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| CMS-PAS-HIN-24-024 | ||
| Unveiling the dynamics of long-range correlations in high-multiplicity jets through substructure engineering in pp collisions at CMS | ||
| CMS Collaboration | ||
| 28 April 2025 | ||
| Abstract: Recent CMS data have revealed long-range correlations at high charged-particle multiplicity ($ N_\text{ch}^\mathrm{j} $) within jets produced in proton-proton (pp) collisions, suggesting collective behavior in systems much smaller than those typical of heavy ion collisions. In the polar coordinate system about the reconstructed jet axis, two-particle azimuthal correlations show an unexpected rise in elliptic anisotropy ($ v^{*}_2 $) at large pseudorapidity separations ($ \Delta\eta^{*} > $ 2) as a function of $ N_\text{ch}^\mathrm{j} $, a trend not reproduced by event generators like PYTHIA or SHERPA. In this paper, we present detailed measurements of long-range correlations using LHC Run 2 data at $ \sqrt{s} = $ 13 TeV and compare the results with model predictions. The transverse momentum and $ \Delta\eta^{*} $dependence of $ v^{*}_2 $ is shown across a wide range in $ N_\text{ch}^\mathrm{j} $. Furthermore, the role of jet substructure, particularly in jets exhibiting two-prong features, is examined to unveil a potential connection between the $ v^{*}_2 $ enhancement and the initial-state jet geometry. A surprising increase in $ v^{*}_2 $ emerges exclusively in these two-prong jets at high $ N_\text{ch}^\mathrm{j} $. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Schematic representation of jets in the ``jet frame,'' a coordinate system where the $ z $-axis is aligned with the jet momentum direction. Left: illustration of a jet exhibiting two sub-jets with unequal momentum magnitudes. Right: illustration of a jet with two sub-jets of approximately equal momentum magnitudes, also referred to as a two-prong jet. |
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Figure 2:
The 2D two-particle angular correlation functions in the jet frame for trigger particles with 0.7 $ < j_{\mathrm{T}}^{\text{trg}} < $ 1.3 GeV and associated particles with 0.3 $ < j_{\mathrm{T}}^{\text{assoc.}} < $ 3.0 GeV. Results are shown for low-$ N_\text{ch}^\mathrm{j} $ (left) and high-$ N_\text{ch}^\mathrm{j} $ (right) jets. The jets are reconstructed using the anti-$ k_{\mathrm{T}} $ algorithm with $ \mathrm{R}= $ 0.8, requiring $ p_{\mathrm{T}}^{\rm jet} > $ 550 GeV and $ |\eta^{\rm jet}| < $ 1.6. |
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Figure 2-a:
The 2D two-particle angular correlation functions in the jet frame for trigger particles with 0.7 $ < j_{\mathrm{T}}^{\text{trg}} < $ 1.3 GeV and associated particles with 0.3 $ < j_{\mathrm{T}}^{\text{assoc.}} < $ 3.0 GeV. Results are shown for low-$ N_\text{ch}^\mathrm{j} $ (left) and high-$ N_\text{ch}^\mathrm{j} $ (right) jets. The jets are reconstructed using the anti-$ k_{\mathrm{T}} $ algorithm with $ \mathrm{R}= $ 0.8, requiring $ p_{\mathrm{T}}^{\rm jet} > $ 550 GeV and $ |\eta^{\rm jet}| < $ 1.6. |
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Figure 2-b:
The 2D two-particle angular correlation functions in the jet frame for trigger particles with 0.7 $ < j_{\mathrm{T}}^{\text{trg}} < $ 1.3 GeV and associated particles with 0.3 $ < j_{\mathrm{T}}^{\text{assoc.}} < $ 3.0 GeV. Results are shown for low-$ N_\text{ch}^\mathrm{j} $ (left) and high-$ N_\text{ch}^\mathrm{j} $ (right) jets. The jets are reconstructed using the anti-$ k_{\mathrm{T}} $ algorithm with $ \mathrm{R}= $ 0.8, requiring $ p_{\mathrm{T}}^{\rm jet} > $ 550 GeV and $ |\eta^{\rm jet}| < $ 1.6. |
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Figure 3:
The elliptic anisotropy coefficient $ v^{\ast}_2 $, obtained from two-particle correlations, as a function of the minimum $ \Delta\eta^{\ast} $ limit for eight $ N_\text{ch}^\mathrm{j} $ intervals. Results correspond to anti-$ k_{\mathrm{T}} \mathrm{R}= $ 0.8 jets with $ p_{\mathrm{T}}^{\rm jet} > $ 550 GeV and $ |\eta^{\rm jet}| < $ 1.6 in pp collisions at 13 TeV. Data points include statistical uncertainties (vertical bars), while systematic uncertainties are represented by shaded boxes. The shaded envelope around the PYTHIA8 model curves indicates statistical uncertainty. |
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Figure 4:
Average $ j_{\mathrm{T}} $\ of charged particles inside jets as a function of $ N_\text{ch}^\mathrm{j} $\ corrresponding to $ \eta^{\ast} < $ 2 (black) and $ \eta^{\ast} < $ 5 (red), for anti-$ k_{\mathrm{T}} \mathrm{R}= $ 0.8 jets with $ p_{\mathrm{T}}^{\rm jet} > $ 550 GeV and $ |\eta^{\rm jet}| < $ 1.6 in pp collisions at 13 TeV from data and PYTHIA8. Vertical bars on data points indicate statistical uncertainties, while shaded boxes represent systematic uncertainties. |
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Figure 5:
The first- and-third order two-particle Fourier coefficients, $ V^{\ast}_{\text{1}\Delta} $ (red) and $ V^{\ast}_{\text{3}\Delta} $ (blue), as a function of $ j_{\mathrm{T}}^{\text{trg}} $ for different $ N_\text{ch}^\mathrm{j} $ intervals, with associated particles in the range 0.3 $ < j_{\mathrm{T}}^{\text{assoc.}} < $ 3 GeV. Results are shown for anti-$ k_{\mathrm{T}} \mathrm{R}= $ 0.8 jets with $ p_{\mathrm{T}}^{\rm jet} > $ 550 GeV and $ |\eta^{\rm jet}| < $ 1.6 in pp collisions at $ \sqrt{s} = $ 13 TeV, comparing data with PYTHIA8 predictions. |
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Figure 6:
The second-order two-particle Fourier coefficient, $ V^{\ast}_{\text{2}\Delta} $, as a function of $ j_{\mathrm{T}}^{\text{trg}} $ for different $ N_\text{ch}^\mathrm{j} $ ranges, with associated particles in the range 0.3 $ < j_{\mathrm{T}}^{\text{assoc.}} < $ 3 GeV. Results are shown for anti-$ k_{\mathrm{T}} \mathrm{R}= $ 0.8 jets with $ p_{\mathrm{T}}^{\rm jet} > $ 550 GeV and $ |\eta^{\rm jet}| < $ 1.6 in pp collisions at $ \sqrt{s} = $ 13 TeV, comparing data with PYTHIA8 predictions. |
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Figure 7:
Average $ z_g\theta_g^\beta $ as a function of $ N_\text{ch}^\mathrm{j} $, for anti-$ k_{\mathrm{T}} \mathrm{R}= $ 0.8 jets with $ p_{\mathrm{T}}^{\rm jet} > $ 550 GeV and $ |\eta^{\rm jet}| < $ 1.6 in pp collisions at 13 TeV from data and PYTHIA8. Shaded boxes represent systematic uncertainties, while statistical uncertainties are smaller than the marker size. |
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Figure 8:
The 2D two-particle angular correlation functions in the jet frame for charged particles with 0.3 $ < j_{\mathrm{T}} < $ 3.0 GeV. Results are shown for low-$ N_\text{ch}^\mathrm{j} $ (left) and high-$ N_\text{ch}^\mathrm{j} $ (right) jets, with further classification based on the jet substructure variable: $ z_g\theta_g^\beta < $ 0.25 (top) or $ z_g\theta_g^\beta > $ 0.25 (bottom). The jets are reconstructed using the anti-$ k_{\mathrm{T}} $ algorithm with $ \mathrm{R}= $ 0.8, requiring $ p_{\mathrm{T}}^{\rm jet} > $ 550 GeV and $ |\eta^{\rm jet}| < $ 1.6. |
png pdf |
Figure 8-a:
The 2D two-particle angular correlation functions in the jet frame for charged particles with 0.3 $ < j_{\mathrm{T}} < $ 3.0 GeV. Results are shown for low-$ N_\text{ch}^\mathrm{j} $ (left) and high-$ N_\text{ch}^\mathrm{j} $ (right) jets, with further classification based on the jet substructure variable: $ z_g\theta_g^\beta < $ 0.25 (top) or $ z_g\theta_g^\beta > $ 0.25 (bottom). The jets are reconstructed using the anti-$ k_{\mathrm{T}} $ algorithm with $ \mathrm{R}= $ 0.8, requiring $ p_{\mathrm{T}}^{\rm jet} > $ 550 GeV and $ |\eta^{\rm jet}| < $ 1.6. |
png pdf |
Figure 8-b:
The 2D two-particle angular correlation functions in the jet frame for charged particles with 0.3 $ < j_{\mathrm{T}} < $ 3.0 GeV. Results are shown for low-$ N_\text{ch}^\mathrm{j} $ (left) and high-$ N_\text{ch}^\mathrm{j} $ (right) jets, with further classification based on the jet substructure variable: $ z_g\theta_g^\beta < $ 0.25 (top) or $ z_g\theta_g^\beta > $ 0.25 (bottom). The jets are reconstructed using the anti-$ k_{\mathrm{T}} $ algorithm with $ \mathrm{R}= $ 0.8, requiring $ p_{\mathrm{T}}^{\rm jet} > $ 550 GeV and $ |\eta^{\rm jet}| < $ 1.6. |
png pdf |
Figure 8-c:
The 2D two-particle angular correlation functions in the jet frame for charged particles with 0.3 $ < j_{\mathrm{T}} < $ 3.0 GeV. Results are shown for low-$ N_\text{ch}^\mathrm{j} $ (left) and high-$ N_\text{ch}^\mathrm{j} $ (right) jets, with further classification based on the jet substructure variable: $ z_g\theta_g^\beta < $ 0.25 (top) or $ z_g\theta_g^\beta > $ 0.25 (bottom). The jets are reconstructed using the anti-$ k_{\mathrm{T}} $ algorithm with $ \mathrm{R}= $ 0.8, requiring $ p_{\mathrm{T}}^{\rm jet} > $ 550 GeV and $ |\eta^{\rm jet}| < $ 1.6. |
png pdf |
Figure 8-d:
The 2D two-particle angular correlation functions in the jet frame for charged particles with 0.3 $ < j_{\mathrm{T}} < $ 3.0 GeV. Results are shown for low-$ N_\text{ch}^\mathrm{j} $ (left) and high-$ N_\text{ch}^\mathrm{j} $ (right) jets, with further classification based on the jet substructure variable: $ z_g\theta_g^\beta < $ 0.25 (top) or $ z_g\theta_g^\beta > $ 0.25 (bottom). The jets are reconstructed using the anti-$ k_{\mathrm{T}} $ algorithm with $ \mathrm{R}= $ 0.8, requiring $ p_{\mathrm{T}}^{\rm jet} > $ 550 GeV and $ |\eta^{\rm jet}| < $ 1.6. |
png pdf |
Figure 9:
The elliptic anisotropy $ v^{\ast}_2 $, obtained from two-particle correlations, as a function of $ N_\text{ch}^\mathrm{j} $ for two jet substructure classes, $ z_g\theta_g^\beta < $ 0.25 (red) and $ z_g\theta_g^\beta > $ 0.25 (blue). Results are presented for two transverse momentum ranges, 0.3 $ < j_{\mathrm{T}} < $ 3 GeV (left) and 0.5 $ < j_{\mathrm{T}} < $ 3 GeV (right), using anti-$ k_{\mathrm{T}} $ jets with $ \mathrm{R}= $ 0.8, $ p_{\mathrm{T}}^{\rm jet} > $ 550 GeV, and $ |\eta^{\rm jet}| < $ 1.6 in pp collisions at $ \sqrt{s} = $ 13 TeV. The data points include statistical uncertainties (vertical bars), while systematic uncertainties are indicated by shaded boxes. The shaded envelopes around the PYTHIA8 curves represent statistical uncertainties. |
| Summary |
| In this paper, we present a systematic investigation of the long-range azimuthal anisotropy observed in high-multiplicity jets produced in proton-proton collisions using data collected by the CMS experiment at $ \sqrt{s}= $ 13 TeV. The second-order Fourier coefficient ($ v^{\ast}_2 $) is studied in a jet-centric reference frame, revealing a clear dependence on both the jet multiplicity and transverse momentum of constituent particles. The most pronounced anisotropy signal is found for particles with higher transverse momentum. Additionally, the $ v^{\ast}_2 $ dependence on the pseudorapidity separation ($ \Delta\eta^{\ast} $) exhibits contrasting behavior for different jet multiplicities: for low-multiplicity jets, $ v^{\ast}_2 $ shows a monotonic decrease with increasing $ |\Delta\eta^{\ast}| $, whereas for high-multiplicity jets, it appears to saturate and remains approximately constant for $ |\Delta\eta^{\ast}| > $ 2. The predictions from PYTHIA8 Monte-Carlo simulations are generally in agreement with the measured trends in the low-multiplicity regime. For high-multiplicity jets, a significant deviation from PYTHIA8 predictions is observed, hinting at the presence of a novel underlying mechanism. Further investigation into the jet substructure reveals that $ v^{\ast}_2 $ is more pronounced in jets exhibiting a two-prong structure, indicating a potential connection between the jet shape and the emergence of collective effects. The two-prong topology is consistent with hard splitting of the initial-state parton, leading to a wider energy distribution within the jet. Thus, the substructure-dependent $ v^{\ast}_2 $ enhancement may suggest that the long-range correlations could originate from intrinsic partonic dynamics together with final-state interactions. While PYTHIA8 serves as a valuable baseline model, its treatment of higher order perturbative quantum chromodynamics processes, particularly those involving multijet production, may introduce uncertainties in its comparison with the observed high-multiplicity jet phenomena. This will be further explored in future works to establish possible new insights into the interplay of jet fragmentation, partonic geometry, and potential medium-like effects. |
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