# Non-linear flow modes of identified particles in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 5.02 TeV

The $p_{\rm{T}}$-differential non-linear flow modes, $v_{4,22}$, $v_{5,32}$, $v_{6,33}$ and $v_{6,222}$ for $\pi^{\pm}$, $\rm{K}^{\pm}$ , $\rm{K}^{0}_{S}$ , p + $\overline{\rm{p}}$, $\Lambda$ + $\overline{\Lambda}$ and $\phi$-meson have been measured for the first time at $\sqrt{s_{\rm{NN}}}$ = 5.02 TeV in Pb-Pb collisions with the ALICE detector at the Large Hadron Collider. The results were obtained with a multi-particle technique, correlating the identified hadrons with reference charged particles from a different pseudorapidity region. These non-linear observables probe the contribution from the second and third order initial spatial anisotropy coefficients to higher flow harmonics. All the characteristic features observed in previous $p_{\rm{T}}$-differential anisotropic flow measurements for various particle species are also present in the non-linear flow modes, i.e. increase of magnitude with increasing centrality percentile, mass ordering at low $p_{\rm{T}}$ and particle type grouping in the intermediate $p_{\rm{T}}$ range. Hydrodynamical calculations (iEBE-VISHNU) that use different initial conditions and values of shear and bulk viscosity to entropy density ratios are confronted with the data at low transverse momenta. These calculations exhibit a better agreement with the anisotropic flow coefficients than the non-linear flow modes. These observations indicate that non-linear flow modes can provide additional discriminatory power in the study of initial conditions as well as new stringent constraints to hydrodynamical calculations.

Submitted to: JHEP
e-Print: arXiv:1912.00740 | PDF | inSPIRE
CERN-EP-2019-271

Figures

## Figure 2

 The \pT-differential $v_{4,22}$ for different centrality intervals of Pb--Pb collisions at \sNN~grouped by particle species. Statistical and systematic uncertainties are shown as bars and boxes, respectively.

## Figure 3

 The \pT-differential $v_{5,32}$ for different centrality intervals of Pb--Pb collisions at \sNN~grouped by particle species. Statistical and systematic uncertainties are shown as bars and boxes, respectively.

## Figure 4

 The \pT-differential $v_{6,33}$ for different centrality intervals of Pb--Pb collisions at \sNN~grouped by particle species. Statistical and systematic uncertainties are shown as bars and boxes, respectively.

## Figure 5

 The \pT-differential $v_{6,222}$ for different centrality intervals of Pb--Pb collisions at \sNN~grouped by particle species. Statistical and systematic uncertainties are shown as bars and boxes, respectively.

## Figure 6

 The \pT-differential $v_{4,22}$ for different particle species grouped into different centrality intervals of Pb--Pb collisions at \sNN. Statistical and systematic uncertainties are shown as bars and boxes, respectively.

## Figure 7

 The \pT-differential $v_{5,32}$ for different particle species grouped into different centrality intervals of Pb--Pb collisions at \sNN. Statistical and systematic uncertainties are shown as bars and boxes, respectively.

## Figure 8

 The \pT-differential $v_{6,33}$ for different particle species grouped into different centrality intervals of Pb--Pb collisions at \sNN. Statistical and systematic uncertainties are shown as bars and boxes, respectively.

## Figure 9

 The \pT-differential $v_{6,222}$ for different particle species grouped into different centrality intervals of Pb--Pb collisions at \sNN. Statistical and systematic uncertainties are shown as bars and boxes, respectively.

## Figure 10

 The $p_{\rm{T}}/n_{q}$-dependence of $v_{4,22}/n_{q}$ for different particle species grouped into different centrality intervals of Pb--Pb collisions at \sNN. Statistical and systematic uncertainties are shown as bars and boxes, respectively.

## Figure 11

 The $p_{\rm{T}}/n_{q}$-dependence of $v_{5,32}/n_{q}$ for different particle species grouped into different centrality intervals of Pb--Pb collisions at \sNN. Statistical and systematic uncertainties are shown as bars and boxes, respectively.

## Figure 12

 The $p_{\rm{T}}/n_{q}$-dependence of $v_{6,33}/n_{q}$ for different particle species grouped into different centrality intervals of Pb--Pb collisions at \sNN. Statistical and systematic uncertainties are shown as bars and boxes, respectively.

## Figure 13

 The $p_{\rm{T}}/n_{q}$-dependence of $v_{6,222}/n_{q}$ for different particle species grouped into different centrality intervals of Pb--Pb collisions at \sNN. Statistical and systematic uncertainties are shown as bars and boxes, respectively.

## Figure 14

 The comparison between $[v_{4,22}^{\pi^{\pm}} - v_{4,22}^{\rm p+\bar{p}}](p_{\rm T}) / v_{4,22}^{\rm h^{\pm}}$ and $[v_{4}^{\pi^{\pm}} - v_{4}^{\rm p+\bar{p}}](p_{\rm T}) / v_{4}^{\rm h^{\pm}}$ grouped into different centrality intervals of Pb--Pb collisions at \sNN. Statistical and systematic uncertainties are shown as bars and boxes, respectively.

## Figure 22

 The $(m_{\rm{T}} - m_{0})/n_{q}$-dependence of $v_{4,22}/n_{q}$ for different particle species grouped into different centrality intervals of Pb--Pb collisions \sNN. Statistical and systematic uncertainties are shown as bars and boxes, respectively. It is seen that the $\rm KE_{T}$ scaling holds for $v_{4,22}$ at an approximate level.

## Figure 23

 The $(m_{\rm{T}} - m_{0})/n_{q}$-dependence of $v_{5,32}/n_{q}$ for different particle species grouped into different centrality intervals of Pb--Pb collisions \sNN. Statistical and systematic uncertainties are shown as bars and boxes, respectively. It is seen that the $\rm KE_{T}$ scaling holds for $v_{5,32}$ at an approximate level.

## Figure 24

 The $(m_{\rm{T}} - m_{0})/n_{q}$-dependence of $v_{6,33}/n_{q}$ for different particle species grouped into different centrality intervals of Pb--Pb collisions \sNN. Statistical and systematic uncertainties are shown as bars and boxes, respectively. It is seen that the $\rm KE_{T}$ scaling holds for $v_{6,33}$ at an approximate level.

## Figure 25

 The $(m_{\rm{T}} - m_{0})/n_{q}$-dependence of $v_{6,222}/n_{q}$ for different particle species grouped into different centrality intervals of Pb--Pb collisions \sNN. Statistical and systematic uncertainties are shown as bars and boxes, respectively. It is seen that the $\rm KE_{T}$ scaling holds for $v_{6,222}$ at an approximate level.

## Figure 26

 The $(m_{\rm{T}} - m_{0})/n_{q}$-dependence of $v_{4,22}/n_{q}$ for different particle species grouped into different centrality intervals of Pb--Pb collisions \sNN. Statistical and systematic uncertainties are shown as bars and boxes, respectively. It is seen that the $\rm KE_{T}$ scaling holds for $v_{4,22}$ at an approximate level.

## Figure 27

 The $(m_{\rm{T}} - m_{0})/n_{q}$-dependence of $v_{5,32}/n_{q}$ for different particle species grouped into different centrality intervals of Pb--Pb collisions \sNN. Statistical and systematic uncertainties are shown as bars and boxes, respectively. It is seen that the $\rm KE_{T}$ scaling holds for $v_{5,32}$ at an approximate level.

## Figure 28

 The $(m_{\rm{T}} - m_{0})/n_{q}$-dependence of $v_{6,33}/n_{q}$ for different particle species grouped into different centrality intervals of Pb--Pb collisions \sNN. Statistical and systematic uncertainties are shown as bars and boxes, respectively. It is seen that the $\rm KE_{T}$ scaling holds for $v_{6,33}$ at an approximate level.

## Figure 29

 The $(m_{\rm{T}} - m_{0})/n_{q}$-dependence of $v_{6,222}/n_{q}$ for different particle species grouped into different centrality intervals of Pb--Pb collisions \sNN. Statistical and systematic uncertainties are shown as bars and boxes, respectively. It is seen that the $\rm KE_{T}$ scaling holds for $v_{6,222}$ at an approximate level.