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

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

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, 032302 (2014) PRL 116, 112302 (2016) Niseem Magdy, Stony Brook University, SQM 2016

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

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

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

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

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

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

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

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

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

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:1305.3341 3 From macroscopic entropy considerations (𝑅𝑇) 3 ∝ 𝑑𝑁 𝑑𝜂 arXiv:1601.06001 The viscous coefficient 𝜻 proportional to the transport coefficient η 𝑠 , ln (𝑣 𝑛 ) 1 𝑛 (𝑣 2 ) 1 2 − ln (𝜖 𝑛 ) 1 𝑛 (𝜖 2 ) 1 2 =𝐴 − 𝑛−2 𝜼 𝒔 / 𝑑𝑁 𝑑𝜂 1 3 +ln⁡(𝑐) 4 𝜻= ln (𝑣 𝑛 ) 1 𝑛 (𝑣 2 ) 1 2 𝑑𝑁 𝑑𝜂 1 3 5 Niseem Magdy, Stony Brook University, SQM 2016

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

STAR Non-monotonic behavior PRL 112,162301(2014) PRL 116, 112302 (2016) Different STAR measurement shows a non-monotonic behavior about the same beam energy domain. Niseem Magdy, Stony Brook University, SQM 2016

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

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