Multiplicity and transverse momentum evolution of charge-dependent correlations in pp, p-Pb, and Pb-Pb collisions at the LHC

We report on two-particle charge-dependent correlations in pp, p-Pb, and Pb-Pb collisions as a function of the pseudorapidity and azimuthal angle difference, $\mathrm{\Delta}\eta$ and $\mathrm{\Delta}\varphi$ respectively. These correlations are studied using the balance function that probes the charge creation time and the development of collectivity in the produced system. The dependence of the balance function on the event multiplicity as well as on the trigger and associated particle transverse momentum ($p_{\mathrm{T}}$) in pp, p-Pb, and Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}} = 7$, 5.02, and 2.76 TeV, respectively, are presented. In the low transverse momentum region, for $0.2 <~ p_{\mathrm{T}} <~ 2.0$ GeV/$c$, the balance function becomes narrower in both $\mathrm{\Delta}\eta$ and $\mathrm{\Delta}\varphi$ directions in all three systems for events with higher multiplicity. The experimental findings favor models that either incorporate some collective behavior (e.g. AMPT) or different mechanisms that lead to effects that resemble collective behavior (e.g. PYTHIA8 with color reconnection). For higher values of transverse momenta the balance function becomes even narrower but exhibits no multiplicity dependence, indicating that the observed narrowing with increasing multiplicity at low $p_{\mathrm{T}}$ is a feature of bulk particle production.

Figures

Figure 1

 The balance function $B(\mathrm{\Delta}\eta,\mathrm{\Delta}\varphi$) for charged particles with $0.2 < \pt_{,assoc}< \pt_{,trig}< 2.0$ Gev/$c$ in Pb-Pb, p-Pb, and pp collisions at $\sqrt{s_{\mathrm{NN}}} = 2.76$, 5.02, and 7 TeV, respectively. From top to bottom the $0-5\%$ for Pb-Pb and $0-10\%$ for p-Pb and pp collisions, $30-40\%$, and the $70-80\%$ multiplicity classes are shown.

Figure 2

 The balance function for charged particles with $0.2 < \pt_{,assoc}< \pt_{,trig}< 2.0$ Gev/$c$ as a function of $\deta$ on the near-side (upper row) and away-side (middle row) and $\dphi$ (lower row) indifferent multiplicity classes of Pb-Pb in panels (a), (d) and (g), p-Pb in panels (b), (e) and (h), and pp collisions in panels (c), (f) and (i) at $\sqrt{s_{\mathrm{NN}}} = 2.76$, 5.02, and 7 TeV, respectively.

Figure 3

 The balance function for charged particles with $0.2 < \pt_{,assoc}< \pt_{,trig}< 2.0$ Gev/$c$ as a function of $\deta$ on the near-side (upper row) and away-side (middle row) and as a function of $\dphi$ (lower row) for Pb-Pb (panels (a), (d) and (g)), p-Pb (panels (b), (e) and (h)) and pp collisions (panels (c), (f) and (i)) compared with results from various event generators. Only the highest multiplicity class is shown, i.e. 0-5 % for Pb-Pb and 0-10 % for p-Pb and pp collisions.

Figure 4

 The multiplicity-class dependence of $\sigma_{\Delta\eta}$ in Pb-Pb, p-Pb, and pp collisions at $\sqrt{s_{\mathrm{NN}}} = 2.76$, 5.02, and 7 TeV compared with results from various event generators in panels (a), (c), and (e). Panels (b), (d), and (f) show the relative decrease of $\sigma_{\Delta\eta}$ calculated with respect to $\sigma_{\Delta\eta}^{70-80\%}$, as a function of the multiplicity class. The transverse momentum values for both the trigger and the associated particles satisfy the condition $0.2 < \pt_{,assoc}< \pt_{,trig}< 2.0$ Gev/$c$.

Figure 5

 The multiplicity-class dependence of $\sigma_{\Delta\phi}$ in Pb-Pb, p-Pb, and pp collisions at $\sqrt{s_{\mathrm{NN}}} = 2.76$, 5.02, and 7 TeV compared with results from various event generators in panels (a), (c), and (e). Panels (b), (d), and (f) show the relative decrease of $\sigma_{\Delta\phi}$ calculated with respect to $\sigma_{\Delta\varphi}^{70-80\%}$ as a function of the multiplicity class. The transverse momentum values for both the trigger and the associated particles satisfy the condition $0.2 < \pt_{,assoc}< \pt_{,trig}< 2.0$ Gev/$c$.

Figure 6

 The balance function for charged particles with $2.0 < \pt_{,assoc}< 3.0< \pt_{,trig}< 4.0$ Gev/$c$ as a function of $\deta$ (upper row) and $\dphi$ (lower row) indifferent multiplicity classes of Pb-Pb, in panels (a) and (d), p-Pb, in panels (b) and (e), and pp collisions, in panels (c) and (f), at $\sqrt{s_{\mathrm{NN}}} = 2.76$, 5.02, and 7 TeV, respectively.

Figure 7

 The balance function for charged particles with $3.0 < \pt_{,assoc}< 8.0< \pt_{,trig}< 15.0$ Gev/$c$ as a function of $\deta$ (upper row) and $\dphi$ (lower row) indifferent multiplicity classes of Pb-Pb in panels (a) and (c) and p-Pb collisions in panels (b) and (d) at $\sqrt{s_{\mathrm{NN}}} = 2.76$ and 5.02 TeV, respectively.

Figure 8

 The multiplicity-class dependence of $\sigma_{\Delta\eta}$ (a) and $\sigma_{\Delta\phi}$ (b) in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}} = 2.76$ TeV. The different markers represent the low (i.e. $0.2 < \pt_{,assoc}< \pt_{,trig}< 2.0$ Gev/$c$ with red circles), intermediate (i.e $2.0 < p_\mathrm{T,assoc} < 3.0 < p_\mathrm{T,trig} < 4.0$ GeV/$c$ with blue squares), and high (i.e. $3.0 < \pt_{,assoc}< 8.0< \pt_{,trig}< 15.0$ Gev/$c$ with green triangles) transverse momentum regions used in this analysis.

Figure 9

 The multiplicity-class dependence of $\sigma_{\Delta\eta}$ (a) and $\sigma_{\Delta\phi}$ (b) in p-Pb collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV. The different markers represent the low (i.e. $0.2 < p_\mathrm{T,trig} < p_\mathrm{T,trig}< 2.0$ Gev/$c$ with red circles), intermediate (i.e $2.0 < p_\mathrm{T,assoc} < 3.0 < p_\mathrm{T,trig} < 4.0$ GeV/$c$ with blue squares), and high (i.e. $3.0 < p_\mathrm{T,assoc}< 8.0< p_\mathrm{T,trig}< 15.0$ Gev/$c$ with green triangles) transverse momentum regions used in this analysis.

Figure 10

 The multiplicity-class dependence of the width of the balance function in $\deta$ (a) and in $\dphi$ (b)in pp collisions at $\sqrt{s} = 7$ TeV. The results correspond to the intermediate transverse momentum region (i.e $2.0 < p_\mathrm{T,assoc} < 3.0 < p_\mathrm{T,trig} < 4.0$ GeV/$c$). The data points are compared with two versions of PYTHIA8 calculations.

Figure 11

 The width of the balance function in $\deta$ (a) and in $\dphi$ (b) for the three systemsanalyzed (pp, p-Pb, and Pb-Pb), as a function of the charged-particle multiplicity, estimated with the V0A for $|\eta| < 0.8$ and $p_{\rm{T}} > 0.2$ GeV/$c$. The low-, intermediate-, and high-$\pt$ intervals correspond to $0.2 < \pt_{,assoc}< \pt_{,trig}< 2.0$ Gev/$c$,$2.0 < \pt_{,assoc}< 3.0< \pt_{,trig}< 4.0$ Gev/$c$, and $3.0 < \pt_{,assoc}< 8.0< \pt_{,trig}< 15.0$ Gev/$c$, respectively.

Figure 12

 The multiplicity-class dependence of the width of the balance function in $\deta$ (a) and in $\dphi$ (b)for the three systems analyzed (pp, p-Pb, and Pb-Pb) relative to the 70-80% multiplicity class.