Strong Coupling and Heavy Ion Collisions

Transcription

1 Strong Coupling and Heavy Ion Collisions Derek Teaney SUNY Stony Brook and RBRC Fellow Simon Caron-Huot, DT, Paul Chesler; PRD, arxiv:2.73 Paul Chesler and DT; arxiv:2.696 Paul Chesler and DT; arxiv:2

2 Outline:. What are strong strongly coupled plasma like? - What are QCD plasmas like? Lattice spectral densities 2. Thermalization of strongly coupled plasmas - Study the non-equilbrium Hawking radiation with AdS/CFT Discussion: p+a results from the LHC Opportunity for the AdS/CFT correspondence

3 Strongly Coupled Plasmas and Lattice

4 QCD Lattice Weak versus strong coupling how to tell? Lattice measures current-current correlation functions ρ JJ = [J(t), J()] Weakly coupled picture consists of two processes: # #2 J() J(t) J() J(t) Pair Production at High Frequency Quasi Particles Moving at Low frequency Duration that quasi-particles move set by the collisional time scale τ c α 2 st

5 Spectral functions weak and strong coupling ρ JJ (ω) = dte iωt [J(t), J()] ρ JJ (ω) ω Weak Coupling Quasi-Particles Pair Continuum ω τ c Width of peak set by collisional time scale τ c T ω α 2 s

6 Spectral functions weak and strong coupling ρ JJ (ω) = Weak Coupling dte iωt [J(t), J()] Strong Coupling ρ JJ (ω) ω Quasi-Particles (ω) D JJ π ρ s ω χ JJ (!)! (b) Pair Continuum 5 4 ω τ c 2 AdS/CFT π ω 2πT 3 T ω ω/(2πt) No distinction between transport and continuum! The most important strong coupling prediction!

7 Lattice Measurements. Lattice measures integrals of ρ G JJ (τ) }{{} lattice measurements = dω 2π ρ JJ (ω) ω }{{} what we want ω cosh ω(τ /2T ) sinh(ω/2t ) 2. Always suffers from systematics 3. As good as it will get for a good while: Brookhaven-Bielefeld group, Ding et al arxiv: lattice.very precise < %. Continuum extrapolated

8 T 2 G V (τt)/(χ q G V free (τt)) 2Tc BW /Γ=.98 Γ/2T= Fits to Euclidean Data.6 τt ρ ii (ω)/ωt Determined spectral function BW+continuum free ω/t

9 Weak View Strong View 5 ρ ii (ω)/ωt 5 ρ ii (ω)/ωt 4 close enough 4 close enough BW+continuum free 2 BW+continuum free ω/t ω/t Lattice data are disastrously in between weak and strong

10 Thermalization of Strongly Coupled QGP

11 Non-equilibrium setup in 4D: (Chesler-Yaffe). Chesler and Yaffe turn on a strong gravitational pulse in our world ds 2 = dt 2 + e B o(t) dx 2 + e 2B o(t) dx 2 where B o (t) e t2 / t 2 Vacuum or Low T plasma Gravitational Pulse Non Equilbrium plasma Equilibrated Plasma Beginning Middle End time

12 The boundary stress tensor The energy density increases by 5 times for a gaussian pulse with t = /πt f T µ ν / ε final Pulse On v - πt final ε/ε f P L /ε f (time) ǫ = energy density P L = 3 ǫ = Longitudinal pressure T µ ν = diag(e, P T, P T, P L ) (Effect. temperature) = β eff (v) E /4

13 My Goal and Motivation: Vacuum or Low T plasma Gravitational Pulse Non Equilbrium plasma Equilibrated Plasma Beginning Middle End time I want to compute the "photon" emission rate in the non-equilibrium plasma.. Study the equilibration of different modes in the plasma. 2. Study the non-equilibrium emission of quanta from the black brane Emission is dual to emission

14 Emission of dilatons weakly interacting with equilibrium strongly coupled SYM plasma Equilibrated Plasma + 4D Dilaton Field is int = i d 4 x φ(x)j(x) Emission: (2π) 3 2k dγ< d 3 k = G< (K) G < (K) = Absorption: The absorption rate of Dilatons is (2π) 3 2k dγ> d 3 k = G> (K) G > (K) = Ĵ() Ĵ(K) Ĵ(K) Ĵ() FDT: The Fluctuation Dissipation Relation reads [ G < (K) }{{} emission ] [ / G > (K) }{{} absorption ] = e ω/t We will compute the emission and absorption rates and check for detailed balance

15 What the classical AdS/CFT usually computes Equilibrated Plasma + 4D Dilaton Field n k = Dilaton occupation number t n k = n k Γ > }{{} absorb + ( + n k ) Γ < }{{} emit For a classical dilaton field n k the damping is The classical absorption rate t n k = n k (Γ > Γ < ) }{{} classical absorption rate G > (K) G < (K) = 2 ImG R (K) Without assuming FDT, only the classical absorption rate is computable with the classical black brane response.

16 Definitions spectral density and statistical fluctuations Spectral Density records classical dissipation (commutator or G > G < ) ρ ra ar (t t 2 ) = [φ(t ), φ(t 2 )] Statistical fluctuations (anti-commutator or 2 (G> + G < )) G rr (t t 2 ) = 2 {φ(t ), φ(t 2 )} Invariably suppressed at large N and only due to Hawking radiation. What do you want to know about these things?

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18 A non-equilibrium definition of the Emission and Absorption Rates Want to know the rate to emit and absorb in a frequency band ω at time t. Wigner Transforms perfect frequency resolution, but no time resolution G < ( t, ω) = d te +iω t J( t t)j( t + t) 2. Gabor Transform Wigner smeared with a minimum uncertainty wave packet Ḡ < ( t o, ω o ) }{{} Gabor = dtdω 2π 2e (ω ω o) 2 σ 2 e ( t t o ) 2 /σ 2 }{{} G < ( t, ω) }{{} minimum wave packet Wigner Trans 3. The total number of dilatons emitted (in the band) n(t, ω o ) = t d t o Ḡ < ( t o, ω o ) This is a good estimate for the local emission rate for a given temporal resolution

19 T µ ν / ε final Pulse On ε/ε f P L /ε f Resolution Temporal Resolution σ v πt f = 2.7 Frequency Resolution ω / 2 8 σ ω % v - πt final

20 Equilibration and the coarse-grained FDT. If the FDT is satisfied G < (K) = e ω/t G > (K) then, the coarse-grained quantities satisfy Ḡ < ( t o, ω o, q) }{{} emission ] = e ω oβ eff [e β2 eff /4σ2 Ḡ > ( t o, ω o β eff /2σ 2, q) }{{} absorption We will monitor the FDT as a function of time to quantify equilibrium

21 Results

22 Emission&Absorption rates and the FDT: T µν / ε final (a) ε/ε f P L /ε f Stress Tensor (b) FDT satisfied.8 Lightlike ḡ < / ḡ < final Timelike FDT-expectation Emission rate Emission & Absorption v - πt final Timelike: ω 8πT f and q = Lightlike: ω 8πT f and q T = q L = ω/ 2

23 Pattern of equilibration: T µν / ε final (a) (b) ε/ε f P L /ε f First the stress/geometry equilibrates then ḡ < / ḡ < final Lightlike Timelike FDT-expectation Emission rate the emission rate equilibrates v - πt final

24 Thermalization of Timelike Modes ḡ < / ḡ < final (c) ω o /πt f v - πt final Timelike Find that massive timkelike modes thermalize in a finite time... will intuit that τ thermalize const ω

25 Thermalization of Lightlike Modes Chesler et al, Arnold&Vaman ḡ < / ḡ < final (d) ω o /πt f v - πt final Lightlike The harder the lightlike mode, the longer it takes to equilibrate... will intuit that τ thermalize (ωσ) /4 for ω where Q 2 = (ω 2 q 2 ) ωσ }{{ } virtuality

26 Summary: (c) (d) ḡ < / ḡ < final ω o /πt f ḡ < / ḡ < final ω o /πt f Timelike.2 Lightlike v - πt final v - πt final. Find that massive timkelike modes thermalize in a finite time... will intuit that τ thermalize const ω 2. The harder the lightlike mode, the longer it takes to equilibrate... will intuit that τ thermalize (ωσ) /4 for ω

27 Non-Equilibrium AdS/CFT and Hawking Radiation

28 Non-equilibrium: (Chesler-Yaffe) Paul and Larry Play God: ds 2 = dt 2 + e B o(t) dx 2 + e 2B o(t) dx 2

29 Non-equilibrium setup in 5D Chesler-Yaffe. Corresponds to non-equilibrium geometry with BH formation in AdS 5 Bndry Pulse Diverging Geodesics Event Horizon Geodesics falling into hole Time ds 2 = A dv 2 + Σ 2[ e B dx 2 + e 2B dx 2 ] + 2dr dv,

30 What we want to compute in the gravitational theory:. We want to compute the five dimensional spectral weight ρ ra ar (v r v 2 r 2 ) = [φ(), φ(2)] }{{} computable with classical BH dissipation 2. And the five dimensional fluctuations (anti-commutator) G rr (v r v 2 r 2 ) = 2 {φ(), φ(2)} }{{} Fluctuations due to Hawking These correlators can be lifted to the boundary determining the boundary quantities

31 Hawking radiation in non-equilibrium geometries Becomes a statistical fluctuation here A UV quantum fluctuation here Surface Properties characterizes diverging geodesics near event horizon κ(v) }{{} Lyapunov exponent Metric coeff {}}{ A(r, v) 2 r r=rh (v)

32 Then propagate the horizon fluctuations up to the boundary General form of near horizon fluctuations in non-equilibrium G h rr(v v 2 ) = 4 g(v )g(v 2 ) π v v2 log e v κ(v )dv e v2 κ(v )dv Event Horizon Can map the near horizon fluctuations up to boundary G rr ( 2) = dv h dv 2h G R ( h ) G R (2 2 h ) }{{} outgoing Green Fcns G h rr( h 2 h ) }{{} horizon flucts. G R G h rr G R

33 Qualitative explanation of our numerical results At large frequencies use a geometric approximation for Green fcns G rr ( 2) = dv h dv 2h G R ( h ) G R (2 2 h ) }{{} outgoing Green Fcns G h rr( h 2 h ) }{{} horizon flucts. Timelike-Geodesics /r q/ω Non-equilibrium flux flying along geodesics Maximally lightlike geodesics.8 non-equilbrium geometry/horizon equilibrium geometry/horizon v - πt final

34 Qualitative Picture Timelike-Geodesics /r q/ω Non-equilibrium flux flying along geodesics Maximally lightlike geodesics.8 non-equilbrium geometry/horizon equilibrium geometry/horizon v - πt final. Time delay (fly-time) 2/πT f between the equilibration of -pnt and 2-pnt fcns. - Timelike geodesics, ω, fly directly to the bndry and equilibrate (fall in)

35 Qualitative Picture (see also Chesler et al, Arnold&Vaman) Timelike-Geodesics /r q/ω Non-equilibrium flux flying along geodesics Maximally lightlike geodesics.8 non-equilbrium geometry/horizon equilibrium geometry/horizon v - πt final 2. For large light like modes it takes a long time to reach the boundary. - For us, the virtuality is of order Q 2 = ω 2 q 2 ωσ - For a lightlike geodesic with small virtuality Q 2 τ fly ( ) ω 2 /4 (ωσ) /4 Q 2

36 Conclusions. Lattice measurements show no direct evidence for or against quasi-particles. 2. Thermalization of emission rates in non-equilibrium plasmas corresponds to Hawking emission from non-equilibrium black holes. 3. General pattern of thermalization: (a) First the one point functions J(t) equilibrate (b) Then the two pnt functions( J(t) J() equilibrate (c) Modes with large invariant mass (large Q 2 ) thermalize first (d) Hard onshell modes (small Q 2 ) take a long time to equilibrate τ (ωσ) /4 This picture of thermalization is not too different from weak-coupling

37 Disucssion of p+a results (Slides from talks of Peter Steinberg and Gunther Roland) (RBRC Workshop April 5-7, 23)

38 Correlations in AA

39 Correlations Detectors see a splash of particles correlated here! Y and particles correlated here! Correlations in AA generally attributed to flow

40 -% -5% 5-% -2% % 3-4% 4-5% 5-6% C(, ) % 7-8% 8-9% ATLAS Pb-Pb - L int = 8 µb 2 < p a T, p s NN =2.76 TeV b T < 3 GeV ATLAS, PRC (22)

41 Correlations in (high multiplicity) pa 8 7 ppb MinBias PbPb 5-% PbPb multiplicit offline N trk Gunther Roland Look at very rare events! RBRC Worksh

42 ncreasing multiplicity Increasing multiplicity p p Pb Pb Typical event Divide&into&4&mul.plicity&bins:& Divide&into&4&mul.plicity&bins N trk offline N trk offline Gunther Roland RBRC Workshop, Apr 5-7, 23 4/6/3 Gunther Roland RBRC Workshop, Apr 5-7, 23 4/6/3

43 Pb p Pb Increasing multiplicity Somewhat rare event 3% Increasing multiplicity p Divide&into&4&mul.plicity&bins:& Divide&into&4&mul.plicity&bins: Gunther Roland RBRC Workshop, Apr 5-7, 23 Gunther Roland RBRC Workshop, Apr 5-7, 23

44 Rare event one in 2 thousand ppb 8 7 ppb MinBias PbPb 5-% Pb using same offline N trk Gunther Roland

45 Comparison PbPb ppb 8 ppb MinBias PbPb and ppb using same multiplicity selection, 22 < N < 26

46 Gunther Roland RBRC Workshop, Apr 5-7, PbPb Δη > 2 ppb vs PbPb: p T dependence Δη < Δη > 2 Δη < ppb

47 Questions:. Is the mechanism for the correlation the same in ppb and PbPb? 2. Is hydrodynamics the origin of ppb correlations? 3. How important are non-equilibrium effects for ppb? PbPb?