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CMS-PAS-HIN-23-010
Search for jet quenching signature using transverse momentum balance in high-multiplicity pPb collisions at the CMS detector
Abstract: The first measurement of the dijet transverse momentum balance ($ x_{j} $) in proton-lead (pPb) collisions at $ \sqrt{s_{\text{NN}}}= $ 8.16 TeV is presented. The analysis uses data collected by the CMS detector in 2016, corresponding to an integrated luminosity of 174.6 $ \,\text{nb}^\text{ $-1 $ } $. The $ x_{j} $ and its average are measured as functions of the event charged particle multiplicity for three different center-of-mass pseudorapidity configurations: forward, backward, and mid-rapidity, enabling measurements in both proton- and lead-going directions. High-multiplicity triggers are used to select events with up to 400 charged particles, aimed at probing potential jet quenching effects. The ratio of $ x_{j} $ in high- versus low-multiplicity events is used to quantify the results. All measurements are consistent with unity and are in good agreement with simulations of the hard scattering process that do not include quark-gluon plasma production. These results indicate no evidence of a jet quenching signature in small colliding systems, even in high-multiplicity events that exhibit the strongest signals of collectivity.
Figures Summary References CMS Publications
Figures

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Figure 1:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-a:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-b:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-c:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-d:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-e:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-f:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-g:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-h:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-i:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-j:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-k:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-l:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-m:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-n:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-o:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-p:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-q:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-r:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-s:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-t:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-u:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-v:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-w:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-x:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 1-y:
The measured $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-a:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-b:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-c:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-d:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-e:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-f:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-g:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-h:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-i:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-j:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-k:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-l:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-m:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-n:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-o:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-p:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-q:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-r:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-s:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-t:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-u:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-v:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-w:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-x:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 2-y:
The unfolded $ x_{j} $ distributions, from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparisons with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed. Simulations cannot be performed for the highest multiplicity range.

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Figure 3:
The measured $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 3-a:
The measured $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 3-b:
The measured $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 3-c:
The measured $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 3-d:
The measured $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 3-e:
The measured $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 3-f:
The measured $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 3-g:
The measured $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 3-h:
The measured $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 3-i:
The measured $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 3-j:
The measured $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 3-k:
The measured $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 3-l:
The measured $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 3-m:
The measured $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 3-n:
The measured $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 3-o:
The measured $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 3-p:
The measured $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 3-q:
The measured $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 3-r:
The measured $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 3-s:
The measured $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 3-t:
The measured $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 4:
The unfolded $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 4-a:
The unfolded $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 4-b:
The unfolded $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 4-c:
The unfolded $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

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Figure 4-d:
The unfolded $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

png pdf
Figure 4-e:
The unfolded $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

png pdf
Figure 4-f:
The unfolded $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

png pdf
Figure 4-g:
The unfolded $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

png pdf
Figure 4-h:
The unfolded $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

png pdf
Figure 4-i:
The unfolded $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

png pdf
Figure 4-j:
The unfolded $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

png pdf
Figure 4-k:
The unfolded $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

png pdf
Figure 4-l:
The unfolded $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

png pdf
Figure 4-m:
The unfolded $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

png pdf
Figure 4-n:
The unfolded $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

png pdf
Figure 4-o:
The unfolded $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

png pdf
Figure 4-p:
The unfolded $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

png pdf
Figure 4-q:
The unfolded $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

png pdf
Figure 4-r:
The unfolded $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

png pdf
Figure 4-s:
The unfolded $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

png pdf
Figure 4-t:
The unfolded $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60, from lower to higher multiplicities (left to right) for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed PYTHIA 8+EPOS simulation (grey band) are also displayed.

png pdf
Figure 5:
Mean $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60 as measured (left panel) and unfolded (right panel) for different multiplicities, for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed (left, grey band) and generator-level (right, grey band) PYTHIA 8+EPOS are also displayed.

png pdf
Figure 5-a:
Mean $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60 as measured (left panel) and unfolded (right panel) for different multiplicities, for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed (left, grey band) and generator-level (right, grey band) PYTHIA 8+EPOS are also displayed.

png pdf
Figure 5-b:
Mean $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60 as measured (left panel) and unfolded (right panel) for different multiplicities, for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed (left, grey band) and generator-level (right, grey band) PYTHIA 8+EPOS are also displayed.

png pdf
Figure 5-c:
Mean $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60 as measured (left panel) and unfolded (right panel) for different multiplicities, for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed (left, grey band) and generator-level (right, grey band) PYTHIA 8+EPOS are also displayed.

png pdf
Figure 5-d:
Mean $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60 as measured (left panel) and unfolded (right panel) for different multiplicities, for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed (left, grey band) and generator-level (right, grey band) PYTHIA 8+EPOS are also displayed.

png pdf
Figure 5-e:
Mean $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60 as measured (left panel) and unfolded (right panel) for different multiplicities, for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed (left, grey band) and generator-level (right, grey band) PYTHIA 8+EPOS are also displayed.

png pdf
Figure 5-f:
Mean $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60 as measured (left panel) and unfolded (right panel) for different multiplicities, for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed (left, grey band) and generator-level (right, grey band) PYTHIA 8+EPOS are also displayed.

png pdf
Figure 5-g:
Mean $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60 as measured (left panel) and unfolded (right panel) for different multiplicities, for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed (left, grey band) and generator-level (right, grey band) PYTHIA 8+EPOS are also displayed.

png pdf
Figure 5-h:
Mean $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60 as measured (left panel) and unfolded (right panel) for different multiplicities, for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed (left, grey band) and generator-level (right, grey band) PYTHIA 8+EPOS are also displayed.

png pdf
Figure 5-i:
Mean $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60 as measured (left panel) and unfolded (right panel) for different multiplicities, for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed (left, grey band) and generator-level (right, grey band) PYTHIA 8+EPOS are also displayed.

png pdf
Figure 5-j:
Mean $ x_{j} $ ratio in the range 10 $ < \text{N}_{\text{trk}}^{\text{offline}} < $ 60 as measured (left panel) and unfolded (right panel) for different multiplicities, for different leading and subleading jet combinations for the midrapidity, forward, and backward (top to bottom) regions, are shown. Comparison with the reconstructed (left, grey band) and generator-level (right, grey band) PYTHIA 8+EPOS are also displayed.

png pdf
Figure 6:
The unfolded response matrices, $ x_{j} $ (reconstructed) versus $ x_{j} $ (generated), from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations in the midrapidity, forward, and backward regions (top to bottom) are shown.

png pdf
Figure 6-a:
The unfolded response matrices, $ x_{j} $ (reconstructed) versus $ x_{j} $ (generated), from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations in the midrapidity, forward, and backward regions (top to bottom) are shown.

png pdf
Figure 6-b:
The unfolded response matrices, $ x_{j} $ (reconstructed) versus $ x_{j} $ (generated), from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations in the midrapidity, forward, and backward regions (top to bottom) are shown.

png pdf
Figure 6-c:
The unfolded response matrices, $ x_{j} $ (reconstructed) versus $ x_{j} $ (generated), from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations in the midrapidity, forward, and backward regions (top to bottom) are shown.

png pdf
Figure 6-d:
The unfolded response matrices, $ x_{j} $ (reconstructed) versus $ x_{j} $ (generated), from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations in the midrapidity, forward, and backward regions (top to bottom) are shown.

png pdf
Figure 6-e:
The unfolded response matrices, $ x_{j} $ (reconstructed) versus $ x_{j} $ (generated), from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations in the midrapidity, forward, and backward regions (top to bottom) are shown.

png pdf
Figure 6-f:
The unfolded response matrices, $ x_{j} $ (reconstructed) versus $ x_{j} $ (generated), from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations in the midrapidity, forward, and backward regions (top to bottom) are shown.

png pdf
Figure 6-g:
The unfolded response matrices, $ x_{j} $ (reconstructed) versus $ x_{j} $ (generated), from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations in the midrapidity, forward, and backward regions (top to bottom) are shown.

png pdf
Figure 6-h:
The unfolded response matrices, $ x_{j} $ (reconstructed) versus $ x_{j} $ (generated), from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations in the midrapidity, forward, and backward regions (top to bottom) are shown.

png pdf
Figure 6-i:
The unfolded response matrices, $ x_{j} $ (reconstructed) versus $ x_{j} $ (generated), from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations in the midrapidity, forward, and backward regions (top to bottom) are shown.

png pdf
Figure 6-j:
The unfolded response matrices, $ x_{j} $ (reconstructed) versus $ x_{j} $ (generated), from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations in the midrapidity, forward, and backward regions (top to bottom) are shown.

png pdf
Figure 6-k:
The unfolded response matrices, $ x_{j} $ (reconstructed) versus $ x_{j} $ (generated), from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations in the midrapidity, forward, and backward regions (top to bottom) are shown.

png pdf
Figure 6-l:
The unfolded response matrices, $ x_{j} $ (reconstructed) versus $ x_{j} $ (generated), from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations in the midrapidity, forward, and backward regions (top to bottom) are shown.

png pdf
Figure 6-m:
The unfolded response matrices, $ x_{j} $ (reconstructed) versus $ x_{j} $ (generated), from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations in the midrapidity, forward, and backward regions (top to bottom) are shown.

png pdf
Figure 6-n:
The unfolded response matrices, $ x_{j} $ (reconstructed) versus $ x_{j} $ (generated), from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations in the midrapidity, forward, and backward regions (top to bottom) are shown.

png pdf
Figure 6-o:
The unfolded response matrices, $ x_{j} $ (reconstructed) versus $ x_{j} $ (generated), from lower to higher multiplicities (left to right) and for different leading and subleading jet combinations in the midrapidity, forward, and backward regions (top to bottom) are shown.

png pdf
Figure 7:
Example of the reconstructed (red) and generator-level (black) $ x_{j} $ distributions for the multiplicity range 10--60, with both leading and subleading jets in the midrapidity region. The nominal PYTHIA8+EPOS distribution is shown on the left, while an oversampled PYTHIA8+EPOS distribution (without invariant $ p_{\mathrm{T}} $ rescaling) is shown on the right. The differences between the left and right plots are due to the different priors. To validate the unfolding method, the response matrix is produced using the priors from the right distribution, which is then reweighted and used to unfold the left distribution. The results of this process are shown in Fig. 8.

png pdf
Figure 7-a:
Example of the reconstructed (red) and generator-level (black) $ x_{j} $ distributions for the multiplicity range 10--60, with both leading and subleading jets in the midrapidity region. The nominal PYTHIA8+EPOS distribution is shown on the left, while an oversampled PYTHIA8+EPOS distribution (without invariant $ p_{\mathrm{T}} $ rescaling) is shown on the right. The differences between the left and right plots are due to the different priors. To validate the unfolding method, the response matrix is produced using the priors from the right distribution, which is then reweighted and used to unfold the left distribution. The results of this process are shown in Fig. 8.

png pdf
Figure 7-b:
Example of the reconstructed (red) and generator-level (black) $ x_{j} $ distributions for the multiplicity range 10--60, with both leading and subleading jets in the midrapidity region. The nominal PYTHIA8+EPOS distribution is shown on the left, while an oversampled PYTHIA8+EPOS distribution (without invariant $ p_{\mathrm{T}} $ rescaling) is shown on the right. The differences between the left and right plots are due to the different priors. To validate the unfolding method, the response matrix is produced using the priors from the right distribution, which is then reweighted and used to unfold the left distribution. The results of this process are shown in Fig. 8.

png pdf
Figure 8:
Validation of the unfolding method using reweighted probability distribution maps of the reconstructed leading and subleading jet transverse momentum from the priors shown in Fig. 7. The generator-level $ x_{j} $ is compared with the unfolded and reconstructed distributions for the multiplicity ranges 60--120 (left) and 185--250 (right), where both leading and subleading jets are in the midrapidity region. Ratios relative to the generator-level distributions are shown.

png pdf
Figure 8-a:
Validation of the unfolding method using reweighted probability distribution maps of the reconstructed leading and subleading jet transverse momentum from the priors shown in Fig. 7. The generator-level $ x_{j} $ is compared with the unfolded and reconstructed distributions for the multiplicity ranges 60--120 (left) and 185--250 (right), where both leading and subleading jets are in the midrapidity region. Ratios relative to the generator-level distributions are shown.

png pdf
Figure 8-b:
Validation of the unfolding method using reweighted probability distribution maps of the reconstructed leading and subleading jet transverse momentum from the priors shown in Fig. 7. The generator-level $ x_{j} $ is compared with the unfolded and reconstructed distributions for the multiplicity ranges 60--120 (left) and 185--250 (right), where both leading and subleading jets are in the midrapidity region. Ratios relative to the generator-level distributions are shown.
Summary
The CMS detector is used to study the dijet transverse momentum balance in proton-lead (pPb) collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} $ = 8.16 TeV as a function of event charged-particle multiplicity. The events are collected by minimum-bias and high-multiplicity triggers during the 2016 data-taking period, corresponding to an integrated luminosity of 174.6 $\,\text{nb}^{-1}$. An anti-$ k_{\mathrm{T}} $ algorithm with a distance parameter of 0.4 is used to reconstruct jets based on the combined tracker and calorimeter information. Back-to-back dijets are selected by requiring the difference in azimuthal angle between the leading and subleading jets to be greater than $ (5/6)\pi $ and their transverse momenta to be greater than 100 and 50 GeV, respectively. The transverse momentum balance is measured as a function of multiplicity for different pseudorapidity configurations by taking the ratio of subleading to leading jet transverse momentum. The average transverse momentum balance and the ratios between higher and lower multiplicity ranges are also calculated. The high-to-low multiplicity ratios of the average momentum balance are close to unity, and the results are in good agreement with simulations that do not include jet quenching effects. This measurement indicates no evidence of a jet quenching signature in high-multiplicity pPb collisions, confirming that the observed dijet transverse momentum imbalance in lead-lead collisions does not originate from initial-state effects.
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Compact Muon Solenoid
LHC, CERN