Two Universal String Predictions for Heavy Ion Collisions David - PowerPoint PPT Presentation

Two Universal String Predictions for Heavy Ion Collisions David Mateos ICREA & University of Barcelona

Plan • Recap from this morning. • Phase transitions for mesons. • Photon emission by sQGP . • Implications for HIC. • A new mechanism for quark energy loss. • Remarks and concluding thoughts.

The QCD challenge • QCD remains a challenge after 36 years!

The QCD challenge • QCD remains a challenge after 36 years! • No analytic and truly systematic methods. • Lattice is good for static properties, but not for real - time physics... • ... and for a theorist it is a black box. • A string reformulation might help. • Topic of this talk -- with focus on QGP .

The QCD challenge • Problem: Dual of QCD is inaccessible within SUGRA. • Certain quantitative observables ( eg. T=0 spectrum ) will require going beyond supergravity. • However, certain predictions may be universal enough to apply in certain regimes. s = 1 η • Good example: Policastro, Son & Starinets ’01 Kovtun, Son & Starinets ‘03 4 π

Exploit two universal properties Deconfined plasma BH Witten ‘98

Exploit two universal properties Glueballs BH N f ≪ N c quark flavours q q ¯ q � Karch & Randall ’01 � Karch & Katz ‘02 Free quarks Mesons

Phase transitions for mesons

First order phase M q transition at T fun T ( Gluons are deconfined in both phases! ) D.M., Myers & Thomson ’06 Babington, Erdmenger, Guralnik & Kirsch ’03 Kruczenski, D.M., Myers & Winters ‘03 Kirsch ‘04

First order phase M q transition at T fun T • Discrete set of mesons with mass gap: M mes ∼ M q √ ∼ T fun λ • Massive quarks. • Heavy mesons survive deconfinement! • In good agreement with lattice QCD, eg. for J/ Ψ : T fun ∼ 1 . 6 T c − 2 . 1 T c

First order phase M q transition at T fun T • No quasi - particle excitations! D.M., Myers & Thomson ’06 Hoyos - Badajoz, Landsteiner & Montero ‘06 • Will illustrate this by computing a spectral function of electromagnetic currents, related to photon production: EM EM � J µ J µ � D.M., Patiño - Jaidar ‘07

Phase transitions for mesons • Mesons absolutely stable at , but acquire widths away N c → ∞ , λ → ∞ from this limit. � � • Finite coupling: String worldsheet instantons. Faulkner & Liu ‘08 S 3 r( ) � √ λ ∼ e − M q /T Γ ∼ e − r m � r m r � r 0 � ’ r 0 � Γ ∼ 1 /N 2 • Finite N: Hawking radiation. c

Photon emission by sQGP

Why photons? • QGP is optically thin → Photons carry valuable information. γ • Holographic results for massless matter: Caron - Huot, Kovtun, Moore, Starinets & Y a ff e ’06 Parnachev & Sahakian ‘06

• To leading order in the electromagnetic coupling constant: e 2 1 d Γ e k 0 /T − 1 η µ ν χ µ ν ( k ) d d k = (2 π ) d 2 | k | | | − re k = ( k 0 , k ), with k 0 = | k | , is the photon null momentum, χ µ ν ( k ) = − 2 Im G R µ ν ( k ) is the spectral density, � d d +1 x e − ik · x Θ ( x 0 ) � [ J EM G R µ ( x ) , J EM µ ν ( k ) = − i (0)] � ν

Spectral function for Minkowski � χ = delta functions

Spectral function for BH M q = 0 1 0.8 0.6 χ µ µ ( ω ) 2 N f N c T 2 ω 0.4 0.2 0 0.5 1 1.5 2 2.5 ω = k 0 / 2 π T Maximum M q

Approaching the M q critical embedding: T Peaks at null momentum! 0.8 0.6 χ µ µ ( ω ) 0.4 2 N f N c T 2 ω 0.2 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 ω = k 0 / 2 π T

Approaching the M q critical embedding: T Dispersion relation for mesons D.M., Myers & Thomson ‘07 Ejaz, Faulkner, Liu, Rajagopal & Wiedemann ‘07 Peaks at null momentum! 0.8 ω ∼ v | � ω = | � k | k | 0.6 v < 1 χ µ µ ( ω ) 0.4 2 N f N c T 2 ω 0.2 Mass gap 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 ω = k 0 / 2 π T

Approaching the M q critical embedding: T Dispersion relation for mesons D.M., Myers & Thomson ‘07 Ejaz, Faulkner, Liu, Rajagopal & Wiedemann ‘07 Limiting velocity = Local speed of light at the tip ω ∼ v | � ω = | � k | k | v < 1 Mass gap

Approaching the M q critical embedding: T Dispersion relation for mesons D.M., Myers & Thomson ‘07 Ejaz, Faulkner, Liu, Rajagopal & Wiedemann ‘07 0.8 0.6 χ µ µ ( ω ) 0.4 ω ∼ v | � 2 N f N c T 2 ω ω = | � k | k | 0.2 v < 1 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 ω = k 0 / 2 π T Meson with Mass gap null momentum γ γ

Implications for HIC

Implications for HIC Casalderey - Solana, D.M. ‘08 • Comparison with HIC experiments requires model for spacetime evolution of the fireball, number and distribution of J/ Ψ ’s, etc.

• Simple model yields, for LHC energies: 2 T diss = 1 . 25 T c 1.75 1.5 Thermal background 1.25 N γ from light quarks 1 0.75 J/ Ψ signal 0.5 0.25 3.5 4 4.5 5 5.5 6 ω [GeV] • Result exponentially sensitive to many parameters. c ¯ c • Quadratically sensitive to cross - section -- not observable at RHIC. • Location of the peak between 3 - 5 GeV .

• Signal is also comparable ( or larger ) than pQCD background: Arleo, d’Enterria and Peressounko ‘07 -2 Pb-Pb +X, 5.5 TeV [0-10% central] dy) (GeV/c) � � 3 10 Total : prompt + thermal � Prompt: NLO N , E = 50 GeV � � 2 10 coll c loss Thermal: QGP 10 Thermal: HRG 2 T dp T ( � =0.1 fm/c) = 650 MeV 1 0 0 � N/( -1 10 2 d -2 10 -3 10 -4 10 -5 10 -6 10 -7 10 0 1 2 3 4 5 6 7 8 p (GeV/c) T

A new mechanism for quark energy loss

A new mechanism for quark energy loss Casalderey - Solana, Fernandez & D.M. ( to appear ) Boundary v > v lim Chesler, Jensen, Karch & Y a ff e ‘08 BH

A new mechanism for quark energy loss Casalderey - Solana, Fernandez & D.M. ( to appear ) Boundary v > v lim Cherenkov Vector mesons ↔ A µ radiation BH

Comments • Will also radiate dx µ dx i S ∼ − 1 � � � � d 8 x − det( g + F ) − d τ A µ d τ − d τφ i scalar mesons: g s d σ • Will also radiate R - charged mesons: • Energy loss is of order . 1 /N c • But exactly calculable and not necessarily subleading for real - world QGP . • Characteristic v - dependence.

Preliminary results for D3/D7 • Focus on sphere zero mode since QCD has no sphere. • Expand in normalizable modes in radial direction: Infinite tower of massive 4D vector mesons. • Energy loss in longitudinal and transverse modes.

• Coupling to each mode is proportional to meson radial wave function at the location of the quark. 3.0 Boundary 1.4 2.5 1.2 2.0 n=0 1.0 n=1 0.8 1.5 0.6 1.0 0.4 0.5 0.2 0.0 30 20 10 � 10 60 50 40 30 20 10 BH

0.7 dE/dt Preliminary results 0.6 for D3/D7 0.5 ( n=0, transverse mode ) 0.4 0.3 0.8 dE/dt 0.2 0.6 0.1 2.0 2.5 3.0 3.5 4.0 4.5 5.0 quark position 0.4 0.2 0.90 0.92 0.94 0.96 0.98 1.00 quark velocity

Remarks

• Photon peak and energy loss may exist in QCD, irrespectively of whether a string dual exists. • Depends on only two assumptions: - V J/ ψ , Υ , ... ector mesons ( ) survive deconfinement. Lattice, e ff ective potentials, etc. - Their limiting velocity in the QGP is subluminal. T Heuristically: T e ff ( v ) = (1 − v 2 ) 1 / 4

• V erifying in QCD is hard. Reassuring that e ff ect is universal property of all gauge theories with gravity dual: Deconfinement Quarks BH

Two phases: Heavy mesons survive deconfinement. 2 1.75 1.5 ω ∼ v | � 1.25 k | N γ 1 v < 1 0.75 0.5 0.25 3.5 4 4.5 5 5.5 6 ω [GeV] v > v lim Vector mesons ↔ A µ BH

Thank you.