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Correlated long-range mixed-harmonic fluctuations measured in $pp$, $p$+Pb and low-multiplicity Pb+Pb collisions with the ATLAS detector

The collaboration
2018.

Abstract
Correlations of two flow harmonics $v_n$ and $v_m$ via three- and four-particle cumulants are measured in 13 TeV $pp$, 5.02 TeV $p$+Pb, and 2.76 TeV peripheral Pb+Pb collisions with the ATLAS detector at the LHC. The goal is to understand the multi-particle nature of the long-range collective phenomenon in these collision systems. The large non-flow background from dijet production present in the standard cumulant method is suppressed using a method of subevent cumulants involving two, three and four subevents separated in pseudorapidity. The results show a negative correlation between $v_2$ and $v_3$ and a positive correlation between $v_2$ and $v_4$ for all collision systems and over the full multiplicity range. However, the magnitudes of the correlations are found to depend strongly on the event multiplicity, the choice of transverse momentum range and collision system. The relative correlation strength, obtained by normalisation of the cumulants with the $\langle v_n^2\rangle$ from a two-particle correlation analysis, is similar in the three collision systems and depends weakly on the event multiplicity and transverse momentum. These results based on the subevent methods provide strong evidence of a similar long-range multi-particle collectivity in $pp$, $p$+Pb and peripheral Pb+Pb collisions.

• #### Table 1

Data from Figure 1 (top left)

10.17182/hepdata.83969.v1/t1

The symmetric cumulant $sc_{2,3}\{4\}$ results as a function of multiplicity ($N_{ch}$) in pp collisions at $\sqrt{s_{NN}}$ = 13 TeV

• #### Table 2

Data from Figure 1 (top right)

10.17182/hepdata.83969.v1/t2

The symmetric cumulant $sc_{2\,3}\{4\}$ results as a function of multiplicity ($N_{ch}$) in pp collisions at $\sqrt{s_{NN}}$ = 13 TeV

• #### Table 3

Data from Figure 1 (middle left)

10.17182/hepdata.83969.v1/t3

The symmetric cumulant $sc_{2\,3}\{4\}$ results as a function of multiplicity ($N_{ch}$) in pPb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV

• #### Table 4

Data from Figure 1 (middle right)

10.17182/hepdata.83969.v1/t4

The symmetric cumulant $sc_{2\,3}\{4\}$ results as a function of multiplicity ($N_{ch}$) in pPb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV

• #### Table 5

Data from Figure 1 (bottom left)

10.17182/hepdata.83969.v1/t5

The symmetric cumulant $sc_{2\,3}\{4\}$ results as a function of multiplicity ($N_{ch}$) in PbPb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

• #### Table 6

Data from Figure 1 (bottom right)

10.17182/hepdata.83969.v1/t6

The symmetric cumulant $sc_{2\,4}\{4\}$ results as a function of multiplicity ($N_{ch}$) in PbPb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

• #### Table 7

Data from Figure 2 (top left)

10.17182/hepdata.83969.v1/t7

The symmetric cumulant $sc_{2\,4}\{4\}$ results as a function of multiplicity ($N_{ch}$) in pp collisions at $\sqrt{s_{NN}}$ = 13 TeV

• #### Table 8

Data from Figure 2 (top right)

10.17182/hepdata.83969.v1/t8

The symmetric cumulant $sc_{2\,4}\{4\}$ results as a function of multiplicity ($N_{ch}$) in pp collisions at $\sqrt{s_{NN}}$ = 13 TeV

• #### Table 9

Data from Figure 2 (middle left)

10.17182/hepdata.83969.v1/t9

The symmetric cumulant $sc_{2\,4}\{4\}$ results as a function of multiplicity ($N_{ch}$) in pPb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV

• #### Table 10

Data from Figure 2 (middle right)

10.17182/hepdata.83969.v1/t10

The symmetric cumulant $sc_{2\,4}\{4\}$ results as a function of multiplicity ($N_{ch}$) in pPb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV

• #### Table 11

Data from Figure 2 (bottom left)

10.17182/hepdata.83969.v1/t11

The symmetric cumulant $sc_{2\,4}\{4\}$ results as a function of multiplicity ($N_{ch}$) in PbPb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

• #### Table 12

Data from Figure 2 (bottom right)

10.17182/hepdata.83969.v1/t12

The symmetric cumulant $sc_{2\,4}\{4\}$ results as a function of multiplicity ($N_{ch}$) in PbPb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

• #### Table 13

Data from Figure 3 (top left)

10.17182/hepdata.83969.v1/t13

The asymmetric cumulant $ac_{2}\{3\}$ results as a function of multiplicity ($N_{ch}$) in pp collisions at $\sqrt{s_{NN}}$ = 13 TeV

• #### Table 14

Data from Figure 3 (top right)

10.17182/hepdata.83969.v1/t14

The asymmetric cumulant $ac_{2}\{3\}$results as a function of multiplicity ($N_{ch}$) in pp collisions at $\sqrt{s_{NN}}$ = 13 TeV

• #### Table 15

Data from Figure 3 (middle left)

10.17182/hepdata.83969.v1/t15

The asymmetric cumulant $ac_{2}\{3\}$results as a function of multiplicity ($N_{ch}$) in pPb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV

• #### Table 16

Data from Figure 3 (middle right)

10.17182/hepdata.83969.v1/t16

The asymmetric cumulant $ac_{2}\{3\}$ results as a function of multiplicity ($N_{ch}$) in pPb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV

• #### Table 17

Data from Figure 3 (bottom left)

10.17182/hepdata.83969.v1/t17

The asymmetric cumulant $ac_{2}\{3\}$ results as a function of multiplicity ($N_{ch}$) in PbPb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

• #### Table 18

Data from Figure 3 (bottom right)

10.17182/hepdata.83969.v1/t18

The asymmetric cumulant $ac_{2}\{3\}$ results as a function of multiplicity ($N_{ch}$) in PbPb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

• #### Table 19

Data from Figure 5 (top left)

10.17182/hepdata.83969.v1/t19

The normalized symmetric cumulant $nsc_{2\,3}\{4\}$ results as a function of multiplicity ($N_{ch}$) in pp collisions at $\sqrt{s_{NN}}$ = 13 TeV

• #### Table 20

Data from Figure 5 (top middle)

10.17182/hepdata.83969.v1/t20

The normalized symmetric cumulant $nsc_{2\,4}\{4\}$ results as a function of multiplicity ($N_{ch}$) in pp collisions at $\sqrt{s_{NN}}$ = 13 TeV

• #### Table 21

Data from Figure 5 (top right)

10.17182/hepdata.83969.v1/t21

The normalized asymmetric cumulant $nac_{2}\{3\}$ results as a function of multiplicity ($N_{ch}$) in pp collisions at $\sqrt{s_{NN}}$ = 13 TeV

• #### Table 22

Data from Figure 5 (bottom left)

10.17182/hepdata.83969.v1/t22

The normalized symmetric cumulant $nsc_{2\,3}\{4\}$ results as a function of multiplicity ($N_{ch}$) in pp collisions at $\sqrt{s_{NN}}$ = 13 TeV

• #### Table 23

Data from Figure 5 (bottom middle)

10.17182/hepdata.83969.v1/t23

The normalized symmetric cumulant $nsc_{2\,4}\{4\}$ results as a function of multiplicity ($N_{ch}$) in pp collisions at $\sqrt{s_{NN}}$ = 13 TeV

• #### Table 24

Data from Figure 5 (bottom right)

10.17182/hepdata.83969.v1/t24

The normalized asymmetric cumulant $nac_{2}\{3\}$ results as a function of multiplicity ($N_{ch}$) in pPb collisions at $\sqrt{s_{NN}}$ = 13 TeV

• #### Table 25

Data from Figure 5 (top left)

10.17182/hepdata.83969.v1/t25

The normalized symmetric cumulant $nsc_{2\,3}\{4\}$ results as a function of multiplicity ($N_{ch}$) in pPb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV

• #### Table 26

Data from Figure 5 (top middle)

10.17182/hepdata.83969.v1/t26

The normalized symmetric cumulant $nsc_{2\,4}\{4\}$ results as a function of multiplicity ($N_{ch}$) in pPb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV

• #### Table 27

Data from Figure 5 (top right)

10.17182/hepdata.83969.v1/t27

The normalized asymmetric cumulant $nac_{2}\{3\}$ results as a function of multiplicity ($N_{ch}$) in pPb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV

• #### Table 28

Data from Figure 5 (bottom left)

10.17182/hepdata.83969.v1/t28

The normalized symmetric cumulant $nsc_{2\,3}\{4\}$ results as a function of multiplicity ($N_{ch}$) in pPb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV

• #### Table 29

Data from Figure 5 (bottom middle)

10.17182/hepdata.83969.v1/t29

The normalized symmetric cumulant $nsc_{2\,4}\{4\}$ results as a function of multiplicity ($N_{ch}$) in pPb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV

• #### Table 30

Data from Figure 5 (bottom right)

10.17182/hepdata.83969.v1/t30

The normalized asymmetric cumulant $nac_{2}\{3\}$ results as a function of multiplicity ($N_{ch}$) in pPb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV

• #### Table 31

Data from Figure 5 (top left)

10.17182/hepdata.83969.v1/t31

The normalized symmetric cumulant $nsc_{2\,3}\{4\}$ results as a function of multiplicity ($N_{ch}$) in PbPb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

• #### Table 32

Data from Figure 5 (top middle)

10.17182/hepdata.83969.v1/t32

The normalized symmetric cumulant $nsc_{2\,4}\{4\}$ results as a function of multiplicity ($N_{ch}$) in PbPb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

• #### Table 33

Data from Figure 5 (top right)

10.17182/hepdata.83969.v1/t33

The normalized asymmetric cumulant $nac_{2}\{3\}$ results as a function of multiplicity ($N_{ch}$) in PbPb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

• #### Table 34

Data from Figure 5 (bottom left)

10.17182/hepdata.83969.v1/t34

The normalized symmetric cumulant $nsc_{2\,3}\{4\}$ results as a function of multiplicity ($N_{ch}$) in PbPb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

• #### Table 35

Data from Figure 5 (bottom middle)

10.17182/hepdata.83969.v1/t35

The normalized symmetric cumulant $nsc_{2\,4}\{4\}$ results as a function of multiplicity ($N_{ch}$) in PbPb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

• #### Table 36

Data from Figure 5 (bottom right)

10.17182/hepdata.83969.v1/t36

The normalized asymmetric cumulant $nac_{2}\{3\}$ results as a function of multiplicity ($N_{ch}$) in PbPb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

• #### Table 37

Data from Figure 7 (top left)

10.17182/hepdata.83969.v1/t37

The $v_{2}\{2\}$ results as a function of multiplicity ($N_{ch}$) in pp collisions at $\sqrt{s_{NN}}$ = 13 TeV

• #### Table 38

Data from Figure 7 (top middle)

10.17182/hepdata.83969.v1/t38

The $v_{3}\{2\}$ results as a function of multiplicity ($N_{ch}$) in pp collisions at $\sqrt{s_{NN}}$ = 13 TeV

• #### Table 39

Data from Figure 7 (top right)

10.17182/hepdata.83969.v1/t39

The $v_{4}\{2\}$ results as a function of multiplicity ($N_{ch}$) in pp collisions at $\sqrt{s_{NN}}$ = 13 TeV

• #### Table 40

Data from Figure 7 (middle left)

10.17182/hepdata.83969.v1/t40

The $v_{2}\{2\}$ results as a function of multiplicity ($N_{ch}$) in pPb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV

• #### Table 41

Data from Figure 7 (middle middle)

10.17182/hepdata.83969.v1/t41

The $v_{3}\{2\}$ results as a function of multiplicity ($N_{ch}$) in pPb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV

• #### Table 42

Data from Figure 7 (middle right)

10.17182/hepdata.83969.v1/t42

The $v_{4}\{2\}$ results as a function of multiplicity ($N_{ch}$) in pPb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV

• #### Table 43

Data from Figure 7 (bottom left)

10.17182/hepdata.83969.v1/t43

The $v_{2}\{2\}$ results as a function of multiplicity ($N_{ch}$) in PbPb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

• #### Table 44

Data from Figure 7 (bottom middle)

10.17182/hepdata.83969.v1/t44

The $v_{3}\{2\}$ results as a function of multiplicity ($N_{ch}$) in PbPb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

• #### Table 45

Data from Figure 7 (bottom right)

10.17182/hepdata.83969.v1/t45

The $v_{4}\{2\}$ results as a function of multiplicity ($N_{ch}$) in PbPb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

• #### Table 46

Data similar to Figure 7 (top left) but for higher pT

10.17182/hepdata.83969.v1/t46

The $v_{2}\{2\}$ results as a function of multiplicity ($N_{ch}$) in pp collisions at $\sqrt{s_{NN}}$ = 13 TeV

• #### Table 47

Data similar to Figure 7 (top middle) but for higher pT

10.17182/hepdata.83969.v1/t47

The $v_{3}\{2\}$ results as a function of multiplicity ($N_{ch}$) in pp collisions at $\sqrt{s_{NN}}$ = 13 TeV

• #### Table 48

Data similar to Figure 7 (top right) but for higher pT

10.17182/hepdata.83969.v1/t48

The $v_{4}\{2\}$ results as a function of multiplicity ($N_{ch}$) in pp collisions at $\sqrt{s_{NN}}$ = 13 TeV

• #### Table 49

Data similar to Figure 7 (middle left) but for higher pT

10.17182/hepdata.83969.v1/t49

The $v_{2}\{2\}$ results as a function of multiplicity ($N_{ch}$) in pPb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV

• #### Table 50

Data similar to Figure 7 (middle middle) but for higher pT

10.17182/hepdata.83969.v1/t50

The $v_{3}\{2\}$ results as a function of multiplicity ($N_{ch}$) in pPb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV

• #### Table 51

Data similar to Figure 7 (middle right) but for higher pT

10.17182/hepdata.83969.v1/t51

The $v_{4}\{2\}$ results as a function of multiplicity ($N_{ch}$) in pPb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV

• #### Table 52

Data similar to Figure 7 (bottom left) but for higher pT

10.17182/hepdata.83969.v1/t52

The $v_{2}\{2\}$ results as a function of multiplicity ($N_{ch}$) in PbPb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

• #### Table 53

Data similar to Figure 7 (bottom middle) but for higher pT

10.17182/hepdata.83969.v1/t53

The $v_{3}\{2\}$ results as a function of multiplicity ($N_{ch}$) in PbPb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

• #### Table 54

Data similar to Figure 7 (bottom right) but for higher pT

10.17182/hepdata.83969.v1/t54

The $v_{4}\{2\}$ results as a function of multiplicity ($N_{ch}$) in PbPb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

• #### Table 55

Data from Figure 8 (left)

10.17182/hepdata.83969.v1/t55

The symmetric cumulant $ac_{2}\{3\}$ in Pb+Pb from different methods

• #### Table 56

Data from Figure 8 (right)

10.17182/hepdata.83969.v1/t56

The symmetric cumulant $ac_{2}\{3\}$ in Pb+Pb from different methods

• #### Table 57

Data from Figure 9 (left)

10.17182/hepdata.83969.v1/t57

The symmetric cumulant $ac_{2}\{3\}$ in p+Pb from different methods

• #### Table 58

Data from Figure 9 (right)

10.17182/hepdata.83969.v1/t58

The symmetric cumulant $ac_{2}\{3\}$ in p+Pb from different methods

• #### Table 59

Data from Figure 10 (left)

10.17182/hepdata.83969.v1/t59

The symmetric cumulant $ac_{2}\{3\}$ in pp from different methods

• #### Table 60

Data from Figure 10 (right)

10.17182/hepdata.83969.v1/t60

The symmetric cumulant $ac_{2}\{3\}$ in pp from different methods