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| CMS-HIN-22-004 ; CERN-EP-2025-290 | ||
| Dependence of two-particle azimuthal correlations on the forward rapidity gap width in $ \mathrm{p}\text{Pb} $ collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV | ||
| CMS Collaboration | ||
| 29 May 2026 | ||
| Submitted to Physical Review C | ||
| Abstract: One of the most striking features of relativistic heavy ion collisions is the presence of collective flow of thousands of produced particles. This flow can be characterized by the Fourier coefficients ($ {V_{n\Delta}} $) of the azimuthal angular distributions of charged particles, and its existence can be explained by the formation of a quark gluon plasma, which behaves as a fluid. Surprisingly, the angular distributions of particles from very small systems such as proton-lead ($ \mathrm{p}\text{Pb} $), proton-proton (pp), electron-positron, and photon-proton ($ \gamma\mathrm{p} $) collisions also exhibit non-zero Fourier coefficients, raising the question of whether collective flow is present. This paper presents measurements of $ {V_{n\Delta}} $ from a sample of $ \mathrm{p}\text{Pb} $ events at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 8.16 TeV that are enriched in photon-lead ($ \gamma\text{Pb} $) and pomeron-lead ($ \mathbb{P} \mathrm{p} $) interactions by requiring no particles in the proton-going region. Measurements are made as a function of the forward rapidity gap width (the rapidity range in which no particles are found), the transverse momentum of the particles, and the multiplicity of particles in the event. The results are compared to previous measurements of pp, $ \mathrm{p}\text{Pb} $, and $ \gamma\mathrm{p}+\mathbb{P} \mathrm{p} $ events as well as modern event generators. | ||
| Links: e-print arXiv:2606.00171 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Sketch of a single-diffractive $ \mathrm{p}\text{Pb} $ event (left). The interaction proceeds via the exchange of a pomeron ($ \mathbb{P} $); the proton remains intact or dissociates into a low-mass state, and the nucleus breaks up (X). A single-diffractive event as seen in the detector (right). Activity is observed only in one side of the detector and a large forward rapidity gap ($ {\Delta\eta^{\mathrm{F}} } $) is present. The blue cone represents the outgoing particles from the interaction, while the blue shading indicates the detected activity. Both diagrams are extracted from Ref. [52]. |
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Figure 1-a:
Sketch of a single-diffractive $ \mathrm{p}\text{Pb} $ event (left). The interaction proceeds via the exchange of a pomeron ($ \mathbb{P} $); the proton remains intact or dissociates into a low-mass state, and the nucleus breaks up (X). A single-diffractive event as seen in the detector (right). Activity is observed only in one side of the detector and a large forward rapidity gap ($ {\Delta\eta^{\mathrm{F}} } $) is present. The blue cone represents the outgoing particles from the interaction, while the blue shading indicates the detected activity. Both diagrams are extracted from Ref. [52]. |
png pdf |
Figure 1-b:
Sketch of a single-diffractive $ \mathrm{p}\text{Pb} $ event (left). The interaction proceeds via the exchange of a pomeron ($ \mathbb{P} $); the proton remains intact or dissociates into a low-mass state, and the nucleus breaks up (X). A single-diffractive event as seen in the detector (right). Activity is observed only in one side of the detector and a large forward rapidity gap ($ {\Delta\eta^{\mathrm{F}} } $) is present. The blue cone represents the outgoing particles from the interaction, while the blue shading indicates the detected activity. Both diagrams are extracted from Ref. [52]. |
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Figure 2:
The $ N_{\text{trk}}^{\text{offline}} $ spectra for inclusive $ \mathrm{p}\text{Pb} $ events (labeled ``$ \mathrm{p}\text{Pb} $'', from Ref. [45]) and events from the nominal sample in different $ {\Delta\eta^{\mathrm{F}} } $ bins. The data points are located in the center of the bin of their corresponding $ N_{\text{trk}}^{\text{offline}} $ category. The vertical bars indicate the size of the statistical uncertainties. |
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Figure 3:
The $ N_{\text{trk}}^{\text{offline}} $ spectra for inclusive $ \mathrm{p}\text{Pb} $ events (labeled ``$ \mathrm{p}\text{Pb} $'', from Ref. [45]) and inclusive diffraction-enhanced events (labeled ``Data (diff. enh.)''). The distribution for the inclusive diffraction-enhanced events is the same as that shown in orange in Fig. 2 ($ {\Delta\eta^{\mathrm{F}} } > $ 2.5). Predictions based on weighting the data by the fractional cross sections from EPOS-LHC are also shown. The lower panel shows the ratio of the predictions to the data. The vertical bars indicate the size of the statistical uncertainties. |
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Figure 4:
The 2D correlation distribution for multiplicity (left) and its projection on the $ {\Delta\phi} $ axis (right) for $ |{\Delta\eta}| > $ 2, 2 $ \leq N_{\text{trk}}^{\text{offline}} < $ 40, and 0.3 $ < p_{\mathrm{T}}^{\text{trig}} < $ 3.0 GeV. The filled circles indicate the data and the vertical bars indicate the size of the statistical uncertainties. The one-dimensional $ {\Delta\phi} $ distributions are symmetrized by construction around $ {\Delta\phi} = $ 0 and $ {\Delta\phi} = \pi $, so all the data are contained in $ [0, \pi] $ and are averaged over $ |{\Delta\eta}| > $ 2. The plotted range in $ {\Delta\phi} $ extends to $ [-\pi, 3\pi/2] $ for visualization purposes. The Fourier coefficients $ {V_{n\Delta}} $ are fitted over the $ {\Delta\phi} $ range $ [0, \pi] $. The dashed lines show the resulting components $ {V_{1\Delta}} $, $ {V_{2\Delta}} $, and $ {V_{3\Delta}} $, along with the fitted values and statistical uncertainties. |
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Figure 4-a:
The 2D correlation distribution for multiplicity (left) and its projection on the $ {\Delta\phi} $ axis (right) for $ |{\Delta\eta}| > $ 2, 2 $ \leq N_{\text{trk}}^{\text{offline}} < $ 40, and 0.3 $ < p_{\mathrm{T}}^{\text{trig}} < $ 3.0 GeV. The filled circles indicate the data and the vertical bars indicate the size of the statistical uncertainties. The one-dimensional $ {\Delta\phi} $ distributions are symmetrized by construction around $ {\Delta\phi} = $ 0 and $ {\Delta\phi} = \pi $, so all the data are contained in $ [0, \pi] $ and are averaged over $ |{\Delta\eta}| > $ 2. The plotted range in $ {\Delta\phi} $ extends to $ [-\pi, 3\pi/2] $ for visualization purposes. The Fourier coefficients $ {V_{n\Delta}} $ are fitted over the $ {\Delta\phi} $ range $ [0, \pi] $. The dashed lines show the resulting components $ {V_{1\Delta}} $, $ {V_{2\Delta}} $, and $ {V_{3\Delta}} $, along with the fitted values and statistical uncertainties. |
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Figure 4-b:
The 2D correlation distribution for multiplicity (left) and its projection on the $ {\Delta\phi} $ axis (right) for $ |{\Delta\eta}| > $ 2, 2 $ \leq N_{\text{trk}}^{\text{offline}} < $ 40, and 0.3 $ < p_{\mathrm{T}}^{\text{trig}} < $ 3.0 GeV. The filled circles indicate the data and the vertical bars indicate the size of the statistical uncertainties. The one-dimensional $ {\Delta\phi} $ distributions are symmetrized by construction around $ {\Delta\phi} = $ 0 and $ {\Delta\phi} = \pi $, so all the data are contained in $ [0, \pi] $ and are averaged over $ |{\Delta\eta}| > $ 2. The plotted range in $ {\Delta\phi} $ extends to $ [-\pi, 3\pi/2] $ for visualization purposes. The Fourier coefficients $ {V_{n\Delta}} $ are fitted over the $ {\Delta\phi} $ range $ [0, \pi] $. The dashed lines show the resulting components $ {V_{1\Delta}} $, $ {V_{2\Delta}} $, and $ {V_{3\Delta}} $, along with the fitted values and statistical uncertainties. |
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Figure 5:
Summary of measurements of $ {V_{1\Delta}} $ (left) and $ {V_{2\Delta}} $ (right) as a function of $ {\Delta\eta^{\mathrm{F}} } $. The results are for tracks with 0.3 $ < p_{\mathrm{T}}^{\text{trig}} < $ 3.0 GeV. The filled circles indicate the data. The open triangles indicate the simulation, in blue for PYTHIA 8.3.10 and red inverse-triangles for EPOS-LHC. The data points are plotted at the center of the corresponding $ {\Delta\eta^{\mathrm{F}} } $ bin. The height of the shaded bands indicates the systematic and statistical uncertainties for data and simulation, respectively. The vertical bars indicate the size of the statistical uncertainties for data. The width of the shaded bands indicate the size of the $ {\Delta\eta^{\mathrm{F}} } $ bin. |
png pdf |
Figure 5-a:
Summary of measurements of $ {V_{1\Delta}} $ (left) and $ {V_{2\Delta}} $ (right) as a function of $ {\Delta\eta^{\mathrm{F}} } $. The results are for tracks with 0.3 $ < p_{\mathrm{T}}^{\text{trig}} < $ 3.0 GeV. The filled circles indicate the data. The open triangles indicate the simulation, in blue for PYTHIA 8.3.10 and red inverse-triangles for EPOS-LHC. The data points are plotted at the center of the corresponding $ {\Delta\eta^{\mathrm{F}} } $ bin. The height of the shaded bands indicates the systematic and statistical uncertainties for data and simulation, respectively. The vertical bars indicate the size of the statistical uncertainties for data. The width of the shaded bands indicate the size of the $ {\Delta\eta^{\mathrm{F}} } $ bin. |
png pdf |
Figure 5-b:
Summary of measurements of $ {V_{1\Delta}} $ (left) and $ {V_{2\Delta}} $ (right) as a function of $ {\Delta\eta^{\mathrm{F}} } $. The results are for tracks with 0.3 $ < p_{\mathrm{T}}^{\text{trig}} < $ 3.0 GeV. The filled circles indicate the data. The open triangles indicate the simulation, in blue for PYTHIA 8.3.10 and red inverse-triangles for EPOS-LHC. The data points are plotted at the center of the corresponding $ {\Delta\eta^{\mathrm{F}} } $ bin. The height of the shaded bands indicates the systematic and statistical uncertainties for data and simulation, respectively. The vertical bars indicate the size of the statistical uncertainties for data. The width of the shaded bands indicate the size of the $ {\Delta\eta^{\mathrm{F}} } $ bin. |
png pdf |
Figure 6:
Summary of measurements of $ {V_{1\Delta}} $ (left) and $ {V_{2\Delta}} $ (right) for the diffraction-enhanced events for different classes of $ N_{\text{ch}}^{|\eta| < 2.4, p_{\mathrm{T}} > 0.3 \text{GeV}} $. The results are for tracks with 0.3 $ < p_{\mathrm{T}}^{\text{trig}} < $ 3.0 GeV. The filled circles indicate the data. The open triangles indicate the simulation, in blue for PYTHIA 8.3.10 and red inverse triangles for EPOS-LHC. The data points are plotted at the mean of $ N_{\text{ch}}^{|\eta| < 2.4, p_{\mathrm{T}} > 0.3 \text{GeV}} $ within the corresponding $ N_{\text{trk}}^{\text{offline}} $ bin. The height of the shaded bands indicates the systematic and statistical uncertainties for data and simulation, respectively. The vertical bars indicate the size of the statistical uncertainties for data. The inclusive $ \mathrm{p}\text{Pb} $ and $ \gamma\mathrm{p} $ results from Ref. [45] are also shown as open circles and open squares, respectively. |
png pdf |
Figure 6-a:
Summary of measurements of $ {V_{1\Delta}} $ (left) and $ {V_{2\Delta}} $ (right) for the diffraction-enhanced events for different classes of $ N_{\text{ch}}^{|\eta| < 2.4, p_{\mathrm{T}} > 0.3 \text{GeV}} $. The results are for tracks with 0.3 $ < p_{\mathrm{T}}^{\text{trig}} < $ 3.0 GeV. The filled circles indicate the data. The open triangles indicate the simulation, in blue for PYTHIA 8.3.10 and red inverse triangles for EPOS-LHC. The data points are plotted at the mean of $ N_{\text{ch}}^{|\eta| < 2.4, p_{\mathrm{T}} > 0.3 \text{GeV}} $ within the corresponding $ N_{\text{trk}}^{\text{offline}} $ bin. The height of the shaded bands indicates the systematic and statistical uncertainties for data and simulation, respectively. The vertical bars indicate the size of the statistical uncertainties for data. The inclusive $ \mathrm{p}\text{Pb} $ and $ \gamma\mathrm{p} $ results from Ref. [45] are also shown as open circles and open squares, respectively. |
png pdf |
Figure 6-b:
Summary of measurements of $ {V_{1\Delta}} $ (left) and $ {V_{2\Delta}} $ (right) for the diffraction-enhanced events for different classes of $ N_{\text{ch}}^{|\eta| < 2.4, p_{\mathrm{T}} > 0.3 \text{GeV}} $. The results are for tracks with 0.3 $ < p_{\mathrm{T}}^{\text{trig}} < $ 3.0 GeV. The filled circles indicate the data. The open triangles indicate the simulation, in blue for PYTHIA 8.3.10 and red inverse triangles for EPOS-LHC. The data points are plotted at the mean of $ N_{\text{ch}}^{|\eta| < 2.4, p_{\mathrm{T}} > 0.3 \text{GeV}} $ within the corresponding $ N_{\text{trk}}^{\text{offline}} $ bin. The height of the shaded bands indicates the systematic and statistical uncertainties for data and simulation, respectively. The vertical bars indicate the size of the statistical uncertainties for data. The inclusive $ \mathrm{p}\text{Pb} $ and $ \gamma\mathrm{p} $ results from Ref. [45] are also shown as open circles and open squares, respectively. |
| Tables | |
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Table 1:
Unweighted average systematic uncertainty contribution by source for the nominal selection. |
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Table 2:
Measured values of $ {V_{n\Delta}} $ as a function of $ {\Delta\eta^{\mathrm{F}} } $. The uncertainties include both statistical and systematic components. The table shows the $ v_2 $ results when they are nonzero. For the other cases, upper limits at 95% CL are displayed with the $ < $ symbol. |
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Table 3:
Measured values of $ {V_{n\Delta}} $ for the diffractive-enhanced sample as a function of $ \langle N_{\text{ch}}^{|\eta| < 2.4, p_{\mathrm{T}} > 0.3 \text{GeV}} \rangle $ and $ N_{\text{trk}}^{\text{offline}} $ for both $ p_{\mathrm{T}}^{\text{trig}} $ bins. The uncertainties include both statistical and systematic components. The table also shows the 95% CL upper limits on $ v_2 $ displayed with the $ < $ symbol. In the lower table, $ v_2 $ values for $ \gamma\mathrm{p} $ events for 0.3 $ < p_{\mathrm{T}}^{\text{trig}} < $ 3.0 GeV [45] in similar $ N_{\text{ch}}^{|\eta| < 2.4, p_{\mathrm{T}} > 0.3 \text{GeV}} $ ranges are given. |
| Summary |
| Long-range azimuthal $ (\phi) $ two-particle correlations have been studied for in proton-lead ($ \mathrm{p}\text{Pb} $) events at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 8.16 TeV as a function of the forward rapidity gap width ($ {\Delta\eta^{\mathrm{F}} } $) and the charged-particle multiplicity ($ N_{\text{ch}}^{|\eta| < 2.4, p_{\mathrm{T}} > 0.3 \text{GeV}} $), where $ p_{\mathrm{T}} $ is the transverse momentum. Varying $ {\Delta\eta^{\mathrm{F}} } $ provides a continuous handle on the degree of exclusivity of the selected $ \mathrm{p}\text{Pb} $ events and therefore complements inclusive small-system correlation measurements. Events have been selected by requiring energy deposition in one of the forward calorimeters and no activity in the forward calorimeter on the opposite side. In addition, we require no energy in the region 2.5 $ < \eta < $ 3, favoring events with activity in the direction of the outgoing Pb beam. For events with $ {\Delta\eta^{\mathrm{F}} } > $ 2.5, the fraction of diffractive events is enhanced, and these events were further studied as a function of charged particle multiplicity. The average track multiplicity is lower in the diffractive sample than for inclusive $ \mathrm{p}\text{Pb} $ events, but larger than for photon-proton ($ \gamma\mathrm{p} $) events. The slope of the multiplicity distribution becomes steeper with increasing $ {\Delta\eta^{\mathrm{F}} } $. The mean track multiplicity $ \langle N_{\text{trk}}^{\text{offline}} \rangle $ decreases by 48% when $ {\Delta\eta^{\mathrm{F}} } $ changes from 0.5 $ < {\Delta\eta^{\mathrm{F}} } < $ 1.0 to $ {\Delta\eta^{\mathrm{F}} } > $ 2.5. The two-dimensional two-particle correlation functions have been averaged over $ |{\Delta\eta}| > $ 2 and the resulting $ {\Delta\phi} $ distributions have been studied in terms of their Fourier coefficients $ {V_{1\Delta}} $ and $ {V_{2\Delta}} $, as a function of $ {\Delta\eta^{\mathrm{F}} } $ and $ N_{\text{ch}}^{|\eta| < 2.4, p_{\mathrm{T}} > 0.3 \text{GeV}} $. The measured values of $ {V_{1\Delta}} $ are negative and decrease with $ {\Delta\eta^{\mathrm{F}} } $, while the central values of $ {V_{2\Delta}} $ increase monotonically with $ {\Delta\eta^{\mathrm{F}} } $, although they are consistent with zero within uncertainties in two of the bins. The results have been compared with the predictions of the PYTHIA 8.3.10 model, which does not include collective effects, and with EPOS-LHC model, which includes such effects. The measured values of the elliptic flow coefficient ($ v_2 $) are provided for the bins $ [0.5,1) $, $ [1,1.5) $, $ [2,2.5) $. In the other bins, the $ v_2 $ results are consistent with zero. In these bins, 95% confidence level upper limits have been determined; they are stable across the $ {\Delta\eta^{\mathrm{F}} } $ and $ N_{\text{ch}}^{|\eta| < 2.4, p_{\mathrm{T}} > 0.3 \text{GeV}} $ regions studied, indicating comparable sensitivity in all bins, and reach values up to 0.13 for the most inclusive $ N_{\text{trk}}^{\text{offline}} $ bin. The values of the upper limits are similar to the values measured in $ \gamma\mathrm{p} $ events. These results constrain scenarios in which ridge-like correlations are expected to persist universally across small systems independent of event topology. They also provide a reference for models that predict reduced collective response when the multiparton interactions and color reconnection processes are suppressed. |
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