1

Radiative energy loss and damping effects

Joerg Aichelin, and Marcus Bluhm, and Pol Gossiaux,and Thierry Gousset (SubaTech)

Sept 7, 2011

Energy loss

Introduction

Energy loss

QCD case

(Q)ED case

Summary

2

quark and gluon energy loss is a central topic inultra-relativistic heavy ion collisions

collisional and radiative

Bethe-Heitler regime, LPM effect. . .

. . . and damping

radiation and energy loss

Introduction

QCD case

∆E

in electrodynamics

coherence

LPM effect

radiation spectrum

formation time

competing effects

without damping

with damping

discussion

(Q)ED case

Summary

3

radiative energy loss of quarks or gluons

an energetic parton in a hot medium (E ≫ T )

E E −∆E

in electrodynamics

Introduction

QCD case

∆E

in electrodynamics

coherence

LPM effect

radiation spectrum

formation time

competing effects

without damping

with damping

discussion

(Q)ED case

Summary

4

e −

relativistic electron

Bethe-Heitler spectrum

→ radiation loss in matter

X0 = radiation length

length scale on which e− looses its energy (on average)

coherence

Introduction

QCD case

∆E

in electrodynamics

coherence

LPM effect

radiation spectrum

formation time

competing effects

without damping

with damping

discussion

(Q)ED case

Summary

5

to be accommodated with another essential of bremsstrahlung

ω

t

t

scatt

form

formation time < radiation length

(v ≈ c = 1)

breaks down at small ω and large E

including multiple scattering: LPM effect

Introduction

QCD case

∆E

in electrodynamics

coherence

LPM effect

radiation spectrum

formation time

competing effects

without damping

with damping

discussion

(Q)ED case

Summary

6

ω

t form(S)

t form(M)

e− multiple scattering speeds up decoherence

⇒ emission process cannot occur at full rate

radiation spectrum

Introduction

QCD case

∆E

in electrodynamics

coherence

LPM effect

radiation spectrum

formation time

competing effects

without damping

with damping

discussion

(Q)ED case

Summary

7

dW/dω for an energetic parton using the scaling behavior

dW/dω ∝ tform

specificallydW

dω=

tformtBH

×dWBH

dω

tform? → diffraction theory

t form

O θ F

R

1

2

v||

formation time

Introduction

QCD case

∆E

in electrodynamics

coherence

LPM effect

radiation spectrum

formation time

competing effects

without damping

with damping

discussion

(Q)ED case

Summary

8

∆ϕ(t, R) = ω(t− tform)− ~k ·−→FR− ω(t− 0) + ~k ·

−−→OR

∆ϕ = −ω tform + ~k ·−−→OF

︸ ︷︷ ︸

k|| v|| tform

k|| = nω

ccos θ, v|| = v cos θs

|∆ϕ| ≡ 1 → tform

tform =1

ω |1− nv cos θs cos θ|

large formation time for ultrarelativistic particles, and smallangles, and n close to 1

competing effects

Introduction

QCD case

∆E

in electrodynamics

coherence

LPM effect

radiation spectrum

formation time

competing effects

without damping

with damping

discussion

(Q)ED case

Summary

9

1. wave propagation in medium (no damping)

n(ω) =

√

1−m2

g

ω2

competing effects

Introduction

QCD case

∆E

in electrodynamics

coherence

LPM effect

radiation spectrum

formation time

competing effects

without damping

with damping

discussion

(Q)ED case

Summary

9

1. wave propagation in medium (no damping) : n-drivenregime (v cos θs → 1, θ → 0)

t1 =1

ω(n− 1)∼

2ω

m2g

competing effects

Introduction

QCD case

∆E

in electrodynamics

coherence

LPM effect

radiation spectrum

formation time

competing effects

without damping

with damping

discussion

(Q)ED case

Summary

9

1. wave propagation in medium (no damping) : n-drivenregime (v cos θs → 1, θ → 0)

t1 =1

ω(n− 1)∼

2ω

m2g

2. (gluon) multiple scattering

k||(t) = nω(1− q t/ω2)

competing effects

Introduction

QCD case

∆E

in electrodynamics

coherence

LPM effect

radiation spectrum

formation time

competing effects

without damping

with damping

discussion

(Q)ED case

Summary

9

1. wave propagation in medium (no damping) : n-drivenregime (v cos θs → 1, θ → 0)

t1 =1

ω(n− 1)∼

2ω

m2g

2. (gluon) multiple scattering : multiple-scattering-drivenregime (n → 1, v cos θs → 1)

t2 =1

ω(q t2/ω2)=

√ω

q

competing effects

Introduction

QCD case

∆E

in electrodynamics

coherence

LPM effect

radiation spectrum

formation time

competing effects

without damping

with damping

discussion

(Q)ED case

Summary

9

1. wave propagation in medium (no damping) : n-drivenregime (v cos θs → 1, θ → 0)

t1 =1

ω(n− 1)∼

2ω

m2g

2. (gluon) multiple scattering : multiple-scattering-drivenregime (n → 1, v cos θs → 1)

t2 =1

ω(q t2/ω2)=

√ω

q

3. damping

1 and 2

Introduction

QCD case

∆E

in electrodynamics

coherence

LPM effect

radiation spectrum

formation time

competing effects

without damping

with damping

discussion

(Q)ED case

Summary

10

[log]

[log] [log]

BH

[log] dWdω

formt

t 1

ω ω

1 and 2

Introduction

QCD case

∆E

in electrodynamics

coherence

LPM effect

radiation spectrum

formation time

competing effects

without damping

with damping

discussion

(Q)ED case

Summary

10

ω LPM

λ

gm ω LPM

dWdωformt

t 1

ω ω

t 2

BHLPM

t1 = t2 ⇒ ωLPM =m4

g

qat which t1 = m2

g/q = λ

+ damping

Introduction

QCD case

∆E

in electrodynamics

coherence

LPM effect

radiation spectrum

formation time

competing effects

without damping

with damping

discussion

(Q)ED case

Summary

11

∼ e−Γt ⇒ damping regime when tform ≫ 1/Γ

+ damping

Introduction

QCD case

∆E

in electrodynamics

coherence

LPM effect

radiation spectrum

formation time

competing effects

without damping

with damping

discussion

(Q)ED case

Summary

11

∼ e−Γt ⇒ damping regime when tform ≫ 1/Γ

ω LPM

λ

gm ω LPM

dWdωformt

t 1

ω ω

t 2

BHLPM

+ damping

Introduction

QCD case

∆E

in electrodynamics

coherence

LPM effect

radiation spectrum

formation time

competing effects

without damping

with damping

discussion

(Q)ED case

Summary

11

∼ e−Γt ⇒ damping regime when tform ≫ 1/Γ

dWdωformt

t 1

ω ωωdamp ωdamp

1/ω

1/ ωt 2

BHLPM

1/Γdamping

t2 = 1/Γ ⇒ ωdamp =q

Γ2

discussion

Introduction

QCD case

∆E

in electrodynamics

coherence

LPM effect

radiation spectrum

formation time

competing effects

without damping

with damping

discussion

(Q)ED case

Summary

12

λ = O(

1/(g2T ))

and Γ = O(

g2T)

1

Γ∼ λ

is data (jet quenching) compatible with Γ ∼ 1λ

?

quantitatively?

microscopic origin of Γ?

goals

Introduction

QCD case

(Q)ED case

goals

arXiv:1106.2856v1

without damping

with damping

Summary

13

confronting the above reasoning with a true calculation

trace back formation time and damping factor

compare computed spectrum with the formation-timescaling law

dW

dω=

tformtBH

×dWBH

dω

(with ED-type formation times)

from arXiv:1106.2856v1

Introduction

QCD case

(Q)ED case

goals

arXiv:1106.2856v1

without damping

with damping

Summary

14

energy loss in an absorptive dielectric medium

n2(ω) = 1−m2

ω2+ 2i

Γ

ω

using linear response theory → mechanical work on charge

W = 2Re

(∫

d3~r′∫

dω ~E(~r′, ω) · ~(~r′, ω)∗)

d2W

dzdω≃ −Re

(

2iα

3π

q

E2

∫ ∞

0dt

ωn2

ǫexp

[

−ω|ni|βt

(

1−q

6E2t

)]

× cos(ωt) exp

[

iωnrβt

(

1−q

6E2t

)])

from arXiv:1106.2856v1

Introduction

QCD case

(Q)ED case

goals

arXiv:1106.2856v1

without damping

with damping

Summary

14

energy loss in an absorptive dielectric medium

n2(ω) = 1−m2

ω2+ 2i

Γ

ω

using linear response theory → mechanical work on charge

W = 2Re

(∫

d3~r′∫

dω ~E(~r′, ω) · ~(~r′, ω)∗)

d2W

dzdω≃ −Re

(

2iα

3π

q

E2

∫ ∞

0dt

ωn2

ǫexp

[

−ω|ni|βt

(

1−q

6E2t

)]

× cos(ωt) exp

[

iωnrβt

(

1−q

6E2t

)])

from arXiv:1106.2856v1

Introduction

QCD case

(Q)ED case

goals

arXiv:1106.2856v1

without damping

with damping

Summary

14

energy loss in an absorptive dielectric medium

n2(ω) = 1−m2

ω2+ 2i

Γ

ω

using linear response theory → mechanical work on charge

W = 2Re

(∫

d3~r′∫

dω ~E(~r′, ω) · ~(~r′, ω)∗)

d2W

dzdω≃ −Re

(

2iα

3π

q

E2

∫ ∞

0dt

ωn2

ǫexp

[

−ω|ni|βt

(

1−q

6E2t

)]

× cos(ωt) exp

[

iωnrβt

(

1−q

6E2t

)])

without damping

Introduction

QCD case

(Q)ED case

goals

arXiv:1106.2856v1

without damping

with damping

Summary

15

0 2 4 6ω/GeV

0

0.01

0.02-(

d W

/dzd

ω)/

α2

Γ = 0, m = 0, 0.3, 0.6, 0.9 GeV

q = 2.5 GeV2/fm, E = 20 GeV, M = 1 GeV

0 2 4 60

2

V

without damping

Introduction

QCD case

(Q)ED case

goals

arXiv:1106.2856v1

without damping

with damping

Summary

15

0 2 4 6ω/GeV

0

0.01

0.02-(

d W

/dzd

ω)/

α2

0 2 4 60

0.01

0.02

ΩGeV

Γ = 0, m = 0, 0.3, 0.6, 0.9 GeV

q = 2.5 GeV2/fm, E = 20 GeV, M = 1 GeV

dW

dω=

tformtBH

×dWBH

dω

with damping

Introduction

QCD case

(Q)ED case

goals

arXiv:1106.2856v1

without damping

with damping

Summary

16

0 2 4 6ω/GeV

0

0.01

0.02-(

d W

/dzd

ω)/

α2

0 2 4 60

0.01

0.02

ΩGeV

m = 0.6 GeV, Γ = 0, 5, 10, 50 MeV

q = 2.5 GeV2/fm, E = 20 GeV, M = 1 GeV

dW

dω=

tformtBH

×dWBH

dω

Summary

Introduction

QCD case

(Q)ED case

Summary

17

Effect of damping on radiative energy loss

Energy loss spectrum from formation time

— light parton

— comparison with complete calculation in ED

Questions:

— strength of damping in a QCD plasma?

— visible effects in quenching?