Universal Peaks in Holographic Photon Production David Mateos University of California at Santa Barbara
Plan Introduction and motivation. Phase transitions for fundamental matter. Photon production. Summary and future prospects.
Introduction and motivation.
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.
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...
Results indicate strong coupling and η/s ~ 1/4π. Animation by Jeffery Mitchell (Brookhaven National Laboratory). Simulation by the UrQMD Collaboration
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
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
Fundamental phase transitions. D.M., Myers & Thomson 06 Babington, Erdmenger, Evans, Guralnik & Kirsch 03 Kruczenski, D.M., Myers & Winters 03
First order phase M transition q at T fun T (Gluons are deconfined in both phases!)
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 (317 403) MeV T fun (371 712) MeV
Holographic photon production. D.M., Patiño-Jaidar 07 Casalderey-Solana, Koch, D.M (in progress)
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
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)]
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
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!
Spectral function for constant m M mes T M q λt 1 m = 0 0.8 χ µ µ(ω) 2N f N c T 2 ω 0.6 0.4 0.2 0 0.5 1 1.5 2 2.5 m at which phase transition to Minkowski embedding happens ω = k 0 /2πT
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 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 ω = k 0 /2πT
Approaching the critical embedding Dispersion relation for mesons M q T ω = k 0.8 0.6 ω v k v < 1 Peaks at null momentum! χ µ µ(ω) 2N f N c T 2 ω Mass gap 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 ω = k 0 /2πT
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
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: 4 3.5 3 2.5 2 1.5 1 0.5 T fun (v) = (1 v 2 ) 1/4 T fun 0 0 5 10 15 20 p T in GeV J/ψ Liu, Rajagopal & Wiedemann 06 Υ
1 Peaks in the total χ µ µ(ω) photon production 2N f N ct 2 ω 0.8 0.6 0.4 0.2 0.015 0.0125 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 ω = k 0 /2πT 1 dγ 4αEMNfNcT 3 d k 0 0.01 0.0075 0.005 0.0025 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 ω = k 0 /2πT
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.
π 2 α EM N f N c (k 0 ) 2 T dec dγ d k 0 25 20 k 0 = 100 MeV T dec = 175 MeV 15 10 5 0 L H C c 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 R H I C x = T dec /T u, d s
π 2 α EM N f N c (k 0 ) 2 T dec dγ d k 0 1.2 1 k 0 = 1 GeV T dec = 175 MeV 0.8 0.6 0.4 0.2 0 L H C c 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 R H I C x = T dec /T u, d s
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.
Summary.
Universal Properties Deconfinement Quarks BH
Two phases: Limiting velocity. Heavy mesons survive deconfinement. No quasi-particles. 0.015 0.0125 ω v k v < 1 1 dγ 4αEMNfNcT 3 d k 0 0.01 0.0075 0.005 Peaks! 0.0025 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 ω = k 0 /2πT
Future Prospects.
Heavy ion collisions at LHC T RHIC ~2T dec, T LHC ~4T dec Last call for predictions!
Thank you.