1. Viscous Damping of Anisotropic Flow in 7.7 − 200 GeV Au+Au Collisions
Niseem Magdy
STAR Collaboration
Stony Brook University
Strangeness in Quark Matter 2016

2. Niseem Magdy, Stony Brook University, SQM 2016
Outline
Introduction
QCD Phase Diagram
STAR Detector
Correlation function technique
Results
𝑣 𝑛 𝑝 𝑇 dependence
𝑣 𝑛 𝐶𝑒𝑛𝑡𝑟𝑎𝑙𝑖𝑡𝑦 dependence
𝑣 𝑛 beam energy dependence
Viscous coefficient
III. Conclusion
Niseem Magdy, Stony Brook University, SQM 2016

3. QCD Phase Diagram
Strong interest in measurements which span a broad ( 𝜇 𝐵 ,T) domain.
Investigate signatures for the first-order phase transition
Search for critical fluctuations
Investigate transport coefficients as a function of ( 𝜇 𝐵 ,T)
Possible non-monotonic patterns
PRL 112,162301(2014)
PRL 112, (2014)
PRL 116, (2016)
Niseem Magdy, Stony Brook University, SQM 2016

4. STAR Detector at RHIC TPC detector covers |𝜂| < 1
Niseem Magdy, Stony Brook University, SQM 2016

5. Correlation function technique
All current techniques used to study 𝑣 𝑛 are related to the correlation function.
Two particle correlation function 𝐶 Δ𝜑= 𝜑 1 − 𝜑 2 𝑢𝑠𝑒𝑑 𝑖𝑛 𝑡ℎ𝑖𝑠 𝑎𝑛𝑎𝑙𝑦𝑠i𝑠,
𝐶 Δ𝜑 = 𝑑𝑁/𝑑Δ𝜑(𝑠𝑎𝑚𝑒) 𝑑𝑁/𝑑Δ𝜑(𝑚𝑖𝑥) and 𝑣 𝑛 2 = Δ𝜑 𝐶 Δ𝜑 cos⁡(𝑛 Δ𝜑) Δ𝜑 𝐶 Δ𝜑
𝑣 𝑛 (𝑝𝑇)= 𝑣 𝑛 2 ( 𝑝 𝑇 𝑟𝑒𝑓 , 𝑝 𝑇 ) 𝑣 𝑛 2 ( 𝑝 𝑇 𝑟𝑒𝑓 )
Factorization ansatz for 𝑣 𝑛 verified.
Non-flow signals, as well as some residual detector effects (track merging/splitting) minimized with |Δ𝜂= 𝜂 1 − 𝜂 2 | >0.7 cut. 1
PLB 708, 249 (2012) 2
Niseem Magdy, Stony Brook University, SQM 2016

6. Niseem Magdy, Stony Brook University, SQM 2016
Results
𝜂 <1 and |Δ𝜂|>0.7
n > 1
𝑣 𝑛 𝑝 𝑇 dependence
𝑣 𝑛 𝑝 𝑇 = 𝑣 𝑛 2 ( 𝑝 𝑇 𝑟𝑒𝑓 , 𝑝 𝑇 ) 𝑣 𝑛 2 ( 𝑝 𝑇 𝑟𝑒𝑓 )
𝑣 𝑛 𝐶𝑒𝑛𝑡𝑟𝑎𝑙𝑖𝑡𝑦
𝑣 𝑛 𝑠 𝑁𝑁
Niseem Magdy, Stony Brook University, SQM 2016

7. Niseem Magdy, Stony Brook University, SQM 2016
𝑣 𝑛 ( 𝑝 𝑇 )
𝜂 <1 and |Δ𝜂|>0.7
n > 1
𝑣 𝑛 𝑝 𝑇 indicate a similar trend for different beam energies.
𝑣 𝑛 𝑝 𝑇 decreases with harmonic order n.
Niseem Magdy, Stony Brook University, SQM 2016

8. Niseem Magdy, Stony Brook University, SQM 2016
𝑣 𝑛 ( 𝑝 𝑇 )
𝜂 <1 and |Δ𝜂|>0.7
n > 1
𝑣 𝑛 𝑝 𝑇 indicate a similar trend for different beam energies.
𝑣 𝑛 𝑝 𝑇 decreases with harmonic order n.
Niseem Magdy, Stony Brook University, SQM 2016

9. Niseem Magdy, Stony Brook University, SQM 2016
𝑣 𝑛 (Cent)
𝜂 <1 and |Δ𝜂|>0.7
0.2< 𝑝 𝑇 <4GeV/c
n > 1
𝑣 𝑛 Cent indicate a similar trend for different beam energies.
𝑣 𝑛 Cent decreases with harmonic order n.
Niseem Magdy, Stony Brook University, SQM 2016

10. Niseem Magdy, Stony Brook University, SQM 2016
𝑣 𝑛 (Cent)
𝜂 <1 and |Δ𝜂|>0.7
0.2< 𝑝 𝑇 <4GeV/c
n > 1
𝑣 𝑛 Cent indicate a similar trend for different beam energies.
𝑣 𝑛 Cent decreases with harmonic order n.
Niseem Magdy, Stony Brook University, SQM 2016

11. Niseem Magdy, Stony Brook University, SQM 2016
𝑣 𝑛 ( 𝑠 𝑁𝑁 )
𝜂 <1 and |Δ𝜂|>0.7
0.2< 𝑝 𝑇 <4GeV/c
n > 1
Mid rapidity 𝑣 𝑛 𝑠 𝑁𝑁 shows a monotonic increase with beam energy.
𝑣 𝑛 𝑠 𝑁𝑁 decreases with harmonic order n.
Niseem Magdy, Stony Brook University, SQM 2016

12. Niseem Magdy, Stony Brook University, SQM 2016
Viscous coefficient
Use 𝒗 𝒏 (pT, cent) to extract the viscous coefficient as a function of 𝒔 𝑵𝑵
the viscous coefficient proportional to the transport coefficient 𝜼 𝒔
Niseem Magdy, Stony Brook University, SQM 2016

13. Viscous coefficient
The 𝑣 𝑛 measurement are sensitive to 𝜀 𝑛 , transport coefficient η/s and the expanding parameter 𝑅𝑇.
Acoustic ansatz
Sound attenuation in the viscous matter reduces the magnitude of 𝑣 𝑛 .
Anisotropic flow attenuation, 𝑣 𝑛 𝜀 𝑛 ∝ 𝑒 −𝛽 𝑛 2 , 𝛽 ∝ η 𝑠 1 𝑅 𝑇
arXiv: 3
From macroscopic entropy considerations (𝑅𝑇) 3 ∝ 𝑑𝑁 𝑑𝜂
arXiv:
The viscous coefficient 𝜻 proportional to
the transport coefficient η 𝑠 ,
ln (𝑣 𝑛 ) 1 𝑛 (𝑣 2 ) − ln (𝜖 𝑛 ) 1 𝑛 (𝜖 2 ) =𝐴 − 𝑛−2 𝜼 𝒔 / 𝑑𝑁 𝑑𝜂 ln⁡(𝑐) 4
𝜻= ln (𝑣 𝑛 ) 1 𝑛 (𝑣 2 ) 𝑑𝑁 𝑑𝜂 5
Niseem Magdy, Stony Brook University, SQM 2016

14. Viscous coefficient 𝜂 <1 and |Δ𝜂|>0.7
𝜻= 𝒍𝒏 (𝒗 𝒏 ) 𝟏 𝒏 (𝒗 𝟐 ) 𝟏 𝟐 𝒅𝑵 𝒅𝜼 𝟏 𝟑
𝜻 ∝ η 𝑠
Viscous coefficient 𝜂 <1 and |Δ𝜂|>0.7
0.2< 𝑝 𝑇 <4GeV/c
The viscous coefficient 𝜉 shows a non-monotonic behavior with beam energy in both cases, n = 3 and n = 4.
Niseem Magdy, Stony Brook University, SQM 2016

15. STAR Non-monotonic behavior
PRL 112,162301(2014)
PRL 116, (2016)
Different STAR measurement shows a non-monotonic behavior about the same beam energy domain.
Niseem Magdy, Stony Brook University, SQM 2016

16. III. Conclusion
Comprehensive set of STAR measurements for
𝑣 𝑛 ( 𝑝 𝑇 ,cent, 𝑠 𝑁𝑁 ) presented.
For a given 𝑠 𝑁𝑁 𝑣 𝑛 decrease with the harmonic order.
Similar patterns but different magnitude for different 𝑠 𝑁𝑁
Mid rapidity 𝑣 𝑛 𝑠 𝑁𝑁 shows a monotonic increase with beam energy.
The viscous coefficient 𝜁, which proportional to the transport coefficient 𝜼 𝒔 , indicates a non-monotonic pattern for the beam energy range studied.
Niseem Magdy, Stony Brook University, SQM 2016

17. Niseem Magdy, Stony Brook University, SQM 2016
THANK YOU
Niseem Magdy, Stony Brook University, SQM 2016