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Charge balancing and the fall off of the ridge Piotr Bo zek and - - PowerPoint PPT Presentation

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Charge balancing and the fall off of the ridge Piotr Bo zek and Wojtek Broniowski Institute of Nuclear Physics Krak ow QM 2012 Piotr Bo zek and Wojtek Broniowski Charge balancing and the fall off of the ridge Two-particle

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SLIDE 1

Charge balancing and the fall off of the ridge

Piotr Bo˙ zek and Wojtek Broniowski

Institute of Nuclear Physics Krak´

  • w

QM 2012

Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

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SLIDE 2

Two-particle correlations

C2(∆η, ∆φ) =

Npairs

phys (∆η,∆φ)

Npairs

mixed(∆η,∆φ)

φ∆ ∆ρ /√ρref η∆

  • 2
  • 1

1 2 2 4

  • 0.4
  • 0.2

0.2 0.4 0.6

STAR flow correlations

(rad) φ ∆

  • 3
  • 2
  • 1

1 2 3

φ ∆ d dN

trigg

N 1

11.2 11.3 11.4 11.5 11.6

Smooth IC

(rad) φ ∆

  • 3
  • 2
  • 1

1 2 3

φ ∆ d dN

trigg

N 1

12.2 12.4 12.6 12.8 13 13.2 13.4

Fluctuating IC

  • J. Takahashi et al. (2009)

Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

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SLIDE 3

3 + 1-D viscous hydrodynamics

5 10 15 20 0.5 1 1.5 2 2.5 3 pT [GeV] 30-40% central 5 10 15 20 10-20% central h+/- v3 [%] 5 10 15 20 25 0-5% central ideal, e-b-e η/s=0.08, e-b-e η/s=0.16, e-b-e

first 3+1D visc. : B.Schenke et al.

0.1 0.2 0.3 200 400 600 800 1000

T [MeV] lQCD Wuppertal-Budapest cs2

lQCD + Hadron Gas η/s = 0.08(0.16)

Au-Au 200GeV

PS

η

  • 6
  • 4
  • 2

2 4 6

PS

η dN/d 100 200 300 400 500 600 700 800 PHOBOS c=0-6%,...,45-55% BRAHMS c=0-5% ideal fluid

  • visc. hydro

[GeV]

T

p 0.5 1 1.5 2 2.5 3 ]

  • 2

dy) [GeV

T

dp

T

p π dN/(2

  • 9

10

  • 7

10

  • 5

10

  • 3

10

  • 1

10 10

3

10 ideal fluid

  • visc. hydro

Au-Au 200GeV PHENIX data +

π

0-5% 40-50%

Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

slide-4
SLIDE 4

2-D correlations

(0.8 < pT < 4 GeV - “unbiased”)

η ∆

0.5 1 1.5

(deg) φ ∆

50 100 150 0.99 1 1.01 (a)

Unlike-sign

η ∆

0.5 1 1.5

(deg) φ ∆

50 100 150 0.99 1 1.01 (b)

Like-sign

STAR data, 2007

Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

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SLIDE 5

2-D correlations

(0.8 < pT < 4 GeV - “unbiased”)

η ∆

0.5 1 1.5

(deg) φ ∆

50 100 150 0.99 1 1.01 (a)

Unlike-sign

η ∆

0.5 1 1.5

(deg) φ ∆

50 100 150 0.99 1 1.01 (b)

Like-sign

STAR data, 2007 No balancing

φ ∆

  • 1

1 2 3 4 5

η ∆

  • 2
  • 1.5
  • 1
  • 0.5

0.5 1 1.5 2

(+-)

2

R

0.994 0.996 0.998 1 1.002 1.004 1.006 1.008 1.01 1.012 1.014 0-5% 0-5%

φ ∆

  • 1

1 2 3 4 5

η ∆

  • 2
  • 1.5
  • 1
  • 0.5

0.5 1 1.5 2

(++,--)

2

R

0.994 0.996 0.998 1 1.002 1.004 1.006 1.008 1.01 0-5% 0-5%

Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

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SLIDE 6

Charge balancing

local charge conservation

u p1 p 2

+ _ + _

charge balance function

Bass et al. (2000) Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

slide-7
SLIDE 7

2-D correlations

R2(∆η, ∆φ) =

Npairs

phys (∆η,∆φ)

Npairs

mixed(∆η,∆φ)

(0.8 < pT < 4 GeV)

η ∆

0.5 1 1.5

(deg) φ ∆

50 100 150 0.99 1 1.01 (a)

Unlike-sign

η ∆

0.5 1 1.5

(deg) φ ∆

50 100 150 0.99 1 1.01 (b)

Like-sign

STAR data With balancing!

φ ∆

  • 1

1 2 3 4 5

η ∆

  • 2
  • 1.5
  • 1
  • 0.5

0.5 1 1.5 2

(+-)

2

R

0.995 1 1.005 1.01 1.015 1.02 1.025 0-5% 0-5%

φ ∆

  • 1

1 2 3 4 5

η ∆

  • 2
  • 1.5
  • 1
  • 0.5

0.5 1 1.5 2

(++,--)

2

R

0.995 1 1.005 1.01 1.015 0-5% 0-5%

Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

slide-8
SLIDE 8

2D balance functions

B(∆η, ∆φ) = N+−−N++

N+

+ N−+−N−−

N−

c = 0 − 5%

η ∆

  • 2
  • 1.5
  • 1
  • 0.5

0.5 1 1.5 2 φ ∆

  • 3
  • 2
  • 1

1 2 3 B 0.2 0.4 0.6 0.8 1 1.2 1.4

Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

slide-9
SLIDE 9

2D balance functions

B(∆η, ∆φ) = N+−−N++

N+

+ N−+−N−−

N−

c = 0 − 5%

η ∆

  • 2
  • 1.5
  • 1
  • 0.5

0.5 1 1.5 2 φ ∆

  • 3
  • 2
  • 1

1 2 3 B 0.2 0.4 0.6 0.8 1 1.2 1.4 η ∆

  • 2
  • 1.5
  • 1
  • 0.5

0.5 1 1.5 2 φ ∆

  • 3
  • 2
  • 1

1 2 3 B

  • 0.05

0.05 0.1 0.15 0.2 0.25 0.3 0.35

big (direct balancing) small (resonance decays only) balancing → collimation important non-flow effect, a way to look at the data

Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

slide-10
SLIDE 10

Model Summary

φ ∆

  • 1

1 2 3 4 5

η ∆

  • 2
  • 1.5
  • 1
  • 0.5

0.5 1 1.5 2

C(++,--)

0.99 0.995 1 1.005 1.01 1.015

(a) 30-40%, unbal. φ ∆

  • 1

1 2 3 4 5

η ∆

  • 2
  • 1.5
  • 1
  • 0.5

0.5 1 1.5 2

C(+-)

0.99 0.995 1 1.005 1.01 1.015

(b) 30-40%, unbal. φ ∆

  • 1

1 2 3 4 5

η ∆

  • 2
  • 1.5
  • 1
  • 0.5

0.5 1 1.5 2

C(++,--)

0.99 0.995 1 1.005 1.01 1.015 1.02

(c) 30-40%, bal. φ ∆

  • 1

1 2 3 4 5

η ∆

  • 2
  • 1.5
  • 1
  • 0.5

0.5 1 1.5 2

C(+-)

0.985 0.99 0.995 1 1.005 1.01 1.015 1.02 1.025 1.03

(d) 30-40%, bal.

Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

slide-11
SLIDE 11

Balance functions in relative rapidity

Jeon & Pratt 2002, ...

charge balance function in ∆η

η ∆

0.5 1 1.5 2

) η ∆ B(

0.1 0.2 0.3 0.4 0.5 0.6 0.7

(a) 0-5%

η ∆

0.5 1 1.5 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7

(b) 30-40%

η ∆

0.5 1 1.5 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7

(c) 60-70%

comparison to the STAR data solid: Tf = 140 MeV, dashed: Tf = 150 MeV

Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

slide-12
SLIDE 12

Non-flow effect on vn

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.02 0.04 0.06 0.08 0.1 0.12 0.14 PHENIX c=0-10% STAR

2

v [GeV]

T

p

2

v + ch. balan.

2

v /s=0.16 η hydro + ch. balan. a) 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 PHENIX c=30-40% STAR

2

v [GeV]

T

p

hydro + ch. bal. hydro b) /s=0.16 η hydro + ch. balan.

η ∆

  • 2
  • 1.5
  • 1
  • 0.5

0.5 1 1.5 2

]

  • 3

[10

2 n

v

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

(a) 0-5%

η dN/d 100 200 300 400 500 600 700 800 (LS)

2

(CI)-v

2

v

  • 1

1 2 3 4 5 6 7

  • 3

10 ×

STAR Data hydro hydro + ch. balan. /s=0.16 η hydro + ch. balan.

event-by-event

Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

slide-13
SLIDE 13

v1 - parity violation observable

transverse-momentum conservation lowers v 2

1 ≡ cos(φ1 − φ2) η ∆

  • 2
  • 1.5
  • 1
  • 0.5

0.5 1 1.5 2

  • 1.5
  • 1
  • 0.5

0.5 1 1.5 2 2.5 3

(b) 30-40%

  • O

O O O O O O O O O O O O O O O X X X X X X 10 20 30 40 50 60 70 1 2 3 4 5

c cosab 103

Os140, Xs150, PT 20, 18, 15, 12, 10, 8, 7, 5 GeV

comparison to the STAR data

Pratt, Schlichting (2011), Bzdak, Koch, Liao (2011) Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

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SLIDE 14

Summary

◮ E-by-e hydro with charge balancing for 2-D correlation

function

◮ Charge balancing explains the shape of the same-side ridge -

major non-flow effect

◮ Charge balancing increases v 2 n{2} by a few % and splits the

like-sign and unlike-sign case

◮ Transverse-momentum conservation important for v 2 1 ,

parity violation obs. semi-quantitative agreement

◮ Substract charge conservation effects to look for early

correlations

Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge