Winter Workshop on Nuclear Dynamics, Feb 2011

Centrality dependence of number and transverse momentum

correlations in Au+Au collisions at 200 GeV

Monika Sharma for the STAR CollaborationWayne State University

Winter Workshop on Nuclear Dynamics, Feb 2011Monika Sharma 2

Outline:Physics motivation

o The ridgeo Viscosityo Delayed hadronization

The ridge - R2, C and Viscosity - hybrid observable: CDelayed hadronization - charge dependent result from

Number density: R2 (R2++, R2--, R2+-)Hybrid observable: C (C++, C--, C+-)

Aim: To understand underlying collision dynamics in heavy-ion scenario

ρ2

ΔpT1ΔpT2

Winter Workshop on Nuclear Dynamics, Feb 2011Monika Sharma 3

Two-particle correlations

Proposed explanations:Glasma flux tubes: A. Dumitru et. al., hep-ph/0804.3858Radial flow + trigger bias: S. Voloshin, nucl-th/0312065

E. Shuryak, nucl-th/0706.3531 S. Gavin et.al., nucl-th/0806.4718

Minijets: STAR, JPG32 (2006) L37And many more…………..

Two-particle correlations at ISR

L. Foa, Physics reports, 22 (1975) 1-56

Fig: Correlation function R() for at various energies.

s =4GeV

s =3GeV

s =63GeV

Components:a) Near-side jet peakb) Near-side ridge c) Away-side and elliptic flow (v2)

STAR, PRC 80 (2000) 64912

Winter Workshop on Nuclear Dynamics, Feb 2011Monika Sharma 4

Measurement of viscosity based on pT correlations

• Viscous friction arises as fluid elements flow past each other, thereby reducing the relative velocity: damping of radial flow.

• Tzr changes the radial momentum current

of the fluid,

• Diffusion equation for the momentum current

• Viscosity reduces fluctuations, distributes excess momentum density over the collision volume: broadens the rapidity profile of fluctuations.

• Width of the correlation grows with diffusion time (system lifetime) relative to its original/initial width

Gavin and Aziz, Phys. Rev. Lett. 97 (2006) 162302

Tzr =− ∂vr ∂z

∂∂t

− v∇2⎛⎝⎜

⎞⎠⎟gt = 0

σ 2 = σ 02 + 2ΔV τ f( )

ΔV τ( ) =2v

τ 0

1−τ 0

τ⎛⎝⎜

⎞⎠⎟

Winter Workshop on Nuclear Dynamics, Feb 2011Monika Sharma 5

σ central

σ peripheral

Rheometry of QGP….

• Integral correlation function (Gavin & Aziz, Phys. Rev. Lett. 97 (2006) 162302)

σ c2 −σ 0

2 = 4υ τ 0−1 − τ f

−1( )

υ = Tcs

shear viscosityTc = critical temperatureS = entropy density = formation timef = freeze-out time

C =

pTi pTji≠j=

n

∑i=

n

∑n n

− pT pT

σ c2 ≈ σ Diffusion

2 +σ 02

Broadening:

C

Δ

Winter Workshop on Nuclear Dynamics, Feb 2011Monika Sharma 6

Delayed hadronization

Is hadronization delayed beyond 1 fm/c timescale?

What is pre-hadronic state? QGP?

Clocking HadronizationClocking Hadronization

OCD =O+−−O++ +O−−( )

O = observable

Can OCD be compared to BF?

Based upon the fact that charge is conserved locally, and produced pairs are initially correlated in coordinate space.

Balance function (BF) quantifies the degree of this separation and relates it with the time of hadronization.B Δy( ) =

N+− Δy( )−N++ Δy( )N+

+N−+ Δy( )−N−− Δy( )

N−

⎧⎨⎩

⎫⎬⎭

Early hadronization scenario: Pairs separate in rapidity due to expansion and rescattering.

Delayed hadronization scenario: Pairs are more strongly correlated in rapidity.

•Bass-Danielewicz-Pratt, PRL 85, 2000

Winter Workshop on Nuclear Dynamics, Feb 2011Monika Sharma 7

2-D (ΔΔ correlations

~ 1 ~ 0

Δ

Near side

Away side

=−ln tan(θ

2)

Δ

Winter Workshop on Nuclear Dynamics, Feb 2011Monika Sharma 8

Definitions:• Number density correlation measure: where

• Transverse momentum correlation measure:

• Hybrid correlation measure,

R2 =ρ Δ,Δφ( )ρρ Δ,Δφ( )

−ρ1 =

d 3N1

dηdφdpT

ρ2 =d 6N2

dη1dφ1dpT1dη 2dφ2dpT2

C =

pTi pTji≠j=

n

∑i=

n

∑n n

− pT pT

ρ2

ΔpT1ΔpT2 =

pTi − pT 1( )i≠ j=1

n2

∑i=1

n1

∑ pT j − pT 2( )

n1n2

Winter Workshop on Nuclear Dynamics, Feb 2011Monika Sharma 9

STAR Analysis

• Data from STAR TPC, 2 coverage• Dataset: RHIC run IV: AuAu 200 GeV• Events analyzed: 8 Million• Minimum bias trigger• Track kinematic cuts

o Goal: measure medium properties i.e., Bulk Correlations o ||<1.0o 0.2< pT < 2.0 GeV/c, No trigger and associated particle

• Analysis done vs. collision centrality measured based on multiplicity in ||<1.0

PMD

Slices: 0-5%, 5-10%……. 70-80%

Modeling nuclear collisions in ideal hydrodynamics is limited to low pT < GeV / c( )

Winter Workshop on Nuclear Dynamics, Feb 2011Monika Sharma 10

• Peripheral collisions (70-80%): ridge-like structure on the away-side and a peak on the near-side.

• Mid-central collisions (30-40%): cos(2Δ type modulations, ridge-like structure emerges on the near-side.

• Central collisions (0-5%): saddle-like shape on the away-side and a wide valley on the near-side.

Results R2 =

ρ Δ,Δφ( )ρρ Δ,Δφ( )

−

ρ1 =d 3N1

dηdφdpTρ2 =

d 6N2

dη1dφ1dpT1dη 2dφ2dpT2

Winter Workshop on Nuclear Dynamics, Feb 2011Monika Sharma 11

The Ridge

• R2 inclusive• Magnitude of unlike sign (R2(+-)) charge combination dominate compared to like sign (R2(++)) on the near-side.

Winter Workshop on Nuclear Dynamics, Feb 2011Monika Sharma 12

Hybrid correlation measure C (++)

• Peripheral collisions (70-80%): broad peak on the near-side and a ridge-like structure on the away-side.

• Mid-central collisions (30-40%): cos(2Δ type modulations, ridge-like structure emerges on the near-side.

• Central collisions (0-5%): saddle-like shape on the away-side and a triangular shape on the near-side.

• Magnitude of unlike sign (C(+-)) charge combination dominate compared to like sign (C(++)) on the near-side, as observed for R2.

C =

pTi pTji≠j=

n

∑i=

n

∑n n

− pT pT

Winter Workshop on Nuclear Dynamics, Feb 2011Monika Sharma 13

Hybrid correlation measure C (CI)

• Advocated to be an experimental probe of viscosity that is independent of elliptic flow.

• Diffusion due to viscous effects broadens the rapidity profile of transverse momentum correlations.

• Not another model for an explanation of near-side ridge!

C =

pTi pTji≠j=

n

∑i=

n

∑n n

− pT pT

Winter Workshop on Nuclear Dynamics, Feb 2011Monika Sharma 14

Quantification of near-side broadening

C(b,aw ,σw,an,σn) =b+ awexp(−Δ / σw

)

+anexp(−Δ / σn

)

• Projection of the near-side,

• Fit parametrization: | Δφ <.

Baseline subtracted to estimate the RMS.

Winter Workshop on Nuclear Dynamics, Feb 2011Monika Sharma 15

RMS vs. collision centrality

• RMS approximately constantin most peripheral bins.

– Incomplete thermalization?– Radial flow effects?– Event centrality selection technique?

Winter Workshop on Nuclear Dynamics, Feb 2011Monika Sharma 16

Estimation of shear viscosity

σ c2 − σ 0

2 = 4υ τ 0−1 − τ c, f

−1( )

σ 0 = 0.536 ± 0.056

σ c = 0.942 ± 0.166

0 = 1fm/c

f = 20fm/c

s

= 0.14 ± 0.02(stats.)

References for freeze out time estimates in peripheral collisions

Bjorken PRD 27 (1983)Teaney, Nucl. Phys. 62 (2009)Dusling et al. arXiv:0911.2720M. Luzum & P. Romatschke

arXiv:0901.4588

Theoretical uncertainties:

Courtesy T. Ullrich

(Model dependent)

Winter Workshop on Nuclear Dynamics, Feb 2011Monika Sharma 17

Winter Workshop on Nuclear Dynamics, Feb 2011Monika Sharma 18

Delayed hadronization

• Narrowing of charge dependent correlation function in azimuth and pseudorapidity.

OCD =O+−−O++ +O−−( )

O = observable

R2 CD( ) =R,+−−R,++ + R,−−( )

C CD( ) =C+−−C++ +C−−( )

Winter Workshop on Nuclear Dynamics, Feb 2011Monika Sharma 19

ρ2

ΔpT1ΔpT2

• Peripheral collisions (70-80%): broad peak on the near-side and a ridge-like structure on the away-side.

• Mid-central collisions (30-40%): cos(2Δ type modulations, ridge-like structure emerges on the near-side.

• Central collisions (0-5%): no valley and no saddle-like structure observed on near and away-side.

ρ2

ΔpT1ΔpT2 =

pTi − pT 1( )i≠ j=1

n2

∑i=1

n1

∑ pT j − pT 2( )

n1n2

Transverse momentum correlation measure (++)

Winter Workshop on Nuclear Dynamics, Feb 2011Monika Sharma 20

Summary• Results shown for three different correlation functions, R2, C and .

• Response of each of these correlation functions is different to the collision dynamics.

• C interpreted to be sensitive to viscous effects.• Charge dependent results of R2 and C sensitive to delayed hadronization, radial flow.

• Striking similarities such as ridge and away-side saddle shape is observed for same-sign (++, --) and unlike-sign (+-) charged combinations for R2, C.

• Near-side valley type structure observed for like-sign charge combinations of C in most central collisions while no such structures are seen in .

ρ2

ΔpT1ΔpT2

ρ2

ΔpT1ΔpT2

Winter Workshop on Nuclear Dynamics, Feb 2011Monika Sharma 21

Back-up

• Delayed Hadronization

Early Hadronization Large y

Late Hadronization Small y

Winter Workshop on Nuclear Dynamics, Feb 2011Monika Sharma 22

0.2<pT<20.0 GeV/c

0.2<pT<2.0 GeV/c

To study the effect of jets

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Near side ( radians) comparison| Δφ <.

0.2<pT<20.0 GeV/c (FF)

0.2<pT<20.0 GeV/c (RFF)

0.2<pT<2.0 GeV/c

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• RMS (0.2 < pT < 2.0 GeV/c) = 0.942

• RMS (0.2 < pT < 20.0 GeV/c) (FF) = 0.875

• RMS (0.2 < pT < 20.0 GeV/c) (RFF) = 0.908

• RMS (0.2 < pT < 20.0 GeV/c) (RFF + FF) = 0.88

• Fractional change = 6.6%

RMS comparison (0-5%)

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0.2<pT<1.0 GeV/c

0.2<pT<2.0 GeV/c

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Near side ( radians) comparison| Δφ <.

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RMS comparison (0-5%)

• RMS (0.2 < pT < 2.0 GeV/c) = 0.942

• RMS (0.2 < pT < 1.0 GeV/c) = 0.95