CMS-SMP-17-008 ; CERN-EP-2020-251 | ||
Measurements of angular distance and momentum ratio distributions in three-jet and Z $+$ two-jet final states in pp collisions | ||
CMS Collaboration | ||
17 February 2021 | ||
Eur. Phys. J. C 81 (2021) 852 | ||
Abstract: Collinear (small-angle) and large-angle, as well as soft and hard radiations are investigated in three-jet and Z $+$ two-jet events collected in proton-proton collisions at the LHC. The normalized production cross sections are measured as a function of the ratio of transverse momenta of two jets and their angular separation. The measurements in the three-jet and Z $+$ two-jet events are based on data collected at a center-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 19.8 fb$^{-1}$. The Z $+$ two-jet events are reconstructed in the dimuon decay channel of the Z boson. The three-jet measurement is extended to include $\sqrt{s} = $ 13 TeV data corresponding to an integrated luminosity of 2.3 fb$^{-1}$. The results are compared to predictions from event generators that include parton showers, multiple parton interactions, and hadronization. The collinear and soft regions are in general well described by parton showers, whereas the regions of large angular separation are often best described by calculations using higher-order matrix elements. | ||
Links: e-print arXiv:2102.08816 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; |
Figures | |
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Figure 1:
Four categories of parton radiation. (a) soft and small-angle radiation, (b) hard and small-angle radiation, (c) soft and large-angle radiation, (d) hard and large-angle radiation. |
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Figure 2:
Three-jet events at $\sqrt {s} = $ 8 TeV compared to theory: (left) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ for small-angle radiation ($ {\Delta R_{23}} < $ 1.0), (right) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ for large-angle radiation ($ {\Delta R_{23}} > $ 1.0). |
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Figure 2-a:
Three-jet events at $\sqrt {s} = $ 8 TeV compared to theory: ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ for small-angle radiation ($ {\Delta R_{23}} < $ 1.0). |
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Figure 2-b:
Three-jet events at $\sqrt {s} = $ 8 TeV compared to theory: ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ for large-angle radiation ($ {\Delta R_{23}} > $ 1.0). |
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Figure 3:
Three-jet events at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions: (left) ${\Delta R_{23}}$ for soft radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} < $ 0.3), (right) ${\Delta R_{23}}$ for hard radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} > $ 0.6). |
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Figure 3-a:
Three-jet events at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions: ${\Delta R_{23}}$ for soft radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} < $ 0.3). |
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Figure 3-b:
Three-jet events at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions: ${\Delta R_{23}}$ for hard radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} > $ 0.6). |
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Figure 4:
Three-jet events at $\sqrt {s} = $ 13 TeV compared to theory: (left) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ for small-angle radiation ($ {\Delta R_{23}} < $ 1.0), (right) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ for large-angle radiation ($ {\Delta R_{23}} > $ 1.0). |
png pdf |
Figure 4-a:
Three-jet events at $\sqrt {s} = $ 13 TeV compared to theory: ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ for small-angle radiation ($ {\Delta R_{23}} < $ 1.0). |
png pdf |
Figure 4-b:
Three-jet events at $\sqrt {s} = $ 13 TeV compared to theory: ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ for large-angle radiation ($ {\Delta R_{23}} > $ 1.0). |
png pdf |
Figure 5:
Three-jet events at $\sqrt {s} = $ 13 TeV and comparison to theoretical predictions: (left) ${\Delta R_{23}}$ for soft radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} < $ 0.3), (right) ${\Delta R_{23}}$ for hard radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} > $ 0.6). |
png pdf |
Figure 5-a:
Three-jet events at $\sqrt {s} = $ 13 TeV and comparison to theoretical predictions: ${\Delta R_{23}}$ for hard radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} > $ 0.6). |
png pdf |
Figure 5-b:
Three-jet events at $\sqrt {s} = $ 13 TeV and comparison to theoretical predictions: ${\Delta R_{23}}$ for soft radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} < $ 0.3). |
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Figure 6:
Z $+$ two-jet events at $\sqrt {s} = $ 8 TeV compared to theory: (left) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ for small-angle radiation ($ {\Delta R_{23}} < $ 1.0), (right) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ for large-angle radiation ($ {\Delta R_{23}} > $ 1.0). |
png pdf |
Figure 6-a:
Z $+$ two-jet events at $\sqrt {s} = $ 8 TeV compared to theory: (left) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ for small-angle radiation ($ {\Delta R_{23}} < $ 1.0), (right) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ for large-angle radiation ($ {\Delta R_{23}} > $ 1.0). |
png pdf |
Figure 6-b:
Z $+$ two-jet events at $\sqrt {s} = $ 8 TeV compared to theory: (left) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ for small-angle radiation ($ {\Delta R_{23}} < $ 1.0), (right) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ for large-angle radiation ($ {\Delta R_{23}} > $ 1.0). |
png pdf |
Figure 7:
Z $+$ two-jet events at $\sqrt {s} = $ 8 TeV compared to theory: (left) ${\Delta R_{23}}$ for soft radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} < $ 0.3), (right) ${\Delta R_{23}}$ for hard radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} > $ 0.6). |
png pdf |
Figure 7-a:
Z $+$ two-jet events at $\sqrt {s} = $ 8 TeV compared to theory: (left) ${\Delta R_{23}}$ for soft radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} < $ 0.3), (right) ${\Delta R_{23}}$ for hard radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} > $ 0.6). |
png pdf |
Figure 7-b:
Z $+$ two-jet events at $\sqrt {s} = $ 8 TeV compared to theory: (left) ${\Delta R_{23}}$ for soft radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} < $ 0.3), (right) ${\Delta R_{23}}$ for hard radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} > $ 0.6). |
png pdf |
Figure 8:
Z $+$ two-jet events at $\sqrt {s} = $ 8 TeV compared to theoretical predictions from {pythia} 8 without initial-state parton showers (IPS), final-state parton showers (FPS), and MPI: (left) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ for small-angle radiation ($ {\Delta R_{23}} < $ 1.0), (right) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ for large-angle radiation ($ {\Delta R_{23}} > $ 1.0). |
png pdf |
Figure 8-a:
Z $+$ two-jet events at $\sqrt {s} = $ 8 TeV compared to theoretical predictions from {pythia} 8 without initial-state parton showers (IPS), final-state parton showers (FPS), and MPI: (left) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ for small-angle radiation ($ {\Delta R_{23}} < $ 1.0), (right) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ for large-angle radiation ($ {\Delta R_{23}} > $ 1.0). |
png pdf |
Figure 8-b:
Z $+$ two-jet events at $\sqrt {s} = $ 8 TeV compared to theoretical predictions from {pythia} 8 without initial-state parton showers (IPS), final-state parton showers (FPS), and MPI: (left) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ for small-angle radiation ($ {\Delta R_{23}} < $ 1.0), (right) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ for large-angle radiation ($ {\Delta R_{23}} > $ 1.0). |
png pdf |
Figure 9:
Z $+$ two-jet events at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions from {pythia} 8 without initial-state parton showers (IPS), final-state parton showers (FPS), and MPI: (left) ${\Delta R_{23}}$ for soft radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} < $ 0.3), (right) ${\Delta R_{23}}$ for hard radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} > $ 0.6). |
png pdf |
Figure 9-a:
Z $+$ two-jet events at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions from {pythia} 8 without initial-state parton showers (IPS), final-state parton showers (FPS), and MPI: (left) ${\Delta R_{23}}$ for soft radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} < $ 0.3), (right) ${\Delta R_{23}}$ for hard radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} > $ 0.6). |
png pdf |
Figure 9-b:
Z $+$ two-jet events at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions from {pythia} 8 without initial-state parton showers (IPS), final-state parton showers (FPS), and MPI: (left) ${\Delta R_{23}}$ for soft radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} < $ 0.3), (right) ${\Delta R_{23}}$ for hard radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} > $ 0.6). |
Tables | |
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Table 1:
Phase space selection for the three-jet and Z $+$ two-jet analyses. |
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Table 2:
Event generator versions, PDF sets, and tunes used to produce MC samples at reconstruction level. |
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Table 3:
MC event generators and version numbers, parton-level processes, PDF sets, and UE tunes used for the comparison with measurements. |
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Table 4:
Systematic uncertainties in the measurements in %. |
Summary |
Two kinematic variables are introduced to quantify the radiation pattern in multijet events: (i) the transverse momentum ratio (${p_{\mathrm{T3}} /p_{\mathrm{T2}}})$ of two jets, and (ii) their angular separation ($\delta R_{23}$). The variable ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ is used to distinguish between soft and hard radiation, while $\delta R_{23}$ classifies events into small- and large-angle radiation types. Events with three or more energetic jets as well as inclusive Z $+$ two-jet events are selected for study using data collected at $\sqrt{s} = $ 8 TeV corresponding to an integrated luminosity of 19.8 fb$^{-1}$. Three-jet events at $\sqrt{s} = $ 13 TeV corresponding to an integrated luminosity of 2.3 fb$^{-1}$ are also analyzed. No significant dependence on the center-of-mass energy is observed in the differential distributions of ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ and $\delta R_{23}$. Overall, large-angle radiation (large $\delta R_{23}$) and hard radiation (large ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$) are well described by the matrix element (ME) calculations (using LO 4j+PS\ formulations), while the parton shower (PS) approach (LO 2j+PS\ and NLO 2j+PS) fail to describe the regions of large-angle and hard radiation. The collinear region (small $\delta R_{23}$) is not well described; LO 2j+PS, NLO 2j+PS, and LO 4j+PS\ distributions show deviations from the measurements. In the soft region (small ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$), the PS approach describes the measurement also in the large-angle region (full range in $\delta R_{23}$), while for large ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ higher-order ME contributions are needed to describe the three-jet measurements. The distributions in Z $+$ two-jet events are reasonably described by all tested generators. Nevertheless, we find an underestimation of third-jet emission at large ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ both in the collinear and large-angle regions, for all of the tested models. These results illustrate how well the collinear/soft, and large-angle/hard regions are described by different approaches. The different kinematic regions and initial-state flavor composition may be the reason why the three-jet measurements are less consistent with the theoretical predictions relative to the Z $+$ two-jet final states. These results clearly indicate that the methods of merging ME with PS calculations are not yet optimal for describing the full region of phase space. |
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