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| CMS-HIN-16-010 ; CERN-EP-2016-147 | ||
| Evidence for collectivity in pp collisions at the LHC | ||
| CMS Collaboration | ||
| 20 June 2016 | ||
| Phys. Lett. B 765 (2017) 193 | ||
| Abstract: Measurements of two- and multi-particle angular correlations in pp collisions at $\sqrt{s} = $ 5, 7, and 13 TeV are presented as a function of charged-particle multiplicity. The data, corresponding to integrated luminosities of 1.0 pb$^{-1}$ (5 TeV), 6.2 pb$^{-1}$ (7 TeV), and 0.7 pb$^{-1}$ (13 TeV), were collected using the CMS detector at the LHC. The second-order ($v_2$) and third-order ($v_3$) azimuthal anisotropy harmonics of unidentified charged particles, as well as $v_2$ of $\mathrm{ K_S }^0$ and $\Lambda/\overline{\Lambda}$ particles, are extracted from long-range two-particle correlations as functions of particle multiplicity and transverse momentum. For high-multiplicity pp events, a mass ordering is observed for the $v_2$ values of charged hadrons (mostly pions), $\mathrm{ K_S }^0$, and $\Lambda/\overline{\Lambda}$, with lighter particle species exhibiting a stronger azimuthal anisotropy signal below $p_{\mathrm{T}} \approx 2$ GeV/$c$. For 13 TeV data, the $v_2$ signals are also extracted from four- and six-particle correlations for the first time in pp collisions, with comparable magnitude to those from two-particle correlations. These observations are similar to those seen in pPb and PbPb collisions, and support the interpretation of a collective origin for the observed long-range correlations in high-multiplicity pp collisions. | ||
| Links: e-print arXiv:1606.06198 [nucl-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures & Tables | Summary | Additional Figures | References | CMS Publications |
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| Figures | |
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Figure 1-a:
The 2D two-particle correlation functions for inclusive charged particles (top), $\mathrm{ K_S }^0 $ particles (middle), and $ \Lambda /\overline{\Lambda} $ particles (bottom), with 1 $ < { {p_{\mathrm {T}}} ^{\text {trig}}} <$ 3 GeV/$c$ and associated charged particles with 1 $ < { {p_{\mathrm {T}}} ^{\text {assoc}}} < $ 3 GeV/$c$, in low-multiplicity (10 $ \leq {N_\text {trk}^\text {offline}} < $ 20) pp collisions at $ {\sqrt {s}} = $ 13 TeV. |
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Figure 1-b:
The 2D two-particle correlation functions for inclusive charged particles (top), $\mathrm{ K_S }^0 $ particles (middle), and $ \Lambda /\overline{\Lambda} $ particles (bottom), with 1 $ < { {p_{\mathrm {T}}} ^{\text {trig}}} <$ 3 GeV/$c$ and associated charged particles with 1 $ < { {p_{\mathrm {T}}} ^{\text {assoc}}} < $ 3 GeV/$c$, in high-multiplicity (105 $ \leq {N_\text {trk}^\text {offline}} < $ 150) pp collisions at $ {\sqrt {s}} = $ 13 TeV. |
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Figure 2:
The 1D ${\Delta \phi }$ correlation functions for the long-range (top) and short- minus long-range (bottom) regions after applying the ZYAM procedure in the multiplicity range 10 $ \leq {N_\text {trk}^\text {offline}} < $ 20 (open symbols) and 105 $ \leq {N_\text {trk}^\text {offline}} < $ 150 (filled symbols) of pp collisions at $ {\sqrt {s}} = $ 13 TeV, for trigger particles composed of inclusive charged particles (left, crosses), $\mathrm{ K_S }^0 $ particles (middle, squares), and $ \Lambda /\overline{\Lambda} $ particles (right, circles). A selection of 1-3 {GeV/$c$} \ for both ${ {p_{\mathrm {T}}} ^{\text {trig}}} $ and ${ {p_{\mathrm {T}}} ^{\text {assoc}}} $ is used in all cases. |
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Figure 3:
The 1D ${\Delta \phi }$ correlation functions for the long-range regions in the multiplicity range 105 $ \leq {N_\text {trk}^\text {offline}} < $ 150 of pp collisions at $ {\sqrt {s}} = $ 13 TeV, after subtracting scaled results from 10 $ \leq {N_\text {trk}^\text {offline}} < $ 20 with the ZYAM procedure applied. A selection of 1-3 GeV/$c$ for both ${ {p_{\mathrm {T}}} ^{\text {trig}}} $ and ${ {p_{\mathrm {T}}} ^{\text {assoc}}} $ is used in all cases. |
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Figure 4-a:
The third-order Fourier coefficients, $V_{3\Delta }$, of long-range ($ {| {\Delta \eta } | }> $ 2 ) two-particle ${\Delta \phi }$ correlations as a function of ${N_\text {trk}^\text {offline}}$ for charged particles, averaged over 0.3 $ < {p_{\mathrm {T}}} <$ 3.0 GeV/$c$, in pp collisions at $ {\sqrt {s}} = $ 13 TeV, before (open) and after (filled) correcting for back-to-back jet correlations, estimated from the 10 $ \leq {N_\text {trk}^\text {offline}} < $ 20 range. Results from PYTHIA-8 tune CUETP8M1 simulation are shown as curves. The error bars correspond to statistical uncertainties, while the shaded areas denote the systematic uncertainties. |
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Figure 4-b:
The third-order Fourier coefficients, $V_{3\Delta }$, of long-range ($ {| {\Delta \eta } | }> $ 2 ) two-particle ${\Delta \phi }$ correlations as a function of ${N_\text {trk}^\text {offline}}$ for charged particles, averaged over 0.3 $ < {p_{\mathrm {T}}} <$ 3.0 GeV/$c$, in pp collisions at $ {\sqrt {s}} = $ 13 TeV, before (open) and after (filled) correcting for back-to-back jet correlations, estimated from the 10 $ \leq {N_\text {trk}^\text {offline}} < $ 20 range. Results from PYTHIA-8 tune CUETP8M1 simulation are shown as curves. The error bars correspond to statistical uncertainties, while the shaded areas denote the systematic uncertainties. |
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Figure 5:
The $v_{2}^\text {sub}$ (top) and $v_{3}^\text {sub}$ (bottom) results of charged particles as a function of ${N_\text {trk}^\text {offline}} $, averaged over 0.3 $ < {p_{\mathrm {T}}} <$ 3.0 GeV/$c$, in pp collisions at $ {\sqrt {s}} = $ 5, 7, and 13 TeV, pPb collisions at $ {\sqrt {s_{_\mathrm {NN}}}} = $ 5 TeV, and PbPb collisions $ {\sqrt {s_{_\mathrm {NN}}}} = $ 2.76 TeV, after correcting for back-to-back jet correlations estimated from low-multiplicity data. The error bars correspond to the statistical uncertainties, while the shaded areas denote the systematic uncertainties. Systematic uncertainties are found to have no dependence on ${\sqrt {s}}$ for pp results and therefore are only shown for 13 TeV. |
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Figure 6-a:
The $v_2$ results of inclusive charged particles, before subtracting correlations from low-multiplicity events, as a function of ${p_{\mathrm {T}}}$ in pp collisions at $ {\sqrt {s}} = $ 13 TeV for 105 $ \leq {N_\text {trk}^\text {offline}} < $ 150 and at $ {\sqrt {s}} = $ 5, 7 TeV for 110 $ \leq {N_\text {trk}^\text {offline}} < $ 150. The error bars correspond to the statistical uncertainties, while the shaded areas denote the systematic uncertainties. Systematic uncertainties are found to have no dependence on $\sqrt {s}$ for pp results and therefore are only shown for 13 TeV. |
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Figure 6-b:
The $v_2$ results of inclusive charged particles, after subtracting correlations from low-multiplicity events, as a function of ${p_{\mathrm {T}}}$ in pp collisions at $ {\sqrt {s}} = $ 13 TeV for 105 $ \leq {N_\text {trk}^\text {offline}} < $ 150 and at $ {\sqrt {s}} = $ 5, 7 TeV for 110 $ \leq {N_\text {trk}^\text {offline}} < $ 150. The error bars correspond to the statistical uncertainties, while the shaded areas denote the systematic uncertainties. Systematic uncertainties are found to have no dependence on $\sqrt {s}$ for pp results and therefore are only shown for 13 TeV. |
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Figure 7-a:
The $v_2$ results for inclusive charged particles, $\mathrm{ K_S }^0 $ and $ \Lambda /\overline{\Lambda} $ particles as a function of ${p_{\mathrm {T}}}$ in pp collisions at $ {\sqrt {s}} = $ 13 TeV, for 10 $ \leq {N_\text {trk}^\text {offline}} < $ 20. The error bars correspond to the statistical uncertainties, while the shaded areas denote the systematic uncertainties. |
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Figure 7-b:
The $v_2$ results for inclusive charged particles, $\mathrm{ K_S }^0 $ and $ \Lambda /\overline{\Lambda} $ particles as a function of ${p_{\mathrm {T}}}$ in pp collisions at $ {\sqrt {s}} = $ 13 TeV, for 105 $ \leq {N_\text {trk}^\text {offline}} < $ 150. The error bars correspond to the statistical uncertainties, while the shaded areas denote the systematic uncertainties. |
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Figure 8:
Top: the $v_{2}^\text {sub}$ results of inclusive charged particles, $\mathrm{ K_S }^0 $ and $ \Lambda /\overline{\Lambda} $ particles as a function of ${p_{\mathrm {T}}}$ for 105 $ \leq {N_\text {trk}^\text {offline}} < $ 150, after correcting for back-to-back jet correlations estimated from low-multiplicity data. Bottom: the $n_\mathrm {q}$-scaled $v_{2}^\text {sub}$ results for $\mathrm{ K_S }^0 $ and $ \Lambda /\overline{\Lambda} $ particles as a function of $ {KE_{\mathrm {T}}} /n_\mathrm {q}$. Ratios of $v_{2}^\text {sub}/n_\mathrm {q}$ for $\mathrm{ K_S }^0 $ and $ \Lambda /\overline{\Lambda} $ particles to a smooth fit function of data for $\mathrm{ K_S }^0 $ particles are also shown. The error bars correspond to the statistical uncertainties, while the shaded areas denote the systematic uncertainties. |
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Figure 9-a:
The $c_{2}\{4\}$ values as a function of ${N_\text {trk}^\text {offline}}$ for charged particles, averaged over 0.3 $ < {p_{\mathrm {T}}} <$ 3.0 GeV/$c$ and $ {| \eta | }< $ 2.4, in pp collisions at $ {\sqrt {s}} = $ 5, 7, and 13 TeV. The pPb data at $ {\sqrt {s_{_\mathrm {NN}}}} = $ 5 TeV are also plotted for comparison. The error bars correspond to the statistical uncertainties, while the shaded areas denote the systematic uncertainties. Systematic uncertainties are found to have no dependence on ${\sqrt {s}}$ for pp results and therefore are only shown for 13 TeV. |
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Figure 9-b:
The $c_{2}\{6\}$ values as a function of ${N_\text {trk}^\text {offline}}$ for charged particles, averaged over 0.3 $ < {p_{\mathrm {T}}} <$ 3.0 GeV/$c$ and $ {| \eta | }< $ 2.4, in pp collisions at $ {\sqrt {s}} = $ 5, 7, and 13 TeV. The pPb data at $ {\sqrt {s_{_\mathrm {NN}}}} = $ 5 TeV are also plotted for comparison. The error bars correspond to the statistical uncertainties, while the shaded areas denote the systematic uncertainties. Systematic uncertainties are found to have no dependence on ${\sqrt {s}}$ for pp results and therefore are only shown for 13 TeV. |
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Figure 10:
Left: The $v_{2}^\text {sub}$, $v_{2}\{4\}$ and $v_{2}\{6\}$ values as a function of ${N_\text {trk}^\text {offline}}$ for charged particles, averaged over 0.3 $ < {p_{\mathrm {T}}} < $ 3.0 GeV/$c$ and $ {| \eta | }< $ 2.4, in pp collisions at $ {\sqrt {s}} = $ 13 TeV. Middle: The $v_{2}^\text {sub}$, $v_{2}\{4\}$, $v_{2}\{6\}$, $v_{2}\{8\}$, and $v_{2}\{\mathrm {LYZ}\}$ values in pPb collisions at $ {\sqrt {s_{_\mathrm {NN}}}} = $ 5 TeV [40]. Right: The $v_{2}^\text {sub}$, $v_{2}\{4\}$, $v_{2}\{6\}$, $v_{2}\{8\}$, and $v_{2}\{\mathrm {LYZ}\}$ values in PbPb collisions at $ {\sqrt {s_{_\mathrm {NN}}}} = $ 2.76 TeV [40]. The error bars correspond to the statistical uncertainties, while the shaded areas denote the systematic uncertainties. |
| Tables | |
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Table 1:
Fraction of MB triggered events after event selections in each multiplicity bin, and the average multiplicity of reconstructed tracks per bin with $ {| \eta | }< $ 2.4 and $ {p_{\mathrm {T}}} > $ 0.4 GeV/$c$, before ($ {N_\text {trk}^\text {offline}} $) and after ($N_\text {trk}^\text {corrected}$) efficiency correction, for pp data at $ {\sqrt {s}} = $ 5, 7, and 13 TeV. |
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Table 2:
Summary of systematic uncertainties for multiplicity-dependent $v_{n}^\text {sub}\{2\}$ from two-particle correlations (after correcting for jet correlations), and $v_{2}\{4\}$, $v_{2}\{6\}$ from multi-particle correlations in pp collisions. Different multiplicity ranges are represented as $ [m,n)$. |
| Summary |
| The CMS detector has been used to measure two- and multi-particle azimuthal correlations with $\mathrm{ K_S }^0$, $\Lambda/\overline{\Lambda}$ and inclusive charged particles over a broad pseudorapidity and transverse momentum range in pp collisions at ${\sqrt{s}} = $ 5, 7, and 13 TeV. With the implementation of high-multiplicity triggers during the LHC 2010 and 2015 pp runs, the correlation data are explored over a broad particle multiplicity range. The observed long-range ($| {\Delta\eta} | > $ 2 ) correlations are quantified in terms of azimuthal anisotropy Fourier harmonics ($v_n$). The elliptic ($v_2$) and triangular ($v_3$) flow Fourier harmonics are extracted from long-range two-particle correlations. After subtracting contributions from back-to-back jet correlations estimated using low-multiplicity data, the $v_2$ and $v_3$ values are found to increase with multiplicity for ${N_\text{trk}^\text{offline}} \le $ 100, and reach a relatively constant value at higher values of ${N_\text{trk}^\text{offline}} $. The $ p_{\mathrm{T}} $ dependence of the $v_2$ harmonics in high-multiplicity pp events is found to have no or very weak dependence on the collision energy. In low-multiplicity events, similar $v_2$ values as a function of $ p_{\mathrm{T}} $ are observed for inclusive charged particles, $\mathrm{ K_S }^0$ and $\Lambda/\overline{\Lambda}$, possibly reflecting a common back-to-back jet origin of the correlations for all particle species. Moving to the higher-multiplicity region, a particle species dependence of $v_2$ is observed with and without correcting for jet correlations. For $p_{\mathrm{T}} \le$ 2 GeV/$c$, the $v_2$ of $\mathrm{ K_S }^0$ is found to be larger than that of $\Lambda/\overline{\Lambda}$. This behavior, which is consistent with predictions of hydrodynamic models, is similar to what was previously observed for identified particles produced in pPb and AA collisions at RHIC and the LHC. This mass ordering is reversed at higher $ p_{\mathrm{T}} $ values. Finally, $v_2$ signals based on four- and six-particle correlations are observed for the first time in pp collisions. The $v_2$ values obtained with two-, four-, and six-particle correlations at ${\sqrt{s}} = $ 13 TeV are found to be comparable within uncertainties. These observations provide strong evidence supporting the interpretation of a collective origin for the observed long-range correlations in high-multiplicity pp collisions. |
| Additional Figures | |
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Additional Figure 1:
Left: The $v_{2}^\text {sub}$, $v_{2}\{4\}$ and $v_{2}\{6\}$ values as a function of ${N_\text {trk}^\text {offline}}$ for charged particles, averaged over 0.3 $< {p_{\mathrm {T}}} < $ 3.0 GeV/$c$ and $ {| \eta | }<$ 2.4, in pp collisions at $ {\sqrt {s}} = $ 13 TeV. Middle: The $v_{2}^\text {sub}$, $v_{2}\{4\}$, $v_{2}\{6\}$, $v_{2}\{8\}$, and $v_{2}\{\mathrm {LYZ}\}$ values in pPb collisions at $ {\sqrt {s_{_\mathrm {NN}}}} = $ 5 TeV [43]. Right: The $v_{2}^\text {sub}$, $v_{2}\{4\}$, $v_{2}\{6\}$, $v_{2}\{8\}$, and $v_{2}\{\mathrm {LYZ}\}$ values in PbPb collisions at $ {\sqrt {s_{_\mathrm {NN}}}} = $ 2.76 TeV [43]. $v_{2}\{2\}$ results without jet subtraction are shown as lines for all three collision systems. The error bars correspond to the statistical uncertainties, while the shaded areas denote the systematic uncertainties. |
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Additional Figure 2:
Comparison of $c_{2}\{4\}$ distributions when $N_{\mathrm {trk}}^{\mathrm {ref}}$ is not fixed (full squares) and fixed (open squares) as a function of ${N_\text {trk}^\text {offline}} $. |
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Additional Figure 3:
$c_{2}\{4\}$ distribution as a function of $N_{\mathrm {trk}}^{\mathrm {ref}}$ for the full $N_{\mathrm {trk}}^{\mathrm {ref}}$ range (full) and for high multiplicity region (insert). |
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Additional Figure 4:
$c_{2}\{4\}$ distributions for different ${p_{\mathrm {T}}}$ range selections as a function of ${N_\text {trk}^\text {offline}} $. The $c_{2}\{4\}$ distributions are computed at fixed $N_{\mathrm {trk}}^{\mathrm {ref}}$. |
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Additional Figure 4-a:
$c_{2}\{4\}$ distributions for different ${p_{\mathrm {T}}}$ range selections as a function of ${N_\text {trk}^\text {offline}} $. The $c_{2}\{4\}$ distributions are computed at fixed $N_{\mathrm {trk}}^{\mathrm {ref}}$. |
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Additional Figure 4-b:
$c_{2}\{4\}$ distributions for different ${p_{\mathrm {T}}}$ range selections as a function of ${N_\text {trk}^\text {offline}} $. The $c_{2}\{4\}$ distributions are computed at fixed $N_{\mathrm {trk}}^{\mathrm {ref}}$. |
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Additional Figure 5:
$v_{2}\{4\}$ as a function of ${N_\text {trk}^\text {offline}}$ (left) and $N_{\mathrm {trk}}^{\mathrm {ref}}$ (right). The results as a function of ${N_\text {trk}^\text {offline}}$ are the ones presented in the paper. |
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Compact Muon Solenoid LHC, CERN |
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