Measurement of long-range pseudorapidity correlations and azimuthal harmonics in $\sqrt{s_{NN}}=5.02$ TeV proton-lead collisions with the ATLAS detector

Measurements of two-particle correlation functions and the first five azimuthal harmonics, $v_1$ to $v_5$, are presented, using 28 ${\mathrm{nb}}^{-1}$ of $p+\text{Pb}$ collisions at a nucleon-nucleon center-of-mass energy of $\sqrt{s_{NN}}=5.02$ TeV measured with the ATLAS detector at the LHC. Significant long-range “ridgelike” correlations are observed for pairs with small relative azimuthal angle ($\left|\Delta \varphi \right|<\pi /3$) and back-to-back pairs ($\left|\Delta \varphi \right|>2\pi /3$) over the transverse momentum range $0.4<p_{\mathrm{T}}<12$ GeV and in different intervals of event activity. The event activity is defined by either the number of reconstructed tracks or the total transverse energy on the Pb-fragmentation side. The azimuthal structure of such long-range correlations is Fourier decomposed to obtain the harmonics $v_n$ as a function of $p_{\mathrm{T}}$ and event activity. The extracted $v_n$ values for $n=2$ to 5 decrease with $n$. The $v_2$ and $v_3$ values are found to be positive in the measured $p_{\mathrm{T}}$ range. The $v_1$ is also measured as a function of $p_{\mathrm{T}}$ and is observed to change sign around $p_{\mathrm{T}}\approx 1.5$–2.0 GeV and then increase to about 0.1 for $p_{\mathrm{T}}>4$ GeV. The $v_2\left(p_{\mathrm{T}}\right)$, $v_3\left(p_{\mathrm{T}}\right)$, and $v_4\left(p_{\mathrm{T}}\right)$ are compared to the $v_n$ coefficients in $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=2.76$ TeV with similar event multiplicities. Reasonable agreement is observed after accounting for the difference in the average $p_{\mathrm{T}}$ of particles produced in the two collision systems.

Figure 1

The distributions of $N_{\mathrm{ch}}^{\mathrm{rec}}$ (left panels) and $E_{\mathrm{T}}^{\mathrm{Pb}}$ (right panels) for MB and $\mathrm{MB}+\mathrm{HMT}$ events before (top panels) and after (bottom panels) applying an event-by-event weight (see text). The smaller symbols in the top panels represent the distributions from the six HMT triggers listed in Table 1.

Figure 2

(a) Correlation between $E_{\mathrm{T}}^{\mathrm{Pb}}$ and $N_{\mathrm{ch}}^{\mathrm{rec}}$ in $\mathrm{MB}+\mathrm{HMT}$ events. (b) The mean $\langle E_{\mathrm{T}}^{\mathrm{Pb}}\rangle$ and root-mean-square ${\sigma }_{{\mathrm{E}}_{\mathrm{T}}^{\mathrm{Pb}}}$ of the $E_{\mathrm{T}}^{\mathrm{Pb}}$ distributions for slices of $N_{\mathrm{ch}}^{\mathrm{rec}}$. The line is a linear fit to all points.

Figure 3

The 2D correlation function in $\Delta \varphi$ and $\Delta \eta$ for the peripheral event class selected by either (a) $E_{\mathrm{T}}^{\mathrm{Pb}}<10$ GeV or (b) $N_{\mathrm{ch}}^{\mathrm{rec}}<20$ and the central event class selected by either (c) $E_{\mathrm{T}}^{\mathrm{Pb}}\ge 100$ GeV or (d) $N_{\mathrm{ch}}^{\mathrm{rec}}\ge 220$.

Figure 4

The 2D correlation function in $\Delta \varphi$ and $\Delta \eta$ for events with $N_{\mathrm{ch}}^{\mathrm{rec}}\ge 220$ (a) before and (b) after subtraction of the peripheral yield. Panel (c) shows the corresponding 1D correlation functions in $\Delta \varphi$ for pairs integrated over $2<\left|\Delta \eta \right|<5$ from panels (a) and (b), together with Fourier fits including the first five harmonics. Panel (d) shows the second-, third-, and fourth-order Fourier coefficients as functions of $\left|\Delta \eta \right|$ calculated from the 2D distributions in panel (a) or panel (b), represented by the open or solid symbols, respectively. The error bars and shaded boxes are statistical and systematic uncertainties, respectively.

Figure 5

The per-trigger yield distributions $Y^{\mathrm{corr}}\left(\Delta \varphi \right)$ and $Y^{\mathrm{recoil}}\left(\Delta \varphi \right)$ for events with $N_{\mathrm{ch}}^{\mathrm{rec}}\ge 220$ in the long-range region $\left|\Delta \eta \right|>2$. The distributions are shown for $1<p_{\mathrm{T}}^{\mathrm{b}}<3$ GeV in various $p_{\mathrm{T}}^{\mathrm{a}}$ ranges. They are compared to the recoil contribution estimated from a peripheral event class defined by $E_{\mathrm{T}}^{\mathrm{Pb}}<10$ GeV using a rescaling procedure [see Eq. (6) and discussion around it]. The curves are Fourier fits including the first five harmonics.

Figure 6

Integrated per-trigger yields $Y_{\mathrm{int}}$ as a function of $p_{\mathrm{T}}^{\mathrm{a}}$ for $1<p_{\mathrm{T}}^{\mathrm{b}}<3$ GeV, for events in various $N_{\mathrm{ch}}^{\mathrm{rec}}$ ranges on (a) the near side and (b) the away side. The errors bars and shaded bands represent the statistical and systematic uncertainties, respectively.

Figure 7

The integrated per-trigger yield, $Y_{\mathrm{int}}$, on the near side (circles), the away side (squares), and their difference (diamonds) as functions of (a) $N_{\mathrm{ch}}^{\mathrm{rec}}$ and (b) $E_{\mathrm{T}}^{\mathrm{Pb}}$ for pairs in $2<\left|\Delta \eta \right|<5$ and $1<p_{\mathrm{T}}^{\mathrm{a},\mathrm{b}}<3$ GeV. The yield difference is compared to the estimated recoil contribution in the away side (solid lines). The error bars or the shaded bands represent the combined statistical and systematic uncertainties.

Figure 8

The Fourier coefficients $v_2$, $v_3$, and $v_4$ as functions of $p_{\mathrm{T}}^{\mathrm{a}}$ extracted from the correlation functions for events with $N_{\mathrm{ch}}^{\mathrm{rec}}\ge 220$, before (denoted by $v_n^{\mathrm{unsub}}$) and after (denoted by $v_n$) the subtraction of the recoil component. Each panel shows the results for one harmonic. The pairs are formed from charged particles with $1<p_{\mathrm{T}}^{\mathrm{b}}<3$ GeV and $\left|\Delta \eta \right|>2$. The error bars and shaded boxes represent the statistical and systematic uncertainties, respectively.

Figure 9

The $v_n\left(p_{\mathrm{T}}^{\mathrm{a}}\right)$ with $n=2$ to 5 for six $N_{\mathrm{ch}}^{\mathrm{rec}}$ event-activity classes obtained for $\left|\Delta \eta \right|>2$ and the $p_{\mathrm{T}}^{\mathrm{b}}$ range of 1–3 GeV. The error bars and shaded boxes represent the statistical and systematic uncertainties, respectively. Results in $220\le N_{\mathrm{ch}}^{\mathrm{rec}}<260$ are compared to the CMS data [28] obtained by subtracting the peripheral events (the number of off-line tracks $N_{\mathrm{trk}}^{\mathrm{off}}<20$), shown by the solid and dashed lines.

Figure 10

The $v_2$ (left column), $v_3$ (middle column), and $v_4$ (right column) as functions of $p_{\mathrm{T}}^{\mathrm{a}}$ extracted using four $p_{\mathrm{T}}^{\mathrm{b}}$ bins in the long-range region $\left|\Delta \eta \right|>2$ for events with $N_{\mathrm{ch}}^{\mathrm{rec}}\ge 220$. The ratio of the $v_n\left(p_{\mathrm{T}}^{\mathrm{a}}\right)$ in each $p_{\mathrm{T}}^{\mathrm{b}}$ bin to those obtained with the default reference $p_{\mathrm{T}}^{\mathrm{b}}$ bin of 1–3 GeV are shown in the bottom part of each column. The error bars and shaded bands represent the statistical and systematic uncertainties, respectively.

Figure 11

The values of factorization variable defined by Eq. (11) before (denoted by $r_n^{\mathrm{unsub}}$) and after (denoted by $r_n$) the subtraction of the recoil component. They are shown for $n=2$ (top row) and $n=3$ (bottom row) as functions of $p_{\mathrm{T}}^{\mathrm{b}}-p_{\mathrm{T}}^{\mathrm{a}}$ in various $p_{\mathrm{T}}^{\mathrm{b}}$ ranges for events in $N_{\mathrm{ch}}^{\mathrm{rec}}\ge 220$. The solid lines represent a theoretical prediction from Ref. [51]. The error bars represent the total experimental uncertainties.

Figure 12

The centrality dependence of $v_2$, $v_3$, and $v_4$ as functions of $N_{\mathrm{ch}}^{\mathrm{rec}}$ (top row) and $E_{\mathrm{T}}^{\mathrm{Pb}}$ (bottom row) for pairs with $0.4<p_{\mathrm{T}}^{\mathrm{a},\mathrm{b}}<3$ GeV and $\left|\Delta \eta \right|>2$. The results are obtained with (symbols) and without (lines) the subtraction of the recoil contribution. The error bars and shaded boxes on $v_n$ data represent the statistical and systematic uncertainties, respectively, while the error bars on the $v_n^{\mathrm{unsub}}$ represent the combined statistical and systematic uncertainties.

Figure 13

The $v_2$ (left panel) and $v_3$ (right panel) as functions of $E_{\mathrm{T}}^{\mathrm{Pb}}$ calculated directly for narrow ranges in $E_{\mathrm{T}}^{\mathrm{Pb}}$ (open circles) or obtained indirectly by mapping from the $N_{\mathrm{ch}}^{\mathrm{rec}}$ dependence of $v_n$ using the correlation data shown in Fig. 2 (solid circles). The error bars and shaded boxes represent the statistical and systematic uncertainties, respectively.

Figure 14

The first-order harmonic of 2PC before recoil subtraction $v_{1,1}^{\mathrm{unsub}}$ (left panel) and after recoil subtraction $v_{1,1}$ (right panel) as functions of $p_{\mathrm{T}}^{\mathrm{a}}$ for different $p_{\mathrm{T}}^{\mathrm{b}}$ ranges for events with $N_{\mathrm{ch}}^{\mathrm{rec}}\ge 220$. The error bars and shaded boxes represent the statistical and systematic uncertainties, respectively.

Figure 15

The $p_{\mathrm{T}}^{\mathrm{a}}$ dependence of $v_1$ extracted using the factorization relations Eqs. (13) and (14) in three reference $p_{\mathrm{T}}^{\mathrm{b}}$ ranges for events with $N_{\mathrm{ch}}^{\mathrm{rec}}\ge 220$. The error bars and shaded boxes represent the statistical and systematic uncertainties, respectively.

Figure 16

The coefficients $v_2$ (top row), $v_3$ (middle row), and $v_4$ (bottom row) as functions of $p_{\mathrm{T}}$ compared between $p+\text{Pb}$ collisions with $220\le N_{\mathrm{ch}}^{\mathrm{rec}}<260$ in this analysis and $\mathrm{Pb}+\mathrm{Pb}$ collisions in 55%–60% centrality from Ref. [9]. The left column shows the original data with their statistical (error bars) and systematic uncertainties (shaded boxes). In the right column, the same $\mathrm{Pb}+\mathrm{Pb}$ data are rescaled horizontally by a constant factor of 1.25, and the $v_2$ and $v_4$ are also downscaled by an empirical factor of 0.66 to match the $p+\text{Pb}$ data.