Measurement of forward-backward multiplicity correlations in lead-lead, proton-lead, and proton-proton collisions with the ATLAS detector

Two-particle pseudorapidity correlations are measured in $\sqrt{s_{\mathrm{NN}}}=2.76\mathrm{TeV}\mathrm{Pb}+\mathrm{Pb}$, $\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}p$+Pb, and $\sqrt{s}=13\mathrm{TeV}pp$ collisions at the Large Hadron Collider (LHC), with total integrated luminosities of approximately $7\mu {\mathrm{b}}^{-1}$, 28 ${\mathrm{nb}}^{-1}$, and 65 ${\mathrm{nb}}^{-1}$, respectively. The correlation function $C_{\mathrm{N}}({\eta }_1,{\eta }_2)$ is measured as a function of event multiplicity using charged particles in the pseudorapidity range $\left|\eta \right|<2.4$. The correlation function contains a significant short-range component, which is estimated and subtracted. After removal of the short-range component, the shape of the correlation function is described approximately by $1+{\langle a_1^2\rangle }^{1/2}{\eta }_1{\eta }_2$ in all collision systems over the full multiplicity range. The values of $\langle a_1^2\rangle {}^{1/2}$ are consistent for the opposite-charge pairs and same-charge pairs, and for the three collision systems at similar multiplicity. The values of $\langle a_1^2\rangle {}^{1/2}$ and the magnitude of the short-range component both follow a power-law dependence on the event multiplicity. The short-range component in $p$ + Pb collisions, after symmetrizing the proton and lead directions, is found to be smaller at a given $\eta$ than in $pp$ collisions with comparable multiplicity.

Figure 1

The normalized distributions of the number of reconstructed tracks, $N_{\mathrm{ch}}^{\mathrm{rec}}$, with $p_{\mathrm{T}}>0.4$ GeV and $\left|\eta \right|<2.5$ in the three collision systems. The $N$ refers to the number of collisions for a given $N_{\mathrm{ch}}^{\mathrm{rec}}$.

Figure 2

The correlation functions for opposite-charge pairs $C^{+-}({\eta }_1,{\eta }_2)$ (top left panel), same-charge pairs $C^{\pm \pm }({\eta }_1,{\eta }_2)$ (top middle panel), and the ratio $R({\eta }_1,{\eta }_2)=C^{+-}({\eta }_1,{\eta }_2)/C^{\pm \pm }({\eta }_1,{\eta }_2)$ (top right panel) for Pb+Pb collisions with $200\le N_{\mathrm{ch}}^{\mathrm{rec}}<220$. The width and magnitude of the short-range peak of the ratio are shown, as a function of ${\eta }_{+}$, in the lower middle panel and lower right panels, respectively. The error bars represent the statistical uncertainties, and the solid lines indicate a quadratic fit. The dotted line in the bottom right panel serves to indicate better the deviation of $f\left({\eta }_{+}\right)$ from 1.

Figure 3

The correlation functions for opposite-charge pairs $C^{+-}({\eta }_1,{\eta }_2)$ (top left panel), same-charge pairs $C^{\pm \pm }({\eta }_1,{\eta }_2)$ (top middle panel), and the ratio $R({\eta }_1,{\eta }_2)=C^{+-}({\eta }_1,{\eta }_2)/C^{\pm \pm }({\eta }_1,{\eta }_2)$ (top right panel) for $p+\text{Pb}$ collisions with $200\le N_{\mathrm{ch}}^{\mathrm{rec}}<220$. The width and magnitude of the short-range peak of the ratio are shown, as a function of ${\eta }_{+}$, in the lower middle panel and lower right panel, respectively. The error bars represent the statistical uncertainties, and the solid lines indicate a quadratic fit. The dotted line in the bottom right panel serves to indicate better the deviation of $f\left({\eta }_{+}\right)$ from 1.

Figure 4

The width of the short-range component in $R({\eta }_{+},{\eta }_{-})$ along the ${\eta }_{-}$ direction as a function of $N_{\mathrm{ch}}$ in the three collision systems.

Figure 5

The width of the short-range component in $R({\eta }_{+},{\eta }_{-})$ along the ${\eta }_{-}$ direction in $pp$ collisions at $\sqrt{s}=13\mathrm{TeV}$, compared between data and two models. The $y$ axis is zero suppressed to demonstrate better the difference between data and models.

Figure 6

The separation of correlation functions for same-charge pairs (first column) into the SRC (third column) and LRC (last column) for Pb+Pb (top row) and $p+\text{Pb}$ (bottom row) collisions with $200\le N_{\mathrm{ch}}^{\mathrm{rec}}<220$. The second column shows the result of the quadratic fit over the $|{\eta }_{-}|>1.5$ range of the one-dimensional (1-D) correlation function projected over the $|{\eta }_{+}|<0.4$ slice, which is used to estimate the SRC component. The error bars represent the statistical uncertainties.

Figure 7

The first two Legendre basis functions associated with $a_{1,1}$ and $a_{2,2}$ in the two-particle correlation function.

Figure 8

The distributions of correlation functions $C_{\mathrm{N}}({\eta }_1,{\eta }_2)$ (top row), the estimated short-range component ${\delta }_{\mathrm{SRC}}({\eta }_1,{\eta }_2)$ (middle row), and long-range component $C_{\mathrm{N}}^{\mathrm{sub}}({\eta }_1,{\eta }_2)$ (bottom row). They are shown for collisions with $100\le N_{\mathrm{ch}}^{\mathrm{rec}}<120$ in Pb+Pb (left column), $p+\text{Pb}$ (middle column), and $pp$ collisions (right column).

Figure 9

The Legendre spectra $〈a_n^2〉$ and $〈a_n{a}_{n+2}〉$ calculated via Eq. (6) from correlation functions $C_{\mathrm{N}}({\eta }_1,{\eta }_2)$ (top row) and $C_{\mathrm{N}}^{\mathrm{sub}}({\eta }_1,{\eta }_2)$ (bottom row) in Pb+Pb (left column), $p+\text{Pb}$ (middle column), and $pp$ (right column) collisions for events with $100\le N_{\mathrm{ch}}^{\mathrm{rec}}<120$. The shaded bands represent the total uncertainties. The results are shown for all-charge (open squares), opposite-charge (open circles), and same-charge pairs (solid circles).

Figure 10

The distributions $C_{\mathrm{N}}^{\mathrm{sub}}\left({\eta }_{-}\right)$ (top left panel), $C_{\mathrm{N}}^{\mathrm{sub}}\left({\eta }_{+}\right)$ (top middle panel), and $r_{\mathrm{N}}^{\mathrm{sub}}\left(\eta \right)$ (top right panel) obtained from $C_{\mathrm{N}}^{\mathrm{sub}}({\eta }_1,{\eta }_2)$ in three ranges of ${\eta }_{+}$, ${\eta }_{-}$, and ${\eta }_{\mathrm{ref}}$, respectively, from Pb+Pb collisions with $100\le N_{\mathrm{ch}}^{\mathrm{rec}}<120$. The solid lines indicate fits to either a quadratic function (top left two panels) or a linear function (top right panel). The $〈a_1^2〉{}^{1/2}$ values from the fits are shown in the corresponding lower panels as a function of the ${\eta }_{+}$, ${\eta }_{-}$, and ${\eta }_{\mathrm{ref}}$, respectively. The error bars and shaded bands represent the statistical and systematic uncertainties, respectively. The solid horizontal line and hashed band indicate the value and uncertainty of $〈a_1^2〉{}^{1/2}$ obtained from a Legendre expansion of the $C_{\mathrm{N}}^{\mathrm{sub}}({\eta }_1,{\eta }_2)$.

Figure 11

The distributions $C_{\mathrm{N}}^{\mathrm{sub}}\left({\eta }_{-}\right)$ (top left panel), $C_{\mathrm{N}}^{\mathrm{sub}}\left({\eta }_{+}\right)$ (top middle panel), and $r_{\mathrm{N}}^{\mathrm{sub}}\left(\eta \right)$ (top right panel) obtained from $C_{\mathrm{N}}^{\mathrm{sub}}({\eta }_1,{\eta }_2)$ in three ranges of ${\eta }_{+}$, ${\eta }_{-}$, and ${\eta }_{\mathrm{ref}}$, respectively, from $p+\text{Pb}$ collisions with $100\le N_{\mathrm{ch}}^{\mathrm{rec}}<120$. The solid lines indicate fits to either a quadratic function (top left two panels) or a linear function (top right panel). The $〈a_1^2〉{}^{1/2}$ values from the fits are shown in the corresponding lower panels as a function of the ${\eta }_{+}$, ${\eta }_{-}$, and ${\eta }_{\mathrm{ref}}$, respectively. The error bars and shaded bands represent the statistical and systematic uncertainties, respectively. The solid horizontal line and hashed band indicate the value and uncertainty of $〈a_1^2〉{}^{1/2}$ obtained from a Legendre expansion of the $C_{\mathrm{N}}^{\mathrm{sub}}({\eta }_1,{\eta }_2)$.

Figure 12

The distributions $C_{\mathrm{N}}^{\mathrm{sub}}\left({\eta }_{-}\right)$ (top left panel), $C_{\mathrm{N}}^{\mathrm{sub}}\left({\eta }_{+}\right)$ (top middle panel), and $r_{\mathrm{N}}^{\mathrm{sub}}\left(\eta \right)$ (top right panel) obtained from $C_{\mathrm{N}}^{\mathrm{sub}}({\eta }_1,{\eta }_2)$ in three ranges of ${\eta }_{+}$, ${\eta }_{-}$, and ${\eta }_{\mathrm{ref}}$, respectively, from $pp$ collisions with $100\le N_{\mathrm{ch}}^{\mathrm{rec}}<120$. The solid lines indicate fits to either a quadratic function (top left two panels) or a linear function (top right panel). The $〈a_1^2〉{}^{1/2}$ values from the fits are shown in the corresponding lower panels as functions of the ${\eta }_{+}$, ${\eta }_{-}$, and ${\eta }_{\mathrm{ref}}$, respectively. The error bars and shaded bands represent the statistical and systematic uncertainties, respectively. The solid horizontal line and hashed band indicate the value and uncertainty of $〈a_1^2〉{}^{1/2}$ obtained from a Legendre expansion of the $C_{\mathrm{N}}^{\mathrm{sub}}({\eta }_1,{\eta }_2)$.

Figure 13

The $〈a_1^2〉{}^{1/2}$ as a function of $N_{\mathrm{ch}}$ from four different methods, fit $C_{\mathrm{N}}^{\mathrm{sub}}\left({\eta }_{-}\right)$ (solid circles), fit $C_{\mathrm{N}}^{\mathrm{sub}}\left({\eta }_{+}\right)$ (open circles), fit $r_{\mathrm{N}}^{\mathrm{sub}}\left(\eta \right)$ (open squares), and Legendre expansion of $C_{\mathrm{N}}^{\mathrm{sub}}({\eta }_1,{\eta }_2)$ (open diamonds), in Pb+Pb (left panel), $p+\text{Pb}$ (middle panel), and $pp$ (right panel) collisions. The error bars and shaded bands represent the statistical and systematic uncertainties, respectively.

Figure 14

The estimated magnitude of the short-range component $\sqrt{{\mathrm{\Delta }}_{\mathrm{SRC}}}$ as a function of $N_{\mathrm{ch}}$ for all-charge (solid circles), opposite-charge (open circles), and same-charge (open squares) pairs in Pb+Pb (left panel), $p+\text{Pb}$ (middle panel), and $pp$ (right panel) collisions. The shaded bands represent the systematic uncertainties, and the statistical uncertainties are smaller than the symbols.

Figure 15

The estimated magnitude of the short-range component $\sqrt{{\mathrm{\Delta }}_{\mathrm{SRC}}}$ (left panel) and $〈a_1^2〉{}^{1/2}$ (right panel) values as a function of $N_{\mathrm{ch}}$ for all-charge pairs in Pb+Pb (solid circles), $p+\text{Pb}$ (open circles), and $pp$ (open squares) collisions. The shaded bands represent the systematic uncertainties, and the statistical uncertainties are smaller than the symbols.

Figure 16

The shape of the SRC in ${\eta }_{+}$ represented by $f\left({\eta }_{+}\right)$ calculated via Eq. (10) for $p+\text{Pb}$, symmetrized-$p+\text{Pb}$, $pp$, and Pb+Pb collisions with $100\le N_{\mathrm{ch}}^{\mathrm{rec}}<120$. The solid lines represent a fit to a quadratic function.

Figure 17

The $\sqrt{{\mathrm{\Delta }}_{\mathrm{SRC}}}$ (left panel) and $〈a_1^2〉{}^{1/2}$ (right panel) as a function of $N_{\mathrm{ch}}$ in $pp$ collisions at $\sqrt{s}=13$ TeV, compared between data and PYTHIA 8 A2 and EPOS LHC. The shaded bands represent the total uncertainties.