Jet evolution in a dense QCD medium Edmond Iancu IPhT ...INT Program 18-3, Seattle, Nov 2018 Jet...

Jet evolution in a dense QCD medium

Edmond Iancu

IPhT Saclay & CNRS

based on work with J.-P. Blaizot, P. Caucal, F. Dominguez, Y. Mehtar-Tani,A. H. Mueller, and G. Soyez (2013-18)

June 19, 2013

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1 10 100

solid: Λ=100 MeVdashed: Λ=200 MeV

D(ω

)/Dva

c(ω)

ω [GeV]

q̂ =1 Gev2/fm,L=3 fmq̂ =2 Gev2/fm,L=3 fmq̂ =2 Gev2/fm,L=4 fm

0.6

0.8

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1.2

1.4

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1 10 100

E=200 GeV, θqq- =0.4, α- s=0.3

INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 1 / 43

Outline

Jets in heavy ion collisions

jet quenching

di-jet asymmetry, fragmentation functions

Two types of radiation

vacuum-like: bremsstrahlung (parton virtualities)medium-induced radiation : BDMPS-Z (collisions in the plasma)

Separately well understood

How to combine them together (within pQCD) ?

How is the “vacuum-like” radiation modified by the medium ?


Jets: pp vs. AA collisions at the LHC

Hard processes in QCD typically create pairs of partons which propagateback–to–back in the transverse plane

In the “vacuum” (pp collisions), this leads to a pair of symmetric jets

A spray of collimated particles produced via radiation (parton branching)

In AA collisions, the two jets can be differently affected by their interactionswith the surrounding, partonic, medium: quark-gluon plasma


Jets in practice

Experimentally, jets are constructed by grouping together hadrons whichpropagate at nearby angles

The jet opening angle ✓

0

(a.k.a. R) is the same for both jets

Medium modifications refer both to the jets and to the outer regions


From di–jets in p+p collisions ...


... to “mono-jets” in Pb+Pb collisions

Central Pb+Pb: ‘mono–jet’ events

The secondary jet can barely be distinguished from thebackground: ET1 � 100 GeV, ET2 > 25 GeV


Di–jet asymmetry at the LHC

Huge difference between the energies of the two jets

The missing energy is found in the underlying event:

many soft (p? < 2 GeV) hadrons propagating at large angles

Very different from the usual jet fragmentation pattern in the vacuumINT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 7 / 43

Di–jet asymmetry : AJ

0 0.5 1

Even

t Fra

ctio

n0.1

0.2 =7.0 TeVspp

PYTHIA

CMS -1L dt = 35.1 pb∫

, R=0.5TAnti-k

(a)

0 0.2 0.4 0.6 0.8 1

Even

t Fra

ctio

n

0

0.1

0.2

20-30%

(d) 0.2 0.4 0.6 0.8 1

0.1

0.2 =2.76 TeVNNsPbPb

PYTHIA+DATA

50-100%

(b)

Iterative Cone, R=0.5

-1bµL dt = 6.7 ∫

)T,2

+pT,1

)/(pT,2

-pT,1

= (pJA0.2 0.4 0.6 0.8 1

0.1

0.2

10-20%

(e) 0.2 0.4 0.6 0.8 1

0.1

0.2

30-50%

(c)

> 120 GeV/cT,1

p

> 50 GeV/cT,2

p

π32 >

12φ∆

0.2 0.4 0.6 0.8 1

0.1

0.2

0-10%

(f)

Event fraction as a function of the di–jet energy imbalance in p+p (a) andPb+Pb (b–f) collisions for different bins of centrality

A

J

=

E

1

� E

2

E

1

+ E

2

(Ei ⌘ pT,i = jet energies)


Di–jet asymmetry : AJ

0 0.5 1

Even

t Fra

ctio

n0.1

0.2 =7.0 TeVspp

PYTHIA

CMS -1L dt = 35.1 pb∫

, R=0.5TAnti-k

(a)

0 0.2 0.4 0.6 0.8 1

Even

t Fra

ctio

n

0

0.1

0.2

20-30%

(d) 0.2 0.4 0.6 0.8 1

0.1

0.2 =2.76 TeVNNsPbPb

PYTHIA+DATA

50-100%

(b)

Iterative Cone, R=0.5

-1bµL dt = 6.7 ∫

)T,2

+pT,1

)/(pT,2

-pT,1

= (pJA0.2 0.4 0.6 0.8 1

0.1

0.2

10-20%

(e) 0.2 0.4 0.6 0.8 1

0.1

0.2

30-50%

(c)

> 120 GeV/cT,1

p

> 50 GeV/cT,2

p

π32 >

12φ∆

0.2 0.4 0.6 0.8 1

0.1

0.2

0-10%

(f)

N.B. A pronounced asymmetry already in p+p collisions !

3-jets events, fluctuations in the branching process

Central Pb+Pb : the asymmetric events occur more often


The nuclear modification factor for jets

The jet yield in Pb+Pb collisions normalized by p+p times the averagenuclear thickness function hTAAi

RAA ⌘1

Nevt

d

2Njet

dpT dy

��AA

hTAAi d

2�jet

dpT dy

��pp

RAA would be equal to one in theabsence of nuclear effects

stronger suppression for morecentral collisions

Naturally interpreted as a consequence of energy loss inside the medium


The nuclear modification factor for jets

The jet yield in Pb+Pb collisions normalized by p+p times the averagenuclear thickness function hTAAi

RAA ⌘1

Nevt

d

2Njet

dpT dy

��AA

hTAAi d

2�jet

dpT dy

��pp

jet spectra are rapidly decreasingwith pT

they are shifted towards lower pT

due to in-medium energy loss

RAA is almost flat at very high pT : energy loss increases with pT


Intra-jet nuclear modifications

Jet fragmentation function: energy distribution of hadrons inside the jet

D(!) ⌘ !

dN

d!

=

Z R

0

d✓ !

dN

d✓d!

! ⌘ pT of a hadron inside the jet

ratio of FFs in Pb+Pb and p+p

slight suppression at intermediate energies

enhancement at low energies (z ⌧ 1) [GeV] Tp

1 10 210

) Tp(D

R

0.5

1

1.5

2

2.5

= 2.76 TeVNNs < 158 GeV, jetTp 126 <

= 5.02 TeVNNs < 158 GeV, jetTp 126 <

=0.4 jetsR tk | < 2.1 anti-jet y|ATLAS

Pb+Pb, 0-10%

Two classes of nuclear modifications: inside & outside the jet cone

We shall argue that they refer to two different types of radiation


Intra-jet nuclear modifications

Jet fragmentation function: energy distribution of hadrons inside the jetSimilar pattern when the distribution is plotted vs. pT or vs. z = pT /p

jetT

z2−10 1−10 1

)z(D

R

0.5

1

1.5

2

2.5

= 2.76 TeVNNs < 158 GeV, jetTp 126 <

= 5.02 TeVNNs < 158 GeV, jetTp 126 <


Pb+Pb, 0-10%

[GeV] Tp

1 10 210 ) Tp(

DR

0.5

1

1.5

2

2.5

= 2.76 TeVNNs < 158 GeV, jetTp 126 <

= 5.02 TeVNNs < 158 GeV, jetTp 126 <


Pb+Pb, 0-10%

Two classes of nuclear modifications: inside & outside the jet cone

We shall argue that they refer to two different types of radiation


Medium-induced jet evolution

The leading particle (LP) is produced by a hard scattering

It subsequently evolves via radiation (branchings) ...

... and via collisions off the medium constituents

Collisions can have several effectstransfer energy and momentum between the jet and the medium

trigger additional radiation (“medium-induced”)

wash out the color coherence (destroy interference pattern)


Transverse momentum broadening

An energetic quark acquires a transverse momentum p? via collisions in themedium, after propagating over a distance L

yp

xp = 0

8L0x =+ 0L

Direct amplitude (DA) ⇥ Complex conjugate amplitude (CCA)

Weakly coupled medium =) independent scattering centers

A random walk in p?: hp2?i ' q̂ L


Dipole picture

The individual collisions are relatively soft : k? ⇠ mD ⌧ E

yp

xp = 0

8L0x =+ 0L

Scattering can be computed in the eikonal approximation: Wilson lines

V

†(x) = P exp

⇢ig

Zdx

+

A

�a (x

+

,x)t

a

�

Two such Wilson lines (DA ⇥ CCA) =) a qq̄ color dipole


Dipole picture

L0x =+

x

yr

dN

d

2

p

=

1

(2⇡)

2

Z

r

e

�ip·rh ˆSxy

i ,

ˆ

S

xy

⌘ 1

Nctr

�V

†x

V

y

�

Average over the Gaussian distribution of the color fields A

�a (x

+

,x):

⌦A

�a (x

+

,k)A

�b (y

+

,�k)

↵0

= n �ab�(x+� y

+

)

g

2

(k

2

+ m

2

D)

2

n = CFnq + Ncng ⇠ T

3: color weighted density of thermal quarks & gluonsINT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 14 / 43

The tree-level approximation (“MV model”)

h ˆSxy

i0

' exp

⇢�1

4

Lq̂

0

(1/r

2

) r

2

�

The tree-level jet quenching parameter q̂

0

(logarithmic scale dependence):

q̂

0

(Q

2

) ⌘ ng

4

CF

Z Q2

d

2

k

(2⇡)

2

k

2

(k

2

+ m

2

D)

2

' 4⇡↵

2

sCFn ln

Q

2

m

2

D

The cross–section for p?–broadening at tree-level:

dN

d

2

p

=

1

(2⇡)

2

Z

r

e

�ip·re

� 14Lq̂0(1/r

2) r

2 ' 1

⇡Q

2

s

e

�p2?/Q2

s

A random walk in transverse momentum: hp2?i = Q

2

s(L) ⌘ Lq̂

0

(Q

2

s)

Power-law tail at large p? � Qs: single hard scattering

dN

d

2

p

' 1

(2⇡)

2

Z

r

e

�ip·r⇢�1

4

Lq̂

0

(1/r

2

) r

2

�' 4⇡↵

2

sCFn

p

4

?


Radiation: Formation time

Uncertainty principle: quantum particles are delocalized

The gluon has been emitted when it has no overlap with its source

k�? =

1

k?' 1

!✓

�x? ' ✓�t & �? =) �t & t

f

⌘ !

k

2

?' 1

!✓

2

“Formation time” : the time it takes to emit a gluon

This argument universally applies to radiation: in vacuum & in the medium

In vacuum, t

f

is measured from the hard scattering


Medium-induced radiation

Collisions introduce a lower limit on the transverse momentum ...

t

f

=

!

k

2

?& k

2

? & q̂t

f

t

f

.r

!

q̂

t

f

< L =) ! !c ⌘ q̂L

2

... hence an upper limit on the formation time !

Three types of emissions:

vacuum-like (usual bremsstrahlung): k

2

? � q̂t

f

, or t

f

⌧ p!/q̂

medium-induced, single hard scattering: k

2

? � q̂t

f

, or t

f

⌧ p!/q̂

medium-induced, multiple soft scattering: k

2

? ' q̂t

f

, or t

f

' p!/q̂


Radiative corrections to p?–broadening

Medium-induced emissions contribute to momentum broadening via recoil

Formally, a higher-order effect, but amplified by logarithms: “evolution”

0 L 0L

k

x

8

y

y+ x+ x+ y+

0 L 0Lx+

k

x8

y

y+

The quark ‘evolves’ by emitting a soft gluon (‘real’ or ‘virtual’)

‘soft’ () ! ⌘ k

+ ⌧ E =) eikonal emission verticesINT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 18 / 43

In-medium BK/JIMWLK evolution

‘Exchange graphs’ between q and q̄, or ‘self–energy’ graphs

0 L

x

y

k

y+ x+ 0 L

x

yk

y+ x+

All partons undergo multiple scattering: non–linear evolution

However, and unlike for a shockwave (DIS, pA), the multiple scatteringcannot be computed in the eikonal approximation

Eikonal scattering: transverse deviation �x? during collision time �t shouldbe small compared to the transverse wavelength �? = 1/p? :

�x? =

p?!

�t ⌧ �? =

1

p?=) �t ⌧ !

p

2

?= t

f

But for the soft gluon emissions at hand, one rather has �t = t

f


The single scattering approximation

The dominant radiative corrections are associated with fluctuations whichundergo only a single scattering (Liou, Mueller, Wu, 2013)

Power-law spectrum / 1/k

4

? yielding a logarithmic enhancement of the recoil

single scattering

k

2

? � q̂t

f

or t

f

⌧p

!/q̂

Gunion-Bertsch (or GLV) spectrum

!

dN

d! d

2

k

' ↵sNc

⇡

2

q̂

0

L

k

4

?0 Lt2tt1

r

B(t)

xy

z

The one-loop contribution to p?-broadening to double-log accuracy:

hp2?irad =

Z

!,kk

2

dN

d! d

2

k

= ↵̄q̂

0

L

Zd!

!

Zdk

2

?k

2

?⌘ L�q̂


A renormalization group equation for q̂

(Liou, Mueller, Wu, 2013; Blaizot and Mehtar-Tani, 2014; E.I., 2014)

The limits of the double-logarithmic phase–space are simpler in terms of theformation time t

f

= 2!/k

2

? (below, � ⌘ 1/T )

�q̂

q̂

0

= ↵̄

Z L

�

dt

f

t

f

Z q̂L

q̂tf

dk

2

?k

2

?=

↵̄

2

ln

2

L

�

a relatively large correction =) needs for resummation

the general (‘BK’) equation reduces to a linear equation : ‘DLA’

q̂(L) = q̂

0

+ ↵̄

Z L

�

dt

f

t

f

Z q̂L

q̂tf

dk

2

?k

2

?q̂(t

f

, k

2

?)

not the standard DLA equation: medium-dependent integration limits

q̂(L) = q̂

0

1p↵̄ ln

�L/�

�I

1

✓2

p↵̄ ln

L

�

◆/ L

2

p↵̄

large anomalous dimension �s = 2

p↵̄ ⇠ 1


Using a running coupling (E.I., D.N. Triantafyllopoulos, 2014)

The running coupling slows down the evolution at large Y ⌘ ln(L/�)

q̂(L) = q̂

0

+

Z L

�

dt

f

t

f

Z q̂L

q̂tf

dk

2

?k

2

?↵̄(k

2

?) q̂(t

f

, k

2

?)

=) ln q̂(L) ' 4

rb

0

ln

L

�

(slower than any exponential)

1 2 3 4 5Y

5

10

15

q̀sHYLêq̀H0L


Radiation from multiple soft scattering(Baier, Dokshitzer, Mueller, Peigné, Schiff; Zakharov; 1996-97)

The single hard scattering regime does not also control the energy loss

h�Eirad =

Z

!,k!

dN

d! d

2

k

= ↵̄q̂

0

L

Z !c

d!

Z q̂L

q̂tf

dk

2

?k

4

?

without the k

2

?-weighting, the integral is controlled by its lower limit

k

2

? ⇠ q̂t

f

⇠p

q̂! & t

f

⇠r

!

q̂

The BDMPS-Z spectrum for medium-induced radiation

!

dN

d! d

2

k

' ↵̄

L

t

f

(!)

1pq̂!

e

� k2?pq̂!

the emission can occur anyway inside the medium: a factor L/t

f

(!)

transverse momentum broadening during formation: hk2

?i 'p

q̂!

Maximal ! for this mechanism: t

f

L ) ! !c ⌘ q̂L

2


Angular distribution

Transverse momentum broadening during formation & after formation

formation angle:

✓

f

(!) ' (q̂!)

1/4

!

'✓

q̂

!

3

◆1/4

the minimal angle

✓c = ✓

f

(!c) =1pq̂L

3

final angle

✓(!) 'p

q̂L

!

= ✓c!c

!

Soft gluons ! ⌧ !c: small formation times (tf

⌧L) & large angles (✓�✓c)

Gluons with angles larger than the jet opening angle ✓

0

move outside the jet


The average energy loss

Differential probability for one emission (integrated over k?)

!

dP

d!

' ↵̄

L

t

f

(!)

' ↵̄

r!c

!

(! < !c ⌘ q̂L

2

/2)

The average energy loss by a particle with energy E > !c

�E =

Z !c

d! !

dP

d!

⇠ ↵s!c ⇠ ↵sq̂L2

integral dominated by its upper limit ! = !c

Hard emissions with ! ⇠ !c : probability of O(↵s)

rare events but which take away a large energy

small emission angle ✓c ) the energy remains inside the jet

Irrelevant for the di-jet asymmetry and also for the typical events


Multiple branchingJ.-P. Blaizot, E. I., Y. Mehtar-Tani, PRL 111, 052001 (2013)

When !(dP/d!) ⇠ 1, multiple branching becomes important

!

dPd!

' ↵̄

r!c

!

⇠ 1 =) ! . !

br

(L) ⌘ ↵̄

2

q̂L

2

LHC: the leading particle has E ⇠ 100GeV � !

br

⇠ 5GeV

In a typical event, the LP emits ...

a number of O(1) of gluons with ! ⇠ !

br

a large number of softer gluons with ! ⌧ !

br

The primary gluons with ! . !

br

keep splitting


Multiple branchingJ.-P. Blaizot, E. I., Y. Mehtar-Tani, PRL 111, 052001 (2013)

When !(dP/d!) ⇠ 1, multiple branching becomes important

!

dPd!

' ↵̄

r!c

!

⇠ 1 =) ! . !

br

(L) ⌘ ↵̄

2

q̂L

2

LHC: the leading particle has E ⇠ 100GeV � !

br

⇠ 5GeV

In a typical event, the LP emits ...

a number of O(1) of gluons with ! ⇠ !

br

a large number of softer gluons with ! ⌧ !

br

The primary gluons with ! . !

br

keep splittingINT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 26 / 43

Democratic branchings

The primary gluons generate ‘mini-jets’ via democratic branchings

daughter gluons carry comparable energy fractions: z ⇠ 1� z ⇠ 1/2

contrast to asymmetric splittings in the vacuum: z ⌧ 1

Via successive democratic branchings, the energy is efficiently transmitted tosofter and softer gluons, which eventually thermalize

Energy appears in many soft quanta propagating at large angles XINT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 27 / 43

Democratic branchings

The primary gluons generate ‘mini-jets’ via democratic branchings

daughter gluons carry comparable energy fractions: z ⇠ 1� z ⇠ 1/2

contrast to asymmetric splittings in the vacuum: z ⌧ 1

Via successive democratic branchings, the energy is efficiently transmitted tosofter and softer gluons, which eventually thermalize

CMS: The jet transverse momentum profile P (�r) (pT in annular rings)

A natural explanation for the di-jet asymmetry and for jet shapes


Intra-jet nucler modifications

How to understand the excess of soft particles inside the jet cone (✓ < R) ?

ratios of fragmentation functions in PbPb / pp

!7

z2−10 1−10 1

)z(D

R

0.5

1

1.5

2

2.5

< 158 GeVjetTp 126 <




, 0-10%-1 = 5.02 TeV, 0.49 nbNNsPb+Pb, -1 = 5.02 TeV, 25 pbs , pp

[GeV] Tp

1 10 210 ) Tp(

DR

0.5

1

1.5

2

2.5





, 0-10%-1 = 5.02 TeV, 0.49 nbNNsPb+Pb, -1 = 5.02 TeV, 25 pbs , pp

1805.05424 Martin Rybar, Wednesday

Medium-induced soft radiation should be pushed at large angles ✓ > R

Can vacuum-like radiation be modified by the medium ?


Vacuum-like emissions (VLE)P. Caucal, E.I., A. H. Mueller and G. Soyez, PRL 120 (2018) 232001

A jet initiated by a colorless qq̄ antenna (decay of a boosted � or Z)

The antenna propagates through the medium along a distance L

Emissions (tf

=

1

!✓2 ) can occur either inside (tf

L), or outside (tf

> L)

Evolution stopped by hadronisation: k? ' !✓ & ⇤

QCD


The vetoed region

Remember: the medium introduces an upper limit on the formation time

t

f

.r

!

q̂

L

No emission within the ranger

!

q̂

<

1

!✓

2

< L

End point of VETOED at

!c = q̂L

2

, ✓c =1pq̂L

3

VLEs in medium occur like in vacuum, but with a smaller phase-space

gluons within VETOED should have k

2

? ⌧ q̂t

f

, which is not possible

a leading-twist effect: DGLAP splitting functions

typical values: q̂ = 1GeV

2

/fm, L = 4 fm, !c = 50GeV, ✓c = 0.05


Jet in the vacuum (DLA)

Radiation triggered by the parton virtualities: bremsstrahlung

dP ' ↵sCR

⇡

d!

!

d✓

2

✓

2

Log enhancement for soft (! ⌧ E) and collinear (✓ ⌧ 1) gluons

Parton cascades: successive emissions are ordered in

energy (!i < !i�1

), by energy conservation

angle (✓i < ✓i�1

), by color coherence

Double-logarithmic approximation (DLA): strong double ordering

d

2

N

d!d✓

2

' ↵̄

! ✓

2

X

n�0

↵̄

n

1

n!

✓ln

E

!

◆n� 1

n!

✓ln

✓

2

0

✓

2

◆n�


Color (de)coherence

In vacuum, wide angle emissions (✓ > ✓qq̄) are suppressed by color coherence

the gluon has overlap with both the quark and the antiquark

In medium, color coherence is washed out by collisions after a time t

coh

q̂t & 1

r

2

?(t)⇠ 1

(✓qq̄t)2

=) t & t

coh

=

1

(q̂✓

2

qq̄)1/3

(Mehtar-Tani, Salgado, Tywoniuk; Casalderrey-Solana, E. I., 2010–12)


Color (de)coherence

In vacuum, wide angle emissions (✓ > ✓qq̄) are suppressed by color coherence

the gluon has overlap with both the quark and the antiquark

In medium, color coherence is washed out by collisions after a time t

coh

t

coh

=

1

(q̂✓

2

qq̄)1/3

⌧ L if ✓qq̄ � ✓c ' 0.05

Angular ordering could be violated for emissions inside the medium


Angular ordering strikes back

... But this is not the case for the VLEs !

✓ > ✓qq̄ & t

f

=

1

!✓

2

> t

coh

=) t

f

�r

!

q̂

Wide angle emissions (✓ > ✓qq̄) have t

f

⌧ t

coh

, hence they are suppressed

Emissions at smaller angles (✓ < ✓qq̄) can occur at any time

DLA cascades inside the medium are still strongly ordered in anglesINT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 33 / 43

There is a life after formation ...

The VLEs inside the medium have short formation times t

f

⌧ L

After formation, gluons propagate in the medium along a distance ⇠ L

They can suffer significant energy loss and momentum broadeningadditional sources for medium-induced radiation

They contribute to the jet multiplicity (fragmentation function)

They can emit (vacuum-like) gluons outside the medium


First emission outside the medium

The respective formation time is necessarily large: t

f

& L

An antenna with opening angle ✓ � ✓c loses coherence in a time t

coh

⌧ L

In-medium sources lose color coherence and can also radiate at larger angles

After the first “outside” emission, one returns to angular-ordering, as usual

Medium effects at DLA (leading twist):vetoed region + lack of angular-ordering for the first “outside” emission


Gluon distribution at DLA

Double differential distribution in energies and emission angles:

T (!, ✓) ⌘ !✓

2

d

2

N

d!d✓

2

0.02

0.05

0.2

0.4

0.01

0.1

0.1 1 10 100

θ

ω [GeV]

0.02

0.05

0.2

0.4

0.01

0.1

0.1 1 10 100

0.8525 1

E=200 GeV, θqq=0.4, α- s=0.3, q̂ =2 Gev2/fm, L=3 fm

T/Tvac

E = 200GeV, ✓qq̄ = 0.4

q̂ = 2GeV

2

/fm, L = 3 fm

T/T

vac

= 0 in the excluded region

T/T

vac

= 1 inside the medium andalso for ! > !c and any ✓

T/T

vac

< 1 outside the mediumat small angles . ✓c

T/T

vac

> 1 outside the mediumat large angles ⇠ ✓qq̄


Jet fragmentation function at DLA

D(!) ⌘ !

dN

d!

=

Z ✓2qq̄

⇤

2/!2

d✓

2

✓

2

T (!, ✓)

0.02

0.05

0.2

0.4

0.01

0.1

0.1 1 10 100

θ

ω [GeV]

0.02

0.05

0.2

0.4

0.01

0.1

0.1 1 10 100

0.8525 1

E=200 GeV, θqq=0.4, α- s=0.3, q̂ =2 Gev2/fm, L=3 fm

T/Tvac

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1 10 100


D(ω

)/Dva

c(ω)

ω [GeV]


0.6

0.8

1

1.2

1.4

1.6

1.8

2

1 10 100

E=200 GeV, θqq- =0.4, α- s=0.3

Slight suppression at intermediate energies (from 3 GeV up to !c)

the phase-space is reduced by the vetoed regionthe amount of suppression increases with L and q̂



D(!) ⌘ !

dN

d!

=

Z ✓2qq̄

⇤

2/!2

d✓

2

✓

2

T (!, ✓)

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1 10 100


D(ω

)/Dva

c(ω)

ω [GeV]


0.6

0.8

1

1.2

1.4

1.6

1.8

2

1 10 100

E=200 GeV, θqq- =0.4, α- s=0.3

Significant enhancement at low energy (below 2 GeV)

lack of angular ordering for the first emission outside the mediumthe enhancement is slowly increasing with the jet energy E (= pT )



D(!) ⌘ !

dN

d!

=

Z ✓2qq̄

⇤

2/!2

d✓

2

✓

2

T (!, ✓)

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1 10 100


D(ω

)/Dva

c(ω)

ω [GeV]


0.6

0.8

1

1.2

1.4

1.6

1.8

2

1 10 100

E=200 GeV, θqq- =0.4, α- s=0.3

Significant enhancement at low energy (below 2 GeV)

A related proposal by Mehtar-Tani and Tywoniuk, arXiv:1401.8293


Beyond DLA: Running coupling & NDLA

Remember the double-logarithmic approximations:strong ordering in both energies (Pgg ' 1/z) and anglesfixed coupling ↵̄

no “higher-twist” effects: no collisions, no medium-induced radiation

100 101 102

� [GeV]

1.0

1.2

1.4

1.6

1.8

2.0

D(�

)/D

vac

(�) Medium: q̂ = 1 GeV2/fm and L = 3 fm

Jet: E = 200 GeV and �̄ = 0.4

DLA - � = 150 MeVrunning coupling - � = 150 MeVnext-to-DLA - � = 150 MeV

100 101 102

� [GeV]

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

D(�

)/D

vac

(�)

Medium: q̂ = 1 GeV2/fm and L = 3 fm

Jet: E = 200 GeV and �̄ = 0.4

next-to-DLA wihout decoherence - � = 150 MeV

next-to-DLA - � = 150 MeV

Adding a running coupling: ↵̄(k

2

?) =1

¯b ln !2✓2

⇤2

, ¯b = 11/12

Finite-part of the splitting function: Pgg(z) ' 1

z +

R1

0

dz

0�Pgg(z

0)� 1

z0

�


Beyond DLA: Monte Carlo implementation(P. Caucal, E.I., A. H. Mueller and G. Soyez, in preparation)

Convolution of three showers:

vacuum cascades inside the medium but outside the vetoed regionfull splitting functions, running coupling, quarks and gluons, Nc = 3

medium-induced cascade in energy with democratic branchingsfixed coupling ↵̄, energy loss, transverse momentum broadening

partons with angles ✓ > ✓0 are leaving the jet

vacuum cascade outside the mediumno angular ordering for the first emission outside the medium

all the partons inside the jet (vacuum-like & medium-induced) can act

as sources

cascades stop at the hadronisation line

Leading parton selected according to the cross-section for pp ! 2 partons

experimental bias towards events with small energy losstypical energy loss: �E ⇠ ↵̄

2

!c, rather than average: h�Ei ⇠ ↵̄!c


MC: preliminary results


MC: preliminary results (2)

Focus on 2 observables:

RAA: jet yield in AA

normalized to pp

ratio of FFs in AA and pp

Various choices for q̂, L and ↵s,med


MC: preliminary results (3)

“No quenching”: just VLEs

no energy loss: RAA = 1

suppression in FF at small ⇠

“No decoherence”: strict angular ordering(including first “outside” emission)

no effect on energy loss (RAA)

little enhancement at small ⇠

“Quenching before VLEs”: no VLEsinside the medium

RAA larger & increasing with pT,jet

Partons created inside the medium via medium-induced emissionssignificantly contribute to the soft radiation outside the medium


Conclusions & perspectives

Vacuum-like emissions inside the medium can be factorized from themedium-induced radiation via systematic approximations in pQCD

Medium effects enter already at leading-twist level :

reduction in the phase-space for VLEs inside the medium

violation of angular ordering by the first emission outside the medium

Angular ordering is preserved for VLEs inside the medium, like in the vacuum

Qualitative agreement with the LHC data for jet fragmentation

VLEs inside the medium act as sources for medium-induced radiation

DLA: fine for multiplicity, but not for energy flow

Probabilistic picture, well suited for Monte-Carlo implementations


Jet evolution in a dense QCD medium Edmond Iancu IPhT ...INT Program 18-3, Seattle, Nov 2018 Jet...

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