Gary Westfall Data are from presentations and proceedings by Hui

Wang for the STAR Collaboration at Quark Matter 2012 and CPOD 2012 and from Hui

Wang’s Ph.D. THesis

•  I have collaborated with Joe a few times over the years •  Once on the Firestreak Model in 1978 •  Once a few years later

6/12/12 Gary Westfall 2

Congratulations to Joe

Relativistic Heavy Ion Collisions

6/12/12 Gary Westfall 3

initial state

pre-equilibrium

QGP and Hydro. expansion

Hadronization

Elastic scattering and kinetic freeze-out Hadronic interaction

and chemical freeze-out

•  Dynamic system •  Study final state

particles to probe the properties of QGP

Motivation

6/12/12 Gary Westfall 4

t (fm/c)4 8 12

ther

mal

izat

ion

hadr

oniz

atio

n

all

Nquarks

�  In heavy ion collisions, most of the detected charge is created during the evolution of the system

�  Charge creation can occur at any time before chemical freeze-out.

�  Balance functions are sensitive to charge formation mechanisms and relative diffusion

Observable – Balance Function •  The balance function is a conditional probability that a

particle a in the bin p1 will be accompanied by a particle b of opposite charge in the bin p2

•  It can be written as

•  The width of balance function is calculated via weighted average

( ) ( ) ( ) ( ) ( ){ }2 1 2 1 2 1 2 1 2 11| , | , , | , , | , , | ,2

B p p b p a p b p b p a p b p a p a pρ ρ ρ ρ= − + −

( ) ( ) ( ) ( )1( )2N N N NB

N Nη η η ηη +− ++ −+ −−

+ −

⎧ ⎫Δ − Δ Δ − ΔΔ = +⎨ ⎬⎩ ⎭

( )shuffled data

shuffled

100W

η ηη

⋅ Δ − Δ=

Δ

( )

( )all

all

i i

i

B

Bη

η

η ηη

ηΔ

Δ

Δ ΔΔ =

Δ

∑∑

6/12/12 Gary Westfall 5

B(!")

0.6

0

0.40.2

!"2.0

0.6

0

0.40.2

0.6

0

0.40.2

0-5% 5-10% 10-20%

20-30% 30-40% 40-50%

50-60% 60-70% 70-80%

1.001.00 1.00

DataMixedShuffled

Balance Function for Δη$

•  The balance function narrows in central collisions

6/12/12 Gary Westfall 6

200 GeV

Balance Function for Δϕ!

•  The balance function narrows in central collisions

6/12/12 Gary Westfall 7

200 GeV

0 1 2 30 1 2 0 1 2!"

B(!"

)

0

0.40.2

0

0.40.2

0

0.40.2

0-5% 5-10% 10-20%

20-30% 30-40% 40-50%

50-60% 60-70% 70-80%

DataShuffled

Charged Particles

Balance Function Width

6/12/12 Gary Westfall 8

Au+Au UrQMD

Au+AuAu+Au Shuffledp+p

d+AuAu+Au HIJING

p+p HIJING

0 100 200 3000.5

0.6

0.7

Npart

<!"

>

( )

( )all

all

i i

i

B

Bη

η

η ηη

ηΔ

Δ

Δ ΔΔ =

Δ

∑∑

partN0 100 200 300

)>!"

<cos

(

0.2

0.4

0.6

0.8

1 Au+Au 0.2 < pt < 2.0 GeV/c1.0 < pt < 10.0 GeV/cAu+Au0.2 < pt < 2.0 GeV/c1.0 < pt < 10.0 GeV/c

UrQMDUrQMD

Charged Particles0

Balance Function

0

0.2

0.4

0.6 7.7 GeV

DataShuffled

19.6 GeV)d

6B(

0

0.2

0.4

0.6 27 GeV 39 GeV 62.4 GeV

d60 0.6 1.2 1.8

0

0.2

0.4

0.6 200 GeV

11.5 GeV

d60 0.6 1.2 1.80.6 1.2

•  Most central (0-5%) events only

•  Shuffled events are created by shuffling charges in a given each event

•  Data are narrower than shuffled events at all energies

6/12/12 Gary Westfall 9

(GeV)NNs10 210

>d6<

0.5

0.6

0.7

0.8DataData Shuffled

UrQMDUrQMD Shuffled

<Δη>$• Most central (0-5%) events

only • Remove lowest bin when

calculating <Δη> to reduce HBT/Coulomb effects

• Both data and UrQMD show a smooth decrease with increasing collision energy, indicating stronger correlations at small Δη

•  Shuffled event widths also change with energy due to acceptance

• Balance function width is sensitive to flow and breakup temperature

( )

( )all

all

i i

i

B

Bη

η

η ηη

ηΔ

Δ

Δ ΔΔ =

Δ

∑∑

!-1 -0.5 0 0.5 1

Counts

0

500

1000

1500

2000

2500

3000

3500

310"

!

!-1 -0.5 0 0.5 1

Counts

0

10

20

30

40

50

60

70

610"

7 GeV 200 GeV

|η| < 1.0

6/12/12 Gary Westfall 10

W Parameter >

d6<

0.3

0.5

0.7

Data

Data Shuffled

W parameter

| acceptanced| 0 .4 0 .6 0 .8 1

W

5

15

25

• 200 GeV central (0-5%) events • Plot <Δη> and W v.s. |η|

acceptance • Data and shuffled events show

different |η| acceptance dependence

• W parameter shows a strong acceptance dependence

( )shuffled data

shuffled

100W

η ηη

⋅ Δ − Δ=

Δ

6/12/12 Gary Westfall 11

M)0 0.6 1.2 1.8

)M)B(

0

0.2

0.4

0.6_Ѡ_������

0 0.6 1.2 1.8

_Ѡ_������'DWD���0L[HG6KXIIOHG0L[HG

(GeV)NNs10 210

W

0

5

10

15

20

25

30| < 0.7MSTAR || < 0.7MUrQMD || < 0.7MNA49 |

STAR | < 1.0M |

midrapidity$

forward$rapidity$

W Parameter

( )shuffled data

shuffled

100W

η ηη

⋅ Δ − Δ=

Δ

•  The NA49 results agree well with STAR (|η|<0.7) at low energies

•  Data show a smooth increase of W with increasing beam energy, which is consistent with the <Δη> results

•  UrQMD reproduces the observed trend in W but predicts a much smaller value of W, corresponding to a much larger width

NA49

6/12/12 Gary Westfall 12

NA49: C. Alt et al. Phys. Rev. C 76, 024914 (2007)$

Chiral Magnetic Effect

6/12/12 Gary Westfall 13

�  In a QGP metastable P-odd domains can be created

�  Non-central collisions of gold produce ultra-strong magnetic fields

�  CME induces a charge separation across the reaction plane

�  A three point correlator was proposed by S. Voloshin to quantify possible local parity violation

( )cos 2 EPαβ α βγ φ φ= + − Ψ

Phys. Rev. Lett.103,251601 (2009)

~1000 trillion Tesla

Three Point Correlator

2

1 2(2 ) ( , )[cos2 cos sin 2 sin ]2p

dMd d BM d

γ γ γ γ φ φ φ φ φ φ φ φφ+− ++ −−= − − = Δ Δ Δ − Δ∫

•  γP is the difference between unlike- and like-sign correlations

•  Blast wave model reproduces observed difference between unlike- and like-sign azimuthal correlations

cos( 2 )RPαβ α βγ φ φ=< + − Ψ >

Phys. Rev. Lett.103,251601 (2009)

14 Gary Westfall 6/12/12

Blast Wave Model

•  STAR parameterization

(STAR,PRC,72,14904(2005))

•  Local charge conservation

6/12/12 Gary Westfall 15

S. Schlichting and S. Pratt Phys. Rev. C 83, 014913 (2011)

•  Extract the initial separation of balancing charges at time of freeze out by fitting the observed charge balance functions

6/12/12 Gary Westfall 16

Blast Wave Model

0

0.1

0.2

0.3

0.4

0.5

0.6

0 10 20 30 40 50 60 70% centrality

σησφ/π

0

0.5

1

1.5

2 0.5 1 1.5

0-5%

ση=0.226STAR

0 0.5 1 1.5

5-10%

ση=0.254STAR

0 0.5 1 1.5 2

10-20%

ση=0.353STAR

0

0.5

1

1.5

20-30%

ση=0.424STAR

30-40%

ση=0.494STAR

40-50%

ση=0.509STAR

0

0.5

1

1.5

50-60%

ση=0.579STAR

60-70%

ση=0.608STAR 200 GeV

�  The narrowing of balance function at central collision can’t be explained by changing of kinetic freeze-out temperature and collective flow alone

S. Schlichting and S. Pratt Phys. Rev. C 83, 014913 (2011)

S. Schlichting and S. Pratt Phys. Rev. C 83, 014913 (2011)

Event-Plane-Dependent Balance Function

( , ) ( , ) ( , ) ( , )1( , ) { }2 ( ) ( )N N N NB

N Nφ φ φ φ φ φ φ φφ φ

φ φ+− ++ −+ −−

+ −

Δ − Δ Δ − ΔΔ = +

17 Gary Westfall 6/12/12

φΔφ

0

0.1

0.2

0.3 0-5%o < 7.5� < o-7.5o < 52.5� < o37.5o < 97.5� < o82.5

5-10% 10-20%

)��

B(

0

0.1

0.2

0.3 20-30% 30-40% 40-50%

0

0.1

0.2

0.3 50-60%

��

60-70%

-100 0 100

70-80%

-100 0 100 -100 0 100

Balance Function v.s. Centrality

37.5° < ϕ-ψ < 52.5° 82.5° < ϕ-ψ < 97.5° -7.5° < ϕ-ψ < 7.5°

(in degree)

18 Gary Westfall 6/12/12

200 GeV Au+Au

Balance function narrows in central collision due to collective flow

��

��

��

����������

Balance Function

•  40-50% centrality

•  45° to event plane balance function is biased toward negative region

•  The out-of-plane balance function is wider than the in-plane balance function

Compare to blast wave model calculations1

19 Gary Westfall 6/12/12

1 S. Schlichting and S. Pratt Phys. Rev. C 83, 014913 (2011)

φΔ

200 GeV Au+Au

37.5° < ϕ-ψ < 52.5° 82.5° < ϕ-ψ < 97.5° -7.5° < ϕ-ψ < 7.5°

Balance Function

1( ) ( , ) cos( )( )1( ) ( , )sin( )( )

bb

bb

c d Bz

s d Bz

φ φ φ φ φφ

φ φ φ φ φφ

≡ Δ Δ Δ

≡ Δ Δ Δ

∫

∫

•  Compare data (points) with blast wave model calculations (solid lines)

•  Data are not corrected for event plane resolution (differences between data and model)

•  cb is related to the balance function width, while sb quantifies the asymmetry of balance function

•  Data show a stronger collective behavior in plane, while the asymmetry is most significant 45° to the reaction plane

( ) ( , )bz d Bφ φ φ φ≡ Δ Δ∫

20 Gary Westfall 6/12/12

200 GeV

!0 50 100 150 200 250 300 350

)!( b)

c

!( bs

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0-5% 20-30% 40-50% 60-70%

STAR Preliminary

Three Point Correlator

2

1 2(2 ) ( , )[cos2 cos sin 2 sin ]2p

dMd d BM d

γ γ γ γ φ φ φ φ φ φ φ φφ+− ++ −−= − − = Δ Δ Δ − Δ∫

•  γP is the difference between unlike- and like-sign correlations

•  Blast wave model reproduces observed difference between unlike- and like-sign azimuthal correlations

cos( 2 )RPαβ α βγ φ φ=< + − Ψ >Centrality

0 10 20 30 40 50 60 70 80

)-3

M/2

(10

p�

-10

-5

0

5

10

15

20

25

30

35

Blast-wave Model

STAR PRL

>b<C2v

2cv 2sv

Balance Function

Phys. Rev. Lett.103,251601 (2009)

21 Gary Westfall 6/12/12

200 GeV Au+Au

Beam Energy Dependence

22 Gary Westfall 6/12/12

)-3M/

2(10

p!

-10

0

10

20

30 Balance Function 20-30% 30-40%

10 210-10

0

10

20

30 40-50%

(GeV)NNs 10 210

50-60%STAR Preliminary

•  Balance functions for Δη narrow in central collisions

•  Balance functions for Δϕ narrow in central collisions

•  In central collisions, the balance narrows as the beam energy is increased

•  Narrowing of the balance function is a signal of delayed hadronization

6/12/12 Gary Westfall 23

Summary 1

Summary 2 •  The reaction-plane-dependent balance function

analysis gives the same difference between the like-sign and unlike-sign charge dependent azimuthal correlations as the three point correlator results published by STAR

•  This thermal blast wave model reproduces most of the difference between like- and unlike-sign charge-dependent azimuthal correlation incorporating local charge conservation and flow

•  As the energy is lowered, γp goes down, just as flow does

24 Gary Westfall 6/12/12