• Hot and dense medium created at the LHC
• Commonly referred to as the Quark-Gluon Plasma (QGP)
• Difference of pressure gradients along different axes drive flow of particles
• Gives rise to anisotropic distribution

anisotropic flow

flow as a function of pseudorapidity

Figure: [ALICE Collaboration, Phys.Lett. B762 (2016)]

• $v_n (\eta)$ give unique information about the hot and dense medium
• Forward rapidities
  [Phys.Rev.Lett. 116 (2016) no.21, 212301][Phys.Rev. C90 (2014) no.4, 044904]
  • Possible change in $\eta /s$
  • Shorter lifetime in the QGP phase
    • Hadronic viscosity play larger role

flow as a function of pseudorapidity

This talk:

• Using Generic Framework [Bilandzic, Ante et al., Phys.Rev. C89 (2014)] w. different combinations of sub-events
• Run 2 measurements w. more statistics
• Significant improvement of systematics

Figure: [ALICE Collaboration, Phys.Lett. B762 (2016)]

• $v_n (\eta)$ give unique information about the hot and dense medium
• Forward rapidities
  [Phys.Rev.Lett. 116 (2016) no.21, 212301][Phys.Rev. C90 (2014) no.4, 044904]
  • Possible change in $\eta /s$
  • Shorter lifetime in the QGP phase
    • Hadronic viscosity play larger role

alice

Forward Multiplicity Detector (FMD)

Time Projection Chamber (TPC)

• FMD3: $-3.5 < \eta < -1.7$
• FMD1 & FMD2: $1.7 < \eta < 5.0$
• Scintillator

• $-1.1 < \eta < 1.1$
• Tracking

V0 Scintillators

• V0A: $2.8 < \eta < 5.1$
• V0C: $-3.7 < \eta < -1.7$
• Trigger

Inner Tracking System (ITS)

• Triggering
• Tracking

• $v_n$ is calculated using the Generic Framework [Bilandzic, Ante et al., Phys.Rev. C89 (2014)]
• Correcting for non-uniform acceptance using weights
  • $Q_{n,p} = \sum_j w_j^p e^{in\varphi_j}$
• E.g. for 2-particle correlations the equations are
  • $\langle 2 \rangle = \frac{p_{n,1} Q_{-n,1} - q_{0,2}}{p_{0,1} Q_{0,1} - q_{0,2}}$
  • $v_n = \sqrt{ \langle \langle 2 \rangle \rangle }$

generic framework

• Non-flow: short-range correlations (e.g. jets and resonance decays)
• $\eta$-gaps have shown be useful for removal of non-flow
  • using the FMD the gap can increase from $\Delta \eta \approx 1$ and up to $\Delta \eta \approx 4$
• E.g. for two particle correlations, the gap case is
  
  
   
• $A \cap B = \emptyset$

non-flow suppression using eta-gaps

How big should a $\eta$-gap be?

$\langle 2 \rangle = \frac{p_{n,1}^A Q_{-n,1}^B}{p_{0,1}^A Q_{0,1}^B}$

$v_n\{2, |\Delta \eta |> x \} = \sqrt{\langle \langle 2  \rangle \rangle }$

• The purely factorizing model express the factorization as,                                               

$\langle v_n(\eta_a)v_n(\eta_b)  \rangle = \langle v_n(\eta_a)\rangle \langle v_n(\eta_b) \rangle$

$f_2(\Delta \eta) = \langle v_n(\eta_a)\rangle / \langle v_n(\eta_b) \rangle , \Delta \eta = \eta_a - \eta_b$

• For factorization to be true ($f_2(\Delta \eta) = 1$) $\rightarrow$ need at least a $\eta$-gap of 2.                         

Figure: Factorization from Pb-Pb 5.02 TeV data.

Figure: Factorization from Pb-Pb 5.02 TeV  AMPT w. String Melting.

estimating factorising          limit

$\Delta \eta$

• Reference particles are chosen from the TPC.
• FMD: $|\Delta \eta|  > 2$
• TPC:  $|\Delta \eta| >  0$
• Example: $v_n'$ in region B is calculated by, (assuming no decorrelation)

TPC

FMD

FMD

TPC

FMD

FMD

• Reference particles are chosen from the FMD.
• FMD: $|\Delta \eta| > 4$
• TPC:  $|\Delta \eta| >  2$
• Example: $v_n'$ in region B is calculated by, (assuming no decorrelation)

sub-events with pseudorapidity gap

Figures: Beginning of arrow is differential region, end of arrow is reference region

Figure: Multiplicity densities of charged particles hitting the SPD and FMD in a HIJING simulation with GEANT3 as transport code for 0 − 5% central events.

distribution of secondary particles from material

• Signal contamination from material interactions (secondaries)
• Dilute observation of $\varphi$
• No tracking
  • need other method to deconvolve signal

Secondaries distributed around primaries: $P(\varphi') = f(\varphi) \circ P(\varphi)$

Observed in the detector: $\Delta \varphi' = \varphi_1' - \varphi_2$

If we know $\mathcal{F}(f(\varphi))$ we can extract $\langle \langle v_n' v_n \rangle \rangle^{true}$

smearing by secondary particles

Figure: Illustration of smearing in $\varphi$ by secondary particles

• $\Delta \phi$ of observed secondary particle to primary particle

• Fourier transform $f(\varphi)$ for each vertex and $\eta$ bin

Figure: Distribution of a secondary particle around its primary mother particle. Plots are shifted by a constant.

Figure: Correction values to $v_2$

distribution of secondaries around primary particles

two particle cumulant with small eta-gap

Figure: $v_n\{2,|\Delta \eta| > 0\}$ as a function of $\eta$.

• Ordering of harmonics $v_2 > v_3 > v_4$

• $v_n$ increasing from 0 - 40 %

• Wide range in $\eta$ shows $v_n$ decreasing as a function of $| \eta |$

two particle cumulant with small eta-gap

Figure: $v_n\{2,|\Delta \eta| > 0\}$ as a function of $\eta$.

• Ordering of harmonics $v_2 > v_3 > v_4$

• $v_n$ increasing from 0 - 40 %

• Wide range in $\eta$ shows $v_n$ decreasing as a function of $| \eta |$

• AMPT w. String Melting [Lin, Zi-Wei et al. Phys.Rev. C72 (2005)]
  • describes the data qualitatively, but not quantitatively

Figure: $v_2\{2,|\Delta \eta| > 2\}$ and $v_2\{4,|\Delta \eta| > 0\}$ as a function of $\eta$.

• Introducing 4-particle cumulant and 2-particle cumulant w. a large $\eta$-gap
• Flat shape $\rightarrow$ Implies small $\eta$-gap in central heavy ion collisions might not be enough:
  • to suppress non-flow
  • for factorization

4-particle cumulant and 2-particle cumulant with a large eta-gap

Figure: $v_2\{2,|\Delta \eta| > 2\}$ and $v_2\{4,|\Delta \eta| > 0\}$ as a function of $\eta$.

4-particle cumulant and 2-particle cumulant with a large eta-gap

• Introducing 4-particle cumulant and 2-particle cumulant w. a large $\eta$-gap
• Flat shape $\rightarrow$ Implies small $\eta$-gap in central heavy ion collisions might not be enough:
  • to suppress non-flow
  • for factorization
• AMPT w. String Melting [Lin, Zi-Wei et al. Phys.Rev. C72 (2005)]
  • describes the data qualitatively, but not quantitatively

• $v_n (\eta)$ with Pb-Pb 5.02 TeV in a wide range in pseudorapidity
• $v_n$ measured w. large gap and 4-particle cumulant: more flat shape than $v_n$ w. a small gap

• AMPT has qualitative agreement, but improvements are needed

• Future comparisons to 3+1D hydrodynamic calculations:

  • can constrain the initial state models

  • study longitudinal dynamics of the created hot and dense matter

summary

Figure: $p_T$ differential flow measurements. 

[ALICE Collaboration, JHEP 1709 (2017)]

• FMD measure all charged particles, i.e. $p_T > 0$ GeV/c
• TPC measure charged particles with
  $p_T > 0.2$ GeV/c
  • additional cut $p_T < 5$ GeV/c
• This will increase flow in TPC, wrt. the FMD
  • is corrected with MC

momentum in the fmd and tpc

Figure: Data points: $v_n \{ 2\},|\Delta \eta|> 0$ in Pb-Pb 5.02 TeV.
Boxes: Standard Q-cumulant $v_n \{ 2\}$ from [ALICE Collaboration,
Phys.Lett. B762 (2016)] in Pb-Pb 2.76 TeV.

pseudorapidity dependence on vn in pb-pb 2.76 tev

Figure: Data points: $v_2 \{ 2\},|\Delta \eta|> 2$ and $v_2 \{ 4\},|\Delta \eta|> 0$ in Pb-Pb 5.02 TeV.
Boxes: Standard Q-cumulant $v_2 \{ 2\}$ and $v_2 \{ 4\}$ from [ALICE Collaboration, Phys.Lett. B762 (2016)] in Pb-Pb 2.76 TeV.

• Analysis repeated in $\eta$
  • $\Delta \eta$ of observed secondary particle to primary particle
  • Fourier transform $f(\eta)$ for each vertex and $\varphi$ bin
• Width of peaks are constant at 0.02

secondaries in the fmd

Figure: Widths of peaks of the distributions.

Figure: Distribution of a secondary particle around its primary mother particle. Plots are shifted by a constant.

secondaries in the fmd - correction to v3 and v4

Figure: Correction to $v_3$ for the contamination of secondary particles in the FMD.

Figure: Correction to $v_3$ for the contamination of secondary particles in the FMD.