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 $\sqrt{s_\mathrm{NN}}$ = 8.16 TeV and lead-lead (PbPb) collisions at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV are reported. The pPb and PbPb data sets 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 toward high-multiplicity collisions in the momentum region $\lt$ 2 GeV, for pPb and PbPb results. Integrals of the balance functions are presented in both systems, and a mild dependence of the charge-balancing fractions on multiplicity is observed. 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. The comparison of results with different center-of-mass energies suggest that the balance functions become narrower at higher energies, which is consistent with the idea of delayed hadronization and the effect of radial flow.

Table 1

Data from figure 2a left panel

10.17182/hepdata.135972.v1/t1

$\Delta\eta$ projection of balance function in low $p_{T}$ in 0-10% centrality
Table 2

Data from figure 2a left panel

10.17182/hepdata.135972.v1/t2

$\Delta\eta$ projection of balance function in low $p_{T}$ in 30-40% centrality
Table 3

Data from figure 2a left panel

10.17182/hepdata.135972.v1/t3

$\Delta\eta$ projection of balance function in low $p_{T}$ in 70-80% centrality
Table 4

Data from figure 2b right panel

10.17182/hepdata.135972.v1/t4

$\Delta\phi$ projection of balance function in low $p_{T}$ in 0-10% centrality
Table 5

Data from figure 2b right panel

10.17182/hepdata.135972.v1/t5

$\Delta\phi$ projection of balance function in low $p_{T}$ in 30-40% centrality
Table 6

Data from figure 2b right panel

10.17182/hepdata.135972.v1/t6

1D $\Delta\eta$ projection of balance function in low $p_{T}$ in 70-80% centrality
Table 7

Data from figure 2c left panel

10.17182/hepdata.135972.v1/t7

$\Delta\eta$ projection of balance function in low $p_{T}$ in 0-40 $N_{trk}$
Table 8

Data from figure 2c left panel

10.17182/hepdata.135972.v1/t8

$\Delta\eta$ projection of balance function in low $p_{T}$ in 120-150 $N_{trk}$
Table 9

Data from figure 2c left panel

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$\Delta\eta$ projection of balance function in low $p_{T}$ in 270-300 $N_{trk}$
Table 10

Data from figure 2d right panel

10.17182/hepdata.135972.v1/t10

$\Delta\phi$ projection of balance function in low $p_{T}$ in 0-40 $N_{trk}$
Table 11

Data from figure 2d right panel

10.17182/hepdata.135972.v1/t11

$\Delta\phi$ projection of balance function in low $p_{T}$ in 120-150 $N_{trk}$
Table 12

Data from figure 2d right panel

10.17182/hepdata.135972.v1/t12

$\Delta\phi$ projection of balance function in low $p_{T}$ in 270-300 $N_{trk}$
Table 13

Data from figure 3a in PbPb left panel

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The width of balance function in $<|\Delta\eta|>$ in low $p_{T}$ for PbPb collisions
Table 14

Data from figure 3b in PbPb right panel

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Balance function width in low $p_{T}$ PbPb relative $<|\Delta\eta|>/<|\Delta\eta|>_{N_{ch}<65}$
Table 15

Data from figure 3c in pPb left panel

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The width of balance function in $<|\Delta\eta|>$ in low $p_{T}$ for pPb collisions
Table 16

Data from figure 3d right panel

10.17182/hepdata.135972.v1/t16

Balance function width in low $p_{T}$ in pPb relative $<|\Delta\eta|>/<|\Delta\eta|>_{N_{ch}<24}$
Table 17

Data from figure 4a left panel

10.17182/hepdata.135972.v1/t17

The width of the balance function in $<|\Delta\phi|>$ in low $p_{T}$ for PbPb collisions
Table 18

Data from figure 4b left panel

10.17182/hepdata.135972.v1/t18

Balance function width in low $p_{T}$ in PbPb for relative $<|\Delta\phi|>/<|\Delta\phi|>_{N_{ch}<65}$
Table 19

Data from figure 4c left panel

10.17182/hepdata.135972.v1/t19

The width of the balance function in $<|\Delta\phi|>$ in low $p_{T}$ for pPb collisions
Table 20

Data from figure 4d right panel

10.17182/hepdata.135972.v1/t20

Balance function width in low $p_{T}$ in pPb for relative $|\Delta\phi|/<|\Delta\phi|>_{N_{ch}<24}$
Table 21

Data from figure 5a left panel

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Balance function projection as a function of $\Delta\eta$ in intermediate $p_{T}$ in PbPb for 0-10% centrality
Table 22

Data from figure 5a left panel

10.17182/hepdata.135972.v1/t22

Balance function projection as a function of $\Delta\eta$ in intermediate $p_{T}$ in PbPb for 30-40% centrality
Table 23

Data from figure 5a left panel

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Balance function projection as a function of $\Delta\eta$ in intermediate $p_{T}$ in PbPb for 70-80% centrality
Table 24

Data from figure 5b right panel

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Balance function projection as a function of $\Delta\phi$ in intermediate $p_{T}$ in PbPb for 0-10% centrality
Table 25

Data from figure 5b right panel

10.17182/hepdata.135972.v1/t25

Balance function projection as a function of $\Delta\phi$ in intermediate $p_{T}$ in PbPb for 30-40% centrality
Table 26

Data from figure 5b right panel

10.17182/hepdata.135972.v1/t26

Balance function projection as a function of $\Delta\phi$ in intermediate $p_{T}$ in PbPb for 70-80% centrality
Table 27

Data from figure 5c left panel

10.17182/hepdata.135972.v1/t27

Balance function projection as a function of $\Delta\eta$ in intermediate $p_{T}$ in pPb for 0-40 $N_{trk}$
Table 28

Data from figure 5c left panel

10.17182/hepdata.135972.v1/t28

Balance function projection as a function of $\Delta\eta$ in intermediate $p_{T}$ in pPb for 120-150 $N_{trk}$
Table 29

Data from figure 5c left panel

10.17182/hepdata.135972.v1/t29

Balance function projection as a function of $\Delta\eta$ in intermediate $p_{T}$ in pPb for 270-300 $N_{trk}$
Table 30

Data from figure 5d right panel

10.17182/hepdata.135972.v1/t30

Balance function projection as a function of $\Delta\phi$ in intermediate $p_{T}$ in pPb for $N_{trk}$ 0-40
Table 31

Data from figure 5d right panel

10.17182/hepdata.135972.v1/t31

Balance function projection as a function of $\Delta\phi$ in intermediate $p_{T}$ in pPb for $N_{trk}$ 120-150
Table 32

Data from figure 5d right panel

10.17182/hepdata.135972.v1/t32

Balance function projection as a function of $\Delta\phi$ in intermediate $p_{T}$ in pPb for $N_{trk}$ 270-300
Table 33

Data from figure 6a left panel

10.17182/hepdata.135972.v1/t33

Balance function projection as a function of $\Delta\eta$ in high $p_{T}$ in PbPb for 0-10% centrality
Table 34

Data from figure 6a left panel

10.17182/hepdata.135972.v1/t34

Balance function projection as a function of $\Delta\eta$ in high $p_{T}$ in PbPb for 30-40% centrality
Table 35

Data from figure 6a left panel

10.17182/hepdata.135972.v1/t35

Balance function projection as a function of $\Delta\eta$ in high $p_{T}$ in PbPb for 70-80% centrality
Table 36

Data from figure 6b right panel

10.17182/hepdata.135972.v1/t36

Balance function projection as a function of $\Delta\phi$ in high $p_{T}$ in PbPb for 0-10% centrality
Table 37

Data from figure 6b right panel

10.17182/hepdata.135972.v1/t37

Balance function projection as a function of $\Delta\phi$ in high $p_{T}$ in PbPb for 30-40% centrality
Table 38

Data from figure 6b right panel

10.17182/hepdata.135972.v1/t38

Balance function projection as a function of $\Delta\phi$ in high $p_{T}$ in PbPb for 70-80% centrality
Table 39

Data from figure 6c left panel

10.17182/hepdata.135972.v1/t39

Balance function projection as a function of $\Delta\eta$ in high $p_{T}$ in pPb for $N_{trk}$ 0-40
Table 40

Data from figure 6c left panel

10.17182/hepdata.135972.v1/t40

Balance function projection as a function of $\Delta\eta$ in high $p_{T}$ in pPb for $N_{trk}$ 120-150
Table 41

Data from figure 6c left panel

10.17182/hepdata.135972.v1/t41

Balance function projection as a function of $\Delta\eta$ in high $p_{T}$ in pPb for $N_{trk}$ 270-300
Table 42

Data from figure 6d right panel

10.17182/hepdata.135972.v1/t42

Balance function projection as a function of $\Delta\phi$ in high $p_{T}$ in PbPb for $N_{trk}$ 0-40
Table 43

Data from figure 6d right panel

10.17182/hepdata.135972.v1/t43

Balance function projection as a function of $\Delta\phi$ in high $p_{T}$ in PbPb for $N_{trk}$ 120-150
Table 44

Data from figure 6d right panel

10.17182/hepdata.135972.v1/t44

Balance function projection as a function of $\Delta\phi$ in high $p_{T}$ in PbPb for $N_{trk}$ 270-300
Table 45

Data from figure 7a left panel

10.17182/hepdata.135972.v1/t45

Average width of the balance function in $\Delta \eta$ with $N_{ch}$ for low $p_{T}$
Table 46

Data from figure 7a left panel

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Average width of the balance function in $\Delta \eta$ with $N_{ch}$ for intermediate $p_{T}$
Table 47

Data from figure 7a left panel

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Average width of the balance function in $\Delta \eta$ with $N_{ch}$ for high $p_{T}$
Table 48

Data from figure 7b right panel

10.17182/hepdata.135972.v1/t48

Average width of the balance function in $\Delta \phi$ with $p_{T}$ for low $p_{T}$
Table 49

Data from figure 7b right panel

10.17182/hepdata.135972.v1/t49

Average width of the balance function in $\Delta \phi$ with $N_{ch}$ for intermediate $p_{T}$
Table 50

Data from figure 7b right panel

10.17182/hepdata.135972.v1/t50

Average width of the balance function in $\Delta \phi$ with $N_{ch}$ for high $p_{T}$
Table 51

Data from figure 7c left panel

10.17182/hepdata.135972.v1/t51

Average width of the balance function in $\Delta \eta$ with $N_{ch}$ for low $p_{T}$
Table 52

Data from figure 7c left panel

10.17182/hepdata.135972.v1/t52

Average width of the balance function in $\Delta \eta$ with $N_{ch}$ for intermediate $p_{T}$
Table 53

Data from figure 7c left panel

10.17182/hepdata.135972.v1/t53

Average width of the balance function in $\Delta \phi$ with $N_{ch}$ for high $p_{T}$
Table 54

Data from figure 7d

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Average width of the balance function in $\Delta \phi$ with $N_{ch}$ for low $p_{T}$
Table 55

Data from figure 7d

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Average width of the balance function in $\Delta \phi$ with $N_{ch}$ for intermediate $p_{T}$
Table 56

Data from figure 7d

10.17182/hepdata.135972.v1/t56

Average width of the balance function in $\Delta \phi$ with $N_{ch}$ for high $p_{T}$

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