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

.

• Certain quantitative observables (eg. T=0 spectrum)

will require going beyond supergravity.

• However, certain predictions may be universal

enough to apply in certain regimes.

The QCD challenge

• Problem: Dual of QCD is inaccessible within SUGRA.
• Good example:

Policastro, Son & Starinets ’01 Kovtun, Son & Starinets ‘03

η s = 1 4π

Exploit two universal properties

BH

Deconfined plasma

Witten ‘98

q

BH

Karch & Randall ’01 Karch & Katz ‘02

Glueballs Mesons

q¯

q

Free quarks

quark flavours Nf ≪ Nc

• Exploit two universal properties

Phase transitions for mesons

Mq T

First order phase transition at Tfun

(Gluons are deconfined in both phases!)

Babington, Erdmenger, Guralnik & Kirsch ’03 Kruczenski, D.M., Myers & Winters ‘03 Kirsch ‘04 D.M., Myers & Thomson ’06

Mq T

• Discrete set of mesons with mass gap:

Mmes ∼ Mq √ λ ∼ Tfun

• Massive quarks.
• Heavy mesons survive deconfinement!

First order phase transition at Tfun

• In good agreement with lattice QCD, eg. for J/Ψ:

Tfun ∼ 1.6 Tc − 2.1Tc

Mq T

• No quasi-particle excitations!

First order phase transition at Tfun

Hoyos-Badajoz, Landsteiner & Montero ‘06 D.M., Myers & Thomson ’06

• Will illustrate this by computing a spectral function of

electromagnetic currents, related to photon production:

J

EM

µ J

EM

µ

D.M., Patiño-Jaidar ‘07

• Mesons absolutely stable at , but acquire widths away

from this limit. Nc → ∞ , λ → ∞

• rm

r0

’

rm

• S3
• r
• r( )

r

• Finite coupling: String worldsheet instantons.

Faulkner & Liu ‘08

Γ ∼ e−

√ λ ∼ e−Mq/T

• Finite N: Hawking radiation.

Γ ∼ 1/N 2

c

Phase transitions for mesons

Photon emission by sQGP

• QGP is optically thin → Photons carry valuable information.

Caron-Huot, Kovtun, Moore, Starinets & Y affe ’06 Parnachev & Sahakian ‘06

• Holographic results for massless matter:

Why photons?

γ

dΓ ddk = e2 (2π)d 2|k| 1 ek0/T − 1 ηµνχµν(k)

| | − re k = (k0, k), with k0 = |k|, is the photon null momentum,

χµν(k) = −2 Im GR

µν(k) is the spectral density,

GR

µν(k) = −i

• dd+1x e−ik·x Θ(x0)[J EM

µ (x), J EM ν

(0)]

• To leading order in the electromagnetic coupling constant:

χ =

• delta functions

Spectral function for Minkowski

Spectral function for BH

0.5 1 1.5 2 2.5 0.2 0.4 0.6 0.8 1

ω = k0/2πT

χµ

µ(ω)

2NfNcT 2ω

Maximum Mq

Mq = 0

Approaching the critical embedding:

Mq T

0.2 0.4 0.6 0.8 1 1.2 1.4 0.2 0.4 0.6 0.8

ω = k0/2πT

χµ

µ(ω)

2NfNcT 2ω

Peaks at null momentum!

0.2 0.4 0.6 0.8 1 1.2 1.4 0.2 0.4 0.6 0.8

ω = k0/2πT

χµ

µ(ω)

2NfNcT 2ω

Peaks at null momentum!

Mq T

Mass gap

ω ∼ v| k| v < 1

ω = | k|

Approaching the critical embedding:

Dispersion relation for mesons

D.M., Myers & Thomson ‘07 Ejaz, Faulkner, Liu, Rajagopal & Wiedemann ‘07

Mq T

Limiting velocity = Local speed of light at the tip

Approaching the critical embedding:

Mass gap

ω = | k| Dispersion relation for mesons

D.M., Myers & Thomson ‘07 Ejaz, Faulkner, Liu, Rajagopal & Wiedemann ‘07

ω ∼ v| k| v < 1

Mq T

Approaching the critical embedding:

0.2 0.4 0.6 0.8 1 1.2 1.4 0.2 0.4 0.6 0.8

ω = k0/2πT

χµ

µ(ω)

2NfNcT 2ω

Meson with null momentum

Mass gap

ω = | k| Dispersion relation for mesons

D.M., Myers & Thomson ‘07 Ejaz, Faulkner, Liu, Rajagopal & Wiedemann ‘07

ω ∼ v| k| v < 1 γ γ

Implications for HIC

• Comparison with HIC experiments requires model for

spacetime evolution of the fireball, number and distribution of J/Ψ’s, etc.

Casalderey-Solana, D.M. ‘08

Implications for HIC

• Simple model yields, for LHC energies:

3.5 4 4.5 5 5.5 6 0.25 0.5 0.75 1 1.25 1.5 1.75 2

ω [GeV]

Tdiss = 1.25 Tc

Nγ

• Result exponentially sensitive to many parameters.
• Location of the peak between 3-5 GeV

.

Thermal background from light quarks

J/Ψ signal

• Quadratically sensitive to cross-section
• - not observable at RHIC.

c¯ c

(GeV/c)

T

p

1 2 3 4 5 6 7 8

• 2

dy) (GeV/c)

2 T

dp

• N/(

2

d

• 7

10

• 6

10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 1 10

2

10

3

10

: prompt + thermal

• Total

= 50 GeV

c

• loss

, E

coll

N

• Prompt: NLO

Thermal: QGP Thermal: HRG

+X, 5.5 TeV [0-10% central]

• Pb-Pb

=0.1 fm/c) = 650 MeV

• (

T

• Signal is also comparable (or larger) than pQCD background:

Arleo, d’Enterria and Peressounko ‘07

A new mechanism for quark energy loss

BH Boundary

v > vlim

Chesler, Jensen, Karch & Y affe ‘08

A new mechanism for quark energy loss

Casalderey-Solana, Fernandez & D.M. (to appear)

Cherenkov radiation

BH Boundary

v > vlim

Vector mesons ↔ Aµ

A new mechanism for quark energy loss

Casalderey-Solana, Fernandez & D.M. (to appear)

Comments

• Will also radiate

scalar mesons:

S ∼ − 1 gs

• d8x
• − det(g + F) −
• dτAµ

dxµ dτ −

• dτφi

dxi dσ

• Will also radiate R-charged

mesons:

• Energy loss is of order .

1/Nc

• 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.

BH Boundary

• Coupling to each mode is proportional to meson

radial wave function at the location of the quark.

n=0 n=1

Preliminary results for D3/D7

2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.90 0.92 0.94 0.96 0.98 1.00 0.2 0.4 0.6 0.8

quark position quark velocity dE/dt dE/dt

(n=0, transverse mode)

Remarks

• Photon peak and energy loss may exist in

QCD, irrespectively of whether a string dual exists.

J/ψ, Υ, ...

• V

ector mesons ( ) survive deconfinement.

Lattice, effective potentials, etc.

• Their limiting velocity in the QGP is subluminal.

Heuristically:

Teff(v) = T (1 − v2)1/4

• Depends on only two assumptions:

Deconfinement

BH

Quarks

• V

erifying in QCD is hard. Reassuring that effect is universal property of all gauge theories with gravity dual:

Two phases:

Heavy mesons survive deconfinement.

ω ∼ v| k| v < 1

3.5 4 4.5 5 5.5 6 0.25 0.5 0.75 1 1.25 1.5 1.75 2

ω [GeV]

Nγ

BH

v > vlim

Vector mesons ↔ Aµ

Thank you.