How to measure elliptic flow in pp@LHC?

Jovan Milosevic

University of Oslo, Norway

FIS, 26-th Sep. 2007, Iriski Venac – p.1/12

A schematic view of a non-central nucleus-nucleus collision

• Does in TeV regime proton-proton collision looks like that?

• With an increase of the inci-

dent energy the edge of the

overlapping region becomes

sharper and the smearing of

it, due to the strong QCD in-

teractions, becomes smaller

K. Boreskov, A. B. Kaidalov and O.

Kancheli, Elliptic flow in pp colli-

sions, in preparation

FIS, 26-th Sep. 2007, Iriski Venac – p.2/12

Building of the anisotropic flow

• Asymmetry in coordinate space (overlap region) develops into an asymmetry in

momentum space due to the collective interactions (pressure gradients)

planereaction

planereaction

space asymmetry

momentum asymmetry

∆ x

∆ yP=0

Pmax

• The initial compression → pressure p →collective flow

• Non-central collisions → ∇px > ∇py →anisotropic flow

• Fourier decomposition: dN/dφ =

N0{1 +P+∞

n=0 2vn cos[n(φ − Φ)]}• Quadrupole component

v2 = 〈cos[2(φ − Φ)]〉 is called elliptic flow

FIS, 26-th Sep. 2007, Iriski Venac – p.3/12

Simulated data

• ”Flow” + ”Hijing” simulation◦ On Hijing Jet data (J) are randomly added soft ”Flow”

particles (F) where: MF ≈ 1.2MJ

◦ Flow particles have similar pseudorapidity and pT

distributions. The distribution of the laboratory azimuthal

angles of particles, φlab, are made in a way to be random

(and isotropic) in the laboratory frame and to have an

(elliptic) flow pattern with respect to the true reaction

plane

◦ The intention is to check could LYZ Method remove the

contribution of Jet (Hijing) particles from the flow.

FIS, 26-th Sep. 2007, Iriski Venac – p.4/12

Simulated data

• ”Flow” + ”Hijing” simulation◦ On Hijing Jet data (J) are randomly added soft ”Flow”

particles (F) where: MF ≈ 1.2MJ

◦ Flow particles have similar pseudorapidity and pT

distributions. The distribution of the laboratory azimuthal

angles of particles, φlab, are made in a way to be random

(and isotropic) in the laboratory frame and to have an

(elliptic) flow pattern with respect to the true reaction

plane

◦ The intention is to check could LYZ Method remove the

contribution of Jet (Hijing) particles from the flow.

FIS, 26-th Sep. 2007, Iriski Venac – p.4/12

Simulated data

• ”Flow” + ”Hijing” simulation◦ On Hijing Jet data (J) are randomly added soft ”Flow”

particles (F) where: MF ≈ 1.2MJ

◦ Flow particles have similar pseudorapidity and pT

distributions. The distribution of the laboratory azimuthal

angles of particles, φlab, are made in a way to be random

(and isotropic) in the laboratory frame and to have an

(elliptic) flow pattern with respect to the true reaction

plane

◦ The intention is to check could LYZ Method remove the

contribution of Jet (Hijing) particles from the flow.

FIS, 26-th Sep. 2007, Iriski Venac – p.4/12

Two particle azimuthal distributions

Flow particles Jet particles ”Jet+Flow” particles

φ∆-1 0 1 2 3 4

φ∆ddN

400

600

800

1000

1200

1400

1600

1800

normalized to

triggN

φ∆-1 0 1 2 3 4

φ∆ddN

400

600

800

1000

1200

1400

1600

1800

φ∆-1 0 1 2 3 4

φ∆ddN

400

600

800

1000

1200

1400

1600

1800

<240part210<N

• Simulated event: Huge elliptic flow signal (left) is hidden by the signal coming fromthe jet particles (middle) in the final distributions of both kind of particles takentogether

• Real event: Strictly speaking, there is no possibility, by means of cuts, todistinguish between flow and jet particles

FIS, 26-th Sep. 2007, Iriski Venac – p.5/12

Lee-Yang Zero Method

• Integrated flow V 2 = 〈∑M

j=1 wj cos[2(φj − Φ)]〉 is connected

with the Fourier coefficient v2 via: V2 = Mwv2, where

Mw =∑M

j=1 wj .

• for each event one calculates the complex-valued function

gθ(ir) =∏M

j=1{1 + irwj cos[2(φj − θ)]} for various values of

the real positive variable r and of the reference angle θ

(0 ≤ θ ≤ π/2). The φj is the measured laboratory azimuthal

angle of a particle and the product goes over all detected

particles.

• One has to average gθ(ir) over events for each value of r

and θ: Gθ(ir) ≡ 〈gθ(ir)〉 = 1N

∑events gθ(ir)

N.Borghini, R.S.Bhalerao, and J.-Y.Ollitrault, nucl-th/0402053 (2004)

FIS, 26-th Sep. 2007, Iriski Venac – p.6/12

Lee-Yang Zero Method

• Integrated flow V 2 = 〈∑M

j=1 wj cos[2(φj − Φ)]〉 is connected

with the Fourier coefficient v2 via: V2 = Mwv2, where

Mw =∑M

j=1 wj .

• for each event one calculates the complex-valued function

gθ(ir) =∏M

j=1{1 + irwj cos[2(φj − θ)]} for various values of

the real positive variable r and of the reference angle θ

(0 ≤ θ ≤ π/2). The φj is the measured laboratory azimuthal

angle of a particle and the product goes over all detected

particles.

• One has to average gθ(ir) over events for each value of r

and θ: Gθ(ir) ≡ 〈gθ(ir)〉 = 1N

∑events gθ(ir)

N.Borghini, R.S.Bhalerao, and J.-Y.Ollitrault, nucl-th/0402053 (2004)

FIS, 26-th Sep. 2007, Iriski Venac – p.6/12

Lee-Yang Zero Method

• Integrated flow V 2 = 〈∑M

j=1 wj cos[2(φj − Φ)]〉 is connected

with the Fourier coefficient v2 via: V2 = Mwv2, where

Mw =∑M

j=1 wj .

• for each event one calculates the complex-valued function

gθ(ir) =∏M

j=1{1 + irwj cos[2(φj − θ)]} for various values of

the real positive variable r and of the reference angle θ

(0 ≤ θ ≤ π/2). The φj is the measured laboratory azimuthal

angle of a particle and the product goes over all detected

particles.

• One has to average gθ(ir) over events for each value of r

and θ: Gθ(ir) ≡ 〈gθ(ir)〉 = 1N

∑events gθ(ir)

N.Borghini, R.S.Bhalerao, and J.-Y.Ollitrault, nucl-th/0402053 (2004)

FIS, 26-th Sep. 2007, Iriski Venac – p.6/12

Lee-Yang Zero Method

• For each θ, the position of rθ0 of the first minimum of the

modulus |Gθ(ir)| has to be found. Then the estimate ofthe integrated flow V 2 is given by: V θ

2 {∞} ≡ j01rθ0

where

j01 ≈ 2.40483 is the first zero of the Bessel function J0.

• Once the integrated flow is obtained, the differentialflow analysis can be done.

vθ2{∞} = V θ

2 {∞}J1(j01)J2(j01)

Re(〈gθ(irθ0)

cos(2(ψ−θ))

1+irθ0wψ cos(2(ψ−θ))〉θ

〈gθ(irθ0)P

j

wj cos(2(φj−θ))

1+irθ0wj cos(2(φj−θ)))evts〉

)

• The necessary statistics is given by the followinginequality: vθ

2 > j01√2MlnN

where M is multiplicity and Nis the number of events.

FIS, 26-th Sep. 2007, Iriski Venac – p.7/12

Lee-Yang Zero Method

• For each θ, the position of rθ0 of the first minimum of the

modulus |Gθ(ir)| has to be found. Then the estimate ofthe integrated flow V 2 is given by: V θ

2 {∞} ≡ j01rθ0

where

j01 ≈ 2.40483 is the first zero of the Bessel function J0.• Once the integrated flow is obtained, the differential

flow analysis can be done.

vθ2{∞} = V θ

2 {∞}J1(j01)J2(j01)

Re(〈gθ(irθ0)

cos(2(ψ−θ))

1+irθ0wψ cos(2(ψ−θ))〉θ

〈gθ(irθ0)P

j

wj cos(2(φj−θ))

1+irθ0wj cos(2(φj−θ)))evts〉

)

• The necessary statistics is given by the followinginequality: vθ

2 > j01√2MlnN

where M is multiplicity and Nis the number of events.

FIS, 26-th Sep. 2007, Iriski Venac – p.7/12

Lee-Yang Zero Method

• For each θ, the position of rθ0 of the first minimum of the

modulus |Gθ(ir)| has to be found. Then the estimate ofthe integrated flow V 2 is given by: V θ

2 {∞} ≡ j01rθ0

where

j01 ≈ 2.40483 is the first zero of the Bessel function J0.• Once the integrated flow is obtained, the differential

flow analysis can be done.

vθ2{∞} = V θ

2 {∞}J1(j01)J2(j01)

Re(〈gθ(irθ0)

cos(2(ψ−θ))

1+irθ0wψ cos(2(ψ−θ))〉θ

〈gθ(irθ0)P

j

wj cos(2(φj−θ))

1+irθ0wj cos(2(φj−θ)))evts〉

)

• The necessary statistics is given by the followinginequality: vθ

2 > j01√2MlnN

where M is multiplicity and Nis the number of events.

FIS, 26-th Sep. 2007, Iriski Venac – p.7/12

True and reconstructed v2 coefficients vs η and pT

very peripheral semicentral rather central

150 < Npart < 180 210 < Npart < 240 270 < Npart < 300

η-10 -8 -6 -4 -2 0 2 4 6 8 10

2v

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

η-10 -8 -6 -4 -2 0 2 4 6 8 10

2v

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14 jet; true RP

flow; true RP

jet; reco. RP

η-10 -8 -6 -4 -2 0 2 4 6 8 10

2v

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

pT(GeV/c)0 2 4 6 8 10 12

2v

0

0.1

0.2

0.3

0.4

0.5

0.6

pT(GeV/c)0 2 4 6 8 10 12

2v

0

0.1

0.2

0.3

0.4

0.5

0.6

pT(GeV/c)0 2 4 6 8 10 12

2v

0

0.1

0.2

0.3

0.4

0.5

0.6

FIS, 26-th Sep. 2007, Iriski Venac – p.8/12

Generating functions

• Only when both, the magnitude of v2 and the multiplicity are high enough, the

generating function show a sharp minimum close to zero

r0 0.1 0.2 0.3 0.4 0.5

| 2|G

0

0.2

0.4

0.6

0.8

1

Graph

<180part150<N°

=12θ

Graph

r0 0.1 0.2 0.3 0.4 0.5

| 2|G

0

0.2

0.4

0.6

0.8

1

<240part210<N°

=12θ

jet

flow

jet+flow

r0 0.1 0.2 0.3 0.4 0.5

| 2|G

0

0.2

0.4

0.6

0.8

1

Graph

<300part270<N°

=12θ

Graph

FIS, 26-th Sep. 2007, Iriski Venac – p.9/12

LYZ reconstructed v2 coefficients

η-10 -8 -6 -4 -2 0 2 4 6 8 10

2v

0

0.02

0.08

0.1

0.12

<180part150<N

η-10 -8 -6 -4 -2 0 2 4 6 8 10

2v

0

0.02

0.08

0.1

0.12

<240part210<N

η-10 -8 -6 -4 -2 0 2 4 6 8 10

2v

0

0.02

0.08

0.1

0.12

<300part270<N

pT(GeV/c)0 2 4 6 8 10 12

2v

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8jet part.

flow part.

jet+flow part

pT(GeV/c)0 2 4 6 8 10 12

2v

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

pT(GeV/c)0 2 4 6 8 10 12

2v0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

FIS, 26-th Sep. 2007, Iriski Venac – p.10/12

True and LYZ reconstructed v2 coefficients

η-10 -8 -6 -4 -2 0 2 4 6 8 10

2v

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

<180part150<N

η-10 -8 -6 -4 -2 0 2 4 6 8 10

2v

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14<240part210<N

η-10 -8 -6 -4 -2 0 2 4 6 8 10

2v

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14 flow; true RP

flow; reco. LYZ

jet+flow; reco LYZ

pT(GeV/c)0 2 4 6 8 10 12

2v

0

0.1

0.2

0.3

0.4

0.5

pT(GeV/c)0 2 4 6 8 10 12

2v

0

0.1

0.2

0.3

0.4

0.5

pT(GeV/c)0 2 4 6 8 10 12

2v

0

0.1

0.2

0.3

0.4

0.5

<300part270<N

FIS, 26-th Sep. 2007, Iriski Venac – p.11/12

Conclusion and outlook

• Preliminary results on the feasibility of the Lee-YangZero method applied on HIJING pp@14TeV/c arepresented

• The LYZ method doesn’t work for very peripheralevents (due to the small multiplicity) and for rathercentral events (where one suppose a small anisotropyand consequently a small v2 magnitude)

• In between these two extremes the shape of thedifferential v2 has been reconstructed but itundershoots the true flow due to the multiplicityfluctuations and unremoved jet remnants

• If the theoretically predicted v2 really exists in pp@LHCit will be a difficult task to extract it from the huge jetcontribution which hides the flow

FIS, 26-th Sep. 2007, Iriski Venac – p.12/12

Conclusion and outlook

• Preliminary results on the feasibility of the Lee-YangZero method applied on HIJING pp@14TeV/c arepresented

• The LYZ method doesn’t work for very peripheralevents (due to the small multiplicity) and for rathercentral events (where one suppose a small anisotropyand consequently a small v2 magnitude)

• In between these two extremes the shape of thedifferential v2 has been reconstructed but itundershoots the true flow due to the multiplicityfluctuations and unremoved jet remnants

• If the theoretically predicted v2 really exists in pp@LHCit will be a difficult task to extract it from the huge jetcontribution which hides the flow

FIS, 26-th Sep. 2007, Iriski Venac – p.12/12

Conclusion and outlook

• Preliminary results on the feasibility of the Lee-YangZero method applied on HIJING pp@14TeV/c arepresented

• The LYZ method doesn’t work for very peripheralevents (due to the small multiplicity) and for rathercentral events (where one suppose a small anisotropyand consequently a small v2 magnitude)

• In between these two extremes the shape of thedifferential v2 has been reconstructed but itundershoots the true flow due to the multiplicityfluctuations and unremoved jet remnants

• If the theoretically predicted v2 really exists in pp@LHCit will be a difficult task to extract it from the huge jetcontribution which hides the flow

FIS, 26-th Sep. 2007, Iriski Venac – p.12/12

Conclusion and outlook

• Preliminary results on the feasibility of the Lee-YangZero method applied on HIJING pp@14TeV/c arepresented

• The LYZ method doesn’t work for very peripheralevents (due to the small multiplicity) and for rathercentral events (where one suppose a small anisotropyand consequently a small v2 magnitude)

• In between these two extremes the shape of thedifferential v2 has been reconstructed but itundershoots the true flow due to the multiplicityfluctuations and unremoved jet remnants

• If the theoretically predicted v2 really exists in pp@LHCit will be a difficult task to extract it from the huge jetcontribution which hides the flow

FIS, 26-th Sep. 2007, Iriski Venac – p.12/12