Equation of state and transport coefficients at finite baryo-chemical potential

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1 Equation of state and transport coefficients at finite baryo-chemical potential Jacquelyn Noronha-Hostler University of Houston: Israel Portillo, Paolo Parotto, Claudia Ratti University of Sao Paulo: Romulo Rougemont, Renato Critelli, Stefano Finazzo,Jorge Noronha Exploring the QCD Phase Diagram through Energy Scans, INT October 6 th 2016

2 Outline 1 Lattice QCD 2 Black Hole Engineering 3 Critical Point 4 Transport Coefficients 5 Freeze-out Line(s) 6 Conclusion and Outlook 7 Backup Backup

3 The Success of Lattice QCD Equation of State agrees for stout (WB) and HISQ (HotQCD) actions WB Phys.Lett. B730 (2014) HotQCD Phys.Rev. D90 (2014)

4 Limitations at Large µ B (Sign problem) Taylor expand pressure in term of µ B, limits results for large µ B P(µ B ) ( µb ) 2 ( µb ) 4 ( µb ) 6 = c T c 2 + c4 + c6 + O(µ 8 B ) T T T Phys.Lett. B751 (2015)

5 Limitations for transport properties Lattice has technical difficulties to compute transport properties We re left with a number of models that don t converge... Ηs UrQMD PHSD kubo kin. HRGHSQGP AdSCFT semiqgp DS YangMills BAMPS monopoles TMeV JNH arxiv: (see for references) Ζs HRGHS PHSD pqcd nonconf. AdS 14 mom TMeV

6 Filling in the gaps with Black Hole Engineering What we need... Strongly coupled system Non-conformal equation of state Equation of State at large baryon chemical potentials Critical Point Perfect fluidity Ability to compute transport coefficients near crossover and at large µ B One alternative Gauge/gravity duality - Black Hole Engineering

7 Gauge/gravity duality Maldacena, Gubser, Polyakov, Witten, 1998 Strong coupling limit of QFT in 4 dimensions (with many d.o.f.) String Theory/Classical gravity in d>4 dimensions curved spacetime = (t, x, y, z, r) where r is the holographic coordinate

8 non-conformal Equation of State S = 1 2κ 2 M 5 d 5 x g R 1 2 ( µφ) 2 V (φ) }{{} φ const (nonconformal) f (φ) 4 F µν 2 }{{} µ B 0 (ϵ-3p) / T μ B =0 [ ] T [MeV] κ 2 gravitational constant V (φ) dilaton potential f (φ) Maxwell-Dilaton coupling all fixed to lattice data at µ B = 0 non-conformality! Allows for ζ/s > 0! See also: DeWolfe, Gubser, Rosen PRD83(2011)086005;PRD84(2011) Rougemont et al JHEP1604(2016)102; Rougemont,Noronha,JNH,PRL115(2015)no.20,202301

9 Baryon susceptibilities Derivatives of the pressure χ B n = n p/ µ n B = n 1 ρ/ µ n 1 B χ 2 B (T,μ B =0)/T 2 χ 4 B (T,μ B =0) T [MeV] R. Rougemont,J. Noronha, JNH, PRL115(2015)no.20,202301

10 Perfect Fluidity Shear viscosity to entropy density* non-conformal EOS needed for bulk viscosity η s = 1 4π Kovtun,Son,Starinets, 2005 *The AdS/CFT bound that wasn t: Magnetic field violates KSS limit PRD90(2014)no.6, η/s(t ) higher-order derivatives of the action PRD77(2008) more Israel-Stewart transport coefficients near Tc S. Finazzo, R. Rougemont, H. Marrochio, J. Noronha, JHEP 1502 (2015) 051

11 Transition Region-Goldilocks Zone Only concerned with the transition region

12 Critical Point Critical Point (T = 90 MeV and µ B = 725 MeV) emerges naturally from the theory

13 Lattice QCD Black Hole Engineering Critical Point Transport Coefficients Freeze-out Line(s) Conclusion and Outlook Backup Equation of State at finite µb Everything at µb > 0 is a prediction Critical behavior very sensitive to µb = 0 Lattice QCD input

14 Strangeness and Electric Charge Since µ S < µ B and µ Q << µ B, assume µ S µ B 0 Caveat: only valid when µ S /µ B and µ Q /µ B are small χ 2 S (T,μB =0)/T [ ] χ 2 Q (T,μB =0)/T [ ] T [MeV] T [MeV]

15 Viscosity vs. Dynamic Universality Class No Critical Point Calculations possible within HRG, Transport etc General in viscosity as µ B Dynamical CP phenomena Review Hohenberg and Halperin,Rev. Mod. Phys. 49, 435 Critical Point Universality Class H 3D Ising Model- Mixing between chiral condensate and baryon density Son and Stephanov PRD70 (2004) Divergence in viscosity as approaching CP See Stephanov and Yin s talks Critical Point Universality Class B Black Hole Engineering Currently B conserved, working on S & Q! in viscosity as approaching CP Original AdS/CFT CP: Phys.Rev. D78 (2008)

16 Do we still have perfect fluidity at finite µ B? CP (Class B- no divergence) HRG/No CP Rougemont, Noronha, JNH, Ratti to appear shortly Kadam, Mishra Nucl.Phys. A934 (2014) See also Denicol, Jeon, Gale, Noronha Phys.Rev. C88 (2013) no.6,

17 Baryon Transport Coefficients σ B (T,μ B )/T T D B (T,μ B ) CFT limit μ B =0 μ B =100MeV μ B =200MeV μ B =300MeV μ B =400MeV T [MeV] CFT limit μ B =0 μ B =100MeV μ B =200MeV μ B =300MeV μ B =400MeV T [MeV] λ T (T,μ B ) / T 4 μ B Λ 2κ 2 φ 1/ν A CFT limit μ B =0 μ B =100MeV μ B =200MeV μ B =300MeV μ B =400MeV T [MeV] DC Conductivity σ B = lim ω 0 h(r)f (φ)e 2A(r) Im[a (r,ω)a (r,ω)] ω Baryon diffusion D B = σ B /χ B 2 Thermal conductivity λ T = (σ B /T ) [(ɛ + p)/ρ] 2 Rougemont, Noronha, JNH Phys.Rev.Lett. 115 (2015) no.20,

18 Electric Charge from various studies at µ B = µ S = µ Q = 0 Greif et al Phys.Rev. D90 (2014) no.9, (see citations within)

19 Strange and Electric Conductivity Transport Coefficients (to appear soon) σ S (T,μ B )/σ S CFT μb = 0 μb = 100 MeV μb = 200 MeV μb = 300 MeV σq(t,μb)/σ Q CFT μ B = 0 μ B = 100 MeV μ B = 200 MeV μ B = 300 MeV 0.0 μb = 400 MeV 0.2 μ B = 400 MeV T[MeV] T[MeV] D S (T,μ B )/D S CFT μb = 0 μb = 100 MeV μb = 200 MeV μb = 300 MeV DQ(T,μB)/D Q CFT μ B = 0 μ B = 100 MeV μ B = 200 MeV μ B = 300 MeV 0.4 μb = 400 MeV 0.75 μ B = 400 MeV T[MeV] T[MeV]

20 Vorticity Viscous Coupling (only at µ B = 0 so far) Israel-Stewart 2 nd order terms: Shear coupling terms: λ 2 η π ν λ Ωµ λ λ 3 Ω µ λ Ων λ Bulk coupling term: +λ 3 Ω µν Ω µν λ 2 = ln 2η πt and In red violates causality ξ Denicol et al Phys.Rev. D85 (2012) ; Phys.Rev. 2 = 2ητ π c 2 ( 1 s 3 ) c2 s D89 (2014) no.7, ; Finazzo et al JHEP 1502 Finazzo et al JHEP 1502 (2015) 051 (2015) 051 Vorticity puzzle: including vorticity in hydro while preserving causality? Models beyond hydro?

21 What defines the transition region? Determine the inflection point of the susceptibilities χ BSQ n s across µ B Determine the inflection point of the transport coefficients across µ B Should the inflection point of transport coefficients match the chemical freeze-out line? Susceptibilities compared to experiments: Compare derivatives of the pressure e.g. χ B 2 /χb 1 to experimental data All caveats from Claudia Ratti s talk

22 Susceptibilities in the black hole model Compare χ 1 /χ 2 and χ 3 /χ 2 to (net-p) data from STAR [STAR] Phys. Rev. Lett. 112 (2014)

23 Extraction of the freeze-out line from susceptibilities

24 Freeze-out line from the blackhole model

25 Inflection Points: Equilibrium vs. Dynamics T eq c,s (µ B) T dyn c,s (µ B) and T eq c,q (µ B) T dyn c,q (µ B) T eq c,b (µ B) decreases with µ B whereas T dyn c,b (µ B) = const 180 Tc(μB) [MeV] B (susceptibility) B (conductivity) 100 Q (susceptibility) Q (conductivity) 80 S (susceptibility) S (conductivity) μ B [MeV]

26 Conclusions and Outlook Black hole engineering provides a strongly interacting theory, non-conformal EoS that matches lattice, and calculable transport coefficients Critical Point arises at T = 90 MeV and µ B = 725 MeV sensitive to Lattice data at µ B = 0! Near crossover, µ B 0, transport coefficients are suppressed compared to conformal field theory Freeze-out line compared to experimental data correlated with minimum of c 2 s Theory work is needed! Inclusion of multiple nonzero chemical potentials