Universal Peaks in Holographic Photon Production. David Mateos University of California at Santa Barbara

Transcription

1 Universal Peaks in Holographic Photon Production David Mateos University of California at Santa Barbara

2 Plan Introduction and motivation. Phase transitions for fundamental matter. Photon production. Summary and future prospects.

3 Introduction and motivation.

4 The QCD challenge QCD remains a challenge after 35 years! A string reformulation might help. Lots of gauge/gravity examples. Unfortunately, QCD dual is not accessible via supergravity.

5 Therefore: Certain quantitative observables (eg. T=0 spectrum) will require going beyond supergravity. However, certain predictions may be universal enough to apply in certain regimes. Good example: η/s = 1/4π Policastro, Son & Starinets 01 Kovtun, Son & Starinets 03 Same for all non-abelian plasmas with gravity dual: Different dimensions, with or without fundamental matter, with or without chemical potential, etc. Suggests a prediction for QCD just above deconfinement...

6 Results indicate strong coupling and η/s ~ 1/4π. Animation by Jeffery Mitchell (Brookhaven National Laboratory). Simulation by the UrQMD Collaboration

7 Observations: Did not know η/s was going to be universal! Kovtun, Son & Starinets 03 Based on universal property: Gravity dual of a deconfined plasma contains a black hole. (explanation in a second) BH Witten 97

8 Observations: Glueballs Combine with another one: N f <<N c quark flavours correspond to N f probe branes Karch & Randall 01 Karch & Katz 02 BH (D3/D7 for concreteness) q q q Free quarks Mesons

9 Fundamental phase transitions. D.M., Myers & Thomson 06 Babington, Erdmenger, Evans, Guralnik & Kirsch 03 Kruczenski, D.M., Myers & Winters 03

10 First order phase M transition q at T fun T (Gluons are deconfined in both phases!)

11 First order phase M transition q at T fun T Discrete set of mesons with mass gap: M mes M q T fun λ No quasi-particle excitations! (despite N f N c scaling) Massive quarks. Absolutely stable -- survive deconfinement! In good agreement with lattice QCD, eg. for J/Ψ: Lattice: Gravity: T fun ( ) MeV T fun ( ) MeV

12 Holographic photon production. D.M., Patiño-Jaidar 07 Casalderey-Solana, Koch, D.M (in progress)

13 Why photons? QGP is optically thin Photons carry valuable information. γ Holographic results for massless matter: Caron-Huot, Kovtun, Moore, Starinets & Yaffe 06 Parnachev & Sahakian 06

14 dγ d d k = e 2 (2π) d 2 k To leading order in the electromagnetic coupling constant: 1 e k0 /T 1 ηµν χ µν (k) k = (k 0, k), with k 0 = k, is the photon null momentum χ µν (k) = 2 Im G R µν(k) is the spectral density, G R µν(k) = i d d+1 x e ik x Θ(x 0 ) [J EM µ (x), J EM ν (0)]

15 Holographic calculation Gauge theory String theory U(N f ) SU(N f ) U(1) B gauge A µ Conserved J B µ = J EM µ AdS/CFT prescription: G R µν δ2 S D7 δa µ δa ν

16 Comments: Concentrate on BH embeddings: χ = delta functions No obvious comparison of M q -dependence to pqcd: M thermal λt M q Arnold, Moore & Yaffe 01 But this assumes existence of quasi-particles!

17 Spectral function for constant m M mes T M q λt 1 m = χ µ µ(ω) 2N f N c T 2 ω m at which phase transition to Minkowski embedding happens ω = k 0 /2πT

18 Approaching the critical embedding: M q T 0.8 Peaks at null momentum! 0.6 χ µ µ(ω) 2N f N c T 2 ω ω = k 0 /2πT

19 Approaching the critical embedding Dispersion relation for mesons M q T ω = k ω v k v < 1 Peaks at null momentum! χ µ µ(ω) 2N f N c T 2 ω Mass gap ω = k 0 /2πT

20 Approaching the critical embedding Dispersion relation for mesons M q T ω = k ω v k v < 1 v(t) = Limiting velocity = Local speed of light at the tip Inverting one gets: T fun (v) = (1 v 2 ) 1/4 T fun Liu, Rajagopal & Wiedemann 06 Ejaz, Faulkner, Liu, Rajagopal & Wiedemann 07 Mass gap

21 Approaching the critical embedding Dispersion relation for mesons M q T Mass gap ω = k ω v k v < 1 T diss (p T ) / T c v(t) = Limiting velocity = Local speed of light at the tip Inverting one gets: T fun (v) = (1 v 2 ) 1/4 T fun p T in GeV J/ψ Liu, Rajagopal & Wiedemann 06 Υ

22 1 Peaks in the total χ µ µ(ω) photon production 2N f N ct 2 ω ω = k 0 /2πT 1 dγ 4αEMNfNcT 3 d k ω = k 0 /2πT

23 Comparison with experiment Have plotted at constant ω k0 T or m M mes T but in reality both vary simultaneously as the QGP cools down.

24 π 2 α EM N f N c (k 0 ) 2 T dec dγ d k k 0 = 100 MeV T dec = 175 MeV L H C c R H I C x = T dec /T u, d s

25 π 2 α EM N f N c (k 0 ) 2 T dec dγ d k k 0 = 1 GeV T dec = 175 MeV L H C c R H I C x = T dec /T u, d s

26 To compare with experiment Plug into hydrodynamic simulation of spacetime evolution of the plasma. Experimentally distinguish different sources: QGP photons, prompt photons, decay photons, etc.

27 Summary.

28 Universal Properties Deconfinement Quarks BH

29 Two phases: Limiting velocity. Heavy mesons survive deconfinement. No quasi-particles ω v k v < 1 1 dγ 4αEMNfNcT 3 d k Peaks! ω = k 0 /2πT

30 Future Prospects.

31 Heavy ion collisions at LHC T RHIC ~2T dec, T LHC ~4T dec Last call for predictions!

32 Thank you.