the systematic uncertainty, and are compared with pythia Tune Z1 and $Z{2}^{*}$ (a,c) and pythia Tune $Z{2}^{*}$ and $4{\mathrm{C}}^{*}$ (b,d).