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CMS-HIN-21-017 ; CERN-EP-2023-075
Multiplicity and transverse momentum dependence of charge-balance functions in pPb and PbPb collisions at LHC energies
Accepted for publication in J. High Energy Phys.
Abstract: Measurements of the charge-dependent two-particle angular correlation function in proton-lead (pPb) collisions at a nucleon-nucleon center-of-mass energy of $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV and lead-lead (PbPb) collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV are reported. The pPb and PbPb datasets correspond to integrated luminosities of 186 nb$^{-1}$ and 0.607 nb$^{-1}$, respectively, and were collected using the CMS detector at the CERN LHC. The charge-dependent correlations are characterized by balance functions of same- and opposite-sign particle pairs. The balance functions, which contain information about the creation time of charged particle pairs and the development of collectivity, are studied as functions of relative pseudorapidity ($ \Delta \eta $) and relative azimuthal angle ($ \Delta \phi $), for various multiplicity and transverse momentum ($ p_{\mathrm{T}} $) intervals. A multiplicity dependence of the balance function is observed in $ \Delta \eta $ and $ \Delta \phi $ for both systems. The width of the balance functions decreases towards high-multiplicity collisions in the momentum region $ < $2 GeV, for pPb and PbPb results. No multiplicity dependence is observed at higher transverse momentum. The data are compared with HYDJET, HIJING and AMPT generator predictions, none of which capture completely the multiplicity dependence seen in the data.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
The balance function is shown in terms of $ \Delta \eta $ and $ \Delta \phi $ in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV (upper panels) and for pPb collisions at 8.16 TeV (lower panels). From left to right, the results are shown for the centrality classes in PbPb ($ N_\text{trk}^\text{offline} $ multiplicity in pPb) of 70-80, 30-40, 0-10% (0-40, 120-150, 270-300). The trigger and associated particles in PbPb (pPb) collisions satisfy the condition 0.5 (0.4) $ < p_\text{T,asso} < p_\text{T,trig} < $ 2.0 GeV.

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Figure 1-a:
The balance function is shown in terms of $ \Delta \eta $ and $ \Delta \phi $ in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. From left to right, the results are shown for the centrality classes in PbPb of 70-80, 30-40, 0-10%. The trigger and associated particles satisfy the condition 0.5 $ < p_\text{T,asso} < p_\text{T,trig} < $ 2.0 GeV.

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Figure 1-b:
The balance function is shown in terms of $ \Delta \eta $ and $ \Delta \phi $ for pPb collisions at 8.16 TeV. From left to right, the results are shown $ N_\text{trk}^\text{offline} $ multiplicity of 70-80, 30-40, 0-10%. The trigger and associated particles satisfy the condition 0.4 $ < p_\text{T,asso} < p_\text{T,trig} < $ 2.0 GeV.

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Figure 2:
The projection of the balance function is presented in the upper panel for PbPb (lower panel for pPb) collisions as a function of $ \Delta\eta $ (left column) and in $ \Delta\phi $ (right column). The statistical uncertainties of the data points are smaller than the marker size and rectangular boxes indicate the systematic uncertainties.

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Figure 2-a:
The projection of the balance function is presented for PbPb collisions as a function of $ \Delta\eta $. The statistical uncertainties of the data points are smaller than the marker size and rectangular boxes indicate the systematic uncertainties.

png pdf
Figure 2-b:
The projection of the balance function is presented for PbPb collisions as a function of $ \Delta\phi $. The statistical uncertainties of the data points are smaller than the marker size and rectangular boxes indicate the systematic uncertainties.

png pdf
Figure 2-c:
The projection of the balance function is presented for pPb collisions as a function of $ \Delta\eta $. The statistical uncertainties of the data points are smaller than the marker size and rectangular boxes indicate the systematic uncertainties.

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Figure 2-d:
The projection of the balance function is presented for pPb collisions as a function of $ \Delta\phi $. The statistical uncertainties of the data points are smaller than the marker size and rectangular boxes indicate the systematic uncertainties.

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Figure 3:
The width of the balance function in $ \langle |\Delta \eta| \rangle $ and the ratio of $ \langle |\Delta \eta| \rangle/ \langle |\Delta \eta| \rangle_{N_\text{ch} < 65} $ and $ \langle |\Delta \eta| \rangle / \langle |\Delta \eta| \rangle_{N_\text{ch} < 24} $ are shown as functions of $ N_\text{ch} $ for PbPb collisions in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV (upper panels) and pPb collisions in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV (lower panels), respectively. The statistical uncertainties of the data points are smaller than the marker size and rectangular boxes indicate the systematic uncertainties.

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Figure 3-a:
The width of the balance function in $ \langle |\Delta \eta| \rangle $ is shown as a function of $ N_\text{ch} $ for PbPb collisions in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. The statistical uncertainties of the data points are smaller than the marker size and rectangular boxes indicate the systematic uncertainties.

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Figure 3-b:
The width of the balance function in $ \langle |\Delta \eta| \rangle $ is shown as a function of $ N_\text{ch} $ for pPb collisions in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV. The statistical uncertainties of the data points are smaller than the marker size and rectangular boxes indicate the systematic uncertainties.

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Figure 3-c:
The ratio of $ \langle |\Delta \eta| \rangle/ \langle |\Delta \eta| \rangle_{N_\text{ch} < 65} $ and $ \langle |\Delta \eta| \rangle / \langle |\Delta \eta| \rangle_{N_\text{ch} < 24} $ is shown as a function of $ N_\text{ch} $ for PbPb collisions in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. The statistical uncertainties of the data points are smaller than the marker size and rectangular boxes indicate the systematic uncertainties.

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Figure 3-d:
The ratio of $ \langle |\Delta \eta| \rangle/ \langle |\Delta \eta| \rangle_{N_\text{ch} < 65} $ and $ \langle |\Delta \eta| \rangle / \langle |\Delta \eta| \rangle_{N_\text{ch} < 24} $ is shown as a function of $ N_\text{ch} $ for pPb collisions in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV. The statistical uncertainties of the data points are smaller than the marker size and rectangular boxes indicate the systematic uncertainties.

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Figure 4:
The width of the balance function in $ \langle |\Delta \phi| \rangle $ and the ratios of $ \langle |\Delta \phi| \rangle/\langle |\Delta \phi| \rangle_{N_\text{ch} < 65} $ and $ \langle |\Delta \phi| \rangle/ \langle |\Delta \phi| \rangle_{N_\text{ch} < 24} $ are shown as functions of $ N_\text{ch} $ for PbPb collisions in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV (upper panels) and pPb collisions in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV (lower panels), respectively. The statistical uncertainties of the data points are smaller than the marker size and rectangular boxes indicate the systematic uncertainties.

png pdf
Figure 4-a:
The width of the balance function in $ \langle |\Delta \phi| \rangle $ is shown as a function of $ N_\text{ch} $ for PbPb collisions in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. The statistical uncertainties of the data points are smaller than the marker size and rectangular boxes indicate the systematic uncertainties.

png pdf
Figure 4-b:
The width of the balance function in $ \langle |\Delta \phi| \rangle $ is shown as a function of $ N_\text{ch} $ for PbPb collisions in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. The statistical uncertainties of the data points are smaller than the marker size and rectangular boxes indicate the systematic uncertainties.

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Figure 4-c:
The ratios of $ \langle |\Delta \phi| \rangle/\langle |\Delta \phi| \rangle_{N_\text{ch} < 65} $ and $ \langle |\Delta \phi| \rangle/ \langle |\Delta \phi| \rangle_{N_\text{ch} < 24} $ is shown as a function of $ N_\text{ch} $ for pPb collisions in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV. The statistical uncertainties of the data points are smaller than the marker size and rectangular boxes indicate the systematic uncertainties.

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Figure 4-d:
The ratios of $ \langle |\Delta \phi| \rangle/\langle |\Delta \phi| \rangle_{N_\text{ch} < 65} $ and $ \langle |\Delta \phi| \rangle/ \langle |\Delta \phi| \rangle_{N_\text{ch} < 24} $ is shown as a function of $ N_\text{ch} $ for pPb collisions in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV. The statistical uncertainties of the data points are smaller than the marker size and rectangular boxes indicate the systematic uncertainties.

png pdf
Figure 5:
The projection of the balance function is presented for PbPb in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV (upper panels) and pPb in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV (lower panels) collisions as a function of $ \Delta \eta $ (left column) and $ \Delta \phi $ (right column), for 2.0 $ < p_\text{T,asso} < 3.0 < p_\text{T,trig} < $ 4.0 GeV ranges. The 1D projection is derived for $ \Delta \eta $ in near-side ($ |\Delta \phi| < \pi/ $ 2) and $ \Delta \phi $ (0.3 $ < |\Delta \eta| < $ 1.0) regions.

png pdf
Figure 5-a:
The projection of the balance function is presented for PbPb in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV collisions as a function of $ \Delta \eta $, for 2.0 $ < p_\text{T,asso} < 3.0 < p_\text{T,trig} < $ 4.0 GeV ranges. The 1D projection is derived in the near-side ($ |\Delta \phi| < \pi/ $ 2) region.

png pdf
Figure 5-b:
The projection of the balance function is presented for PbPb in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV collisions as a function of $ \Delta \phi $, for 2.0 $ < p_\text{T,asso} < 3.0 < p_\text{T,trig} < $ 4.0 GeV ranges. The 1D projection is derived in the 0.3 $ < |\Delta \eta| < $ 1.0 region.

png pdf
Figure 5-c:
The projection of the balance function is presented for pPb in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV collisions as a function of $ \Delta \eta $, for 2.0 $ < p_\text{T,asso} < 3.0 < p_\text{T,trig} < $ 4.0 GeV ranges. The 1D projection is derived in the near-side ($ |\Delta \phi| < \pi/ $ 2) region.

png pdf
Figure 5-d:
The projection of the balance function is presented for pPb in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV collisions as a function of $ \Delta \phi $, for 2.0 $ < p_\text{T,asso} < 3.0 < p_\text{T,trig} < $ 4.0 GeV ranges. The 1D projection is derived in the 0.3 $ < |\Delta \eta| < $ 1.0 region.

png pdf
Figure 6:
The projection of the balance function is presented for PbPb in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV (upper panels) and pPb in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV (lower panels) collisions as a function of $ \Delta \eta $ (left column) and $ \Delta \phi $ (right column), for 3.0 $ < p_\text{T,asso} < $ 8.0 $< p_\text{T,trig} < $ 15.0 GeV ranges. The 1D projection is derived for $ \Delta \eta $ in near-side ($ |\Delta \phi| < \pi/ $ 2) and $ \Delta \phi $ (0.3 $ < |\Delta \eta| < $ 1.0) regions.

png pdf
Figure 6-a:
The projection of the balance function is presented for PbPb in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV collisions as a function of $ \Delta \eta $, for 3.0 $ < p_\text{T,asso} < $ 8.0 $< p_\text{T,trig} < $ 15.0 GeV ranges. The 1D projection is derived in the near-side ($ |\Delta \phi| < \pi/ $ 2) region.

png pdf
Figure 6-b:
The projection of the balance function is presented for PbPb in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV collisions as a function of $ \Delta \phi $, for 3.0 $ < p_\text{T,asso} < $ 8.0 $< p_\text{T,trig} < $ 15.0 GeV ranges. The 1D projection is derived in the 0.3 $ < |\Delta \eta| < $ 1.0 region.

png pdf
Figure 6-c:
The projection of the balance function is presented for pPb in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV collisions as a function of $ \Delta \eta $, for 3.0 $ < p_\text{T,asso} < $ 8.0 $< p_\text{T,trig} < $ 15.0 GeV ranges. The 1D projection is derived in the near-side ($ |\Delta \phi| < \pi/ $ 2) region.

png pdf
Figure 6-d:
The projection of the balance function is presented for pPb in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV collisions as a function of $ \Delta \phi $, for 3.0 $ < p_\text{T,asso} < $ 8.0 $< p_\text{T,trig} < $ 15.0 GeV ranges. The 1D projection is derived in the 0.3 $ < |\Delta \eta| < $ 1.0 region.

png pdf
Figure 7:
The width of the balance function in $ \Delta \eta $ (left column) and $ \Delta \phi $ (right column) is calculated for different $ p_{\mathrm{T}} $ interval in PbPb in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV (upper panels) and pPb collisions in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV (lower panels). The vertical lines indicate the statistical uncertainties of the data points, and the rectangular boxes indicate the systematic uncertainties.

png pdf
Figure 7-a:
The width of the balance function in $ \Delta \eta $ is calculated for different $ p_{\mathrm{T}} $ interval in PbPb in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. The vertical lines indicate the statistical uncertainties of the data points, and the rectangular boxes indicate the systematic uncertainties.

png pdf
Figure 7-b:
The width of the balance function in $ \Delta \phi $ is calculated for different $ p_{\mathrm{T}} $ interval in PbPb in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. The vertical lines indicate the statistical uncertainties of the data points, and the rectangular boxes indicate the systematic uncertainties.

png pdf
Figure 7-c:
The width of the balance function in $ \Delta \eta $ is calculated for different $ p_{\mathrm{T}} $ interval in pPb collisions in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV. The vertical lines indicate the statistical uncertainties of the data points, and the rectangular boxes indicate the systematic uncertainties.

png pdf
Figure 7-d:
The width of the balance function in $ \Delta \phi $ is calculated for different $ p_{\mathrm{T}} $ interval in pPb collisions in $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV. The vertical lines indicate the statistical uncertainties of the data points, and the rectangular boxes indicate the systematic uncertainties.
Tables

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Table 1:
Corrected average $ N_\text{ch} $ ($ \langle N_\text{ch} \rangle $) values, calculated for different multiplicities in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV and in pPb collisions at 8.16 TeV.

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Table 2:
Summary of percentage systematic uncertainties calculated in $ \langle |\Delta \eta| \rangle $ and $ \langle |\Delta\phi| \rangle $ for PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV and pPb collisions at 8.16 TeV.
Summary
This paper presents a measurement of the charge-balance function for nonidentified charged particles in proton-lead (pPb) and lead-lead (PbPb) collisions using the broad pseudorapidity coverage of the CMS detector. For both systems, the dependence of the balance function on relative pseudorapidity ($ \Delta\eta $) and relative azimuthal angle $ \Delta\phi $ of particle pairs is studied for different multiplicity classes and transverse momentum ($ p_{\mathrm{T}} $) ranges. It is observed that the width in both $ \Delta\eta $ and $ \Delta\phi $ decreases with charged particle multiplicity ($ N_\text{ch} $) in pPb and PbPb systems for $ p_{\mathrm{T}} < $ 2 GeV. These results are consistent with the system possessing a large radial flow, with particle creation at a later stage of the collision, or both. The multiplicity dependence is weaker for higher $ p_{\mathrm{T}} $ as compared with the $ p_{\mathrm{T}} < $ 2 GeV region, which implies that the balancing partners are strongly correlated. The data are compared with HYDJET, HIJING and AMPT generator predictions, none of which capture completely the multiplicity dependence seen in the data.
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Compact Muon Solenoid
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