Jet Structure in Heavy Ion Collisions

Yacine Mehtar-TaniINT, University of Washington

June 26, 2015JET Symposium, McGill University, Montréal

2

a Jet is an energetic and collimated bunch of particles produced in a high-energy collision

e!

e+

*

q

q_

e!

e+

*

2Q = s

LEP (OPAL)

events

1993

Jets in QCD

3

• Jets originate from energetic partons that successively branch (similarly to an accelerated electron that radiates photons)

• Elementary branching process is enhanced in the collinear region ⟹ Collimated jets

𝜃 ≪ 1 dP ⇠ ↵s CRd✓

✓

d!

!

!

E

branching prob.

Jets substructure in vacuum

hadronspartons

Q0 ⇠ ⇤QCD

4

The jet is a coherent object, successive branchings are ordered from larger to smaller angles

Jet transverse mass

Q ⌘ E ✓jet

𝜃1 > 𝜃2 > … > 𝜃n

𝜃1

𝜃2

𝜃3

(coherence leads to destructive interferences between radiations at large angles)

Jets substructure in vacuum[Bassetto, Ciafaloni, Marchesini, Mueller, Dokshitzer, Khoze, Troyan,…80']

5

Jets in Heavy Ion collisions

6

• Experimental jet definition depends on experimental procedure: jet reconstruction algorithm, background subtraction, unfolding, etc. But to what extend?

• Theory of jets in the QGP: 2 types of interfering parton showers: vacuum and medium-induced. Multi-scale problem.

• Q: is relevant physics under control? Monte Carlo Event-Generators are available or under construction: MARTINI, JEWEL, Q-PYTHIA, PYQUEN/HYDJET, YAJEM, MATTER

Jets in HIC are more involved than in vacuum

Medium-induced QCD cascade and angular broadening

7

𝜔 and 𝛳

E

8

[Baier, Dokshitzer, Mueller, Peigné, Schiff (1995-2000) Zakharov (1996)] Gyulassy, Levai, Vitev (2000) Arnold, Moore, Yaffe (2002)

Medium-induced radiation

• Radiation triggered by multiple scatterings, related to momentum broadening:

tf =�

k2�

�

��

q̂formation time

Coherent radiation

�k2�� = q̂ tf

9

• Landau-Pomeranchuk-Migdal suppression

�dN

d�� L

t�(�)

• Characteristic time scale: effective inelastic mean free path

t�(�) �1

�stf(�)

• Multiple (independent) branching regime:

�dN

d�= �s

L

tf� �sNeff

tf � t� � L

• Maximum suppression when or tf > L � > �c = q̂L2

• Minimum angle � > �c � 1/�

q̂L3

Medium-induced radiation

Evolution of the gluon distribution

𝜔𝜔

10

𝜔/zGain

@

@tD(!, ✓) =

Z 1

0dzK(z)

D(!/z, ✓)

t⇤(!/z)� D(!, ✓)

t⇤(!)

�� q̂

!2r2

✓ D(!, ✓)

𝜔/zLoss Diffusion btw 2 branchings

t⇤(!) =1

↵s

r!

q̂K(z) ⇠ 1

z3/2(1� z)3/2

Splitting kernel Inelastic mean-free-path

Energy loss: Baier, Mueller, Schiff, Son [2001], Moore, Jeon [2003] Energy recovery: Blaizot, Dominguez, Iancu, MT [2013]

D(�, �) � �dN

d�d�2

• Coll. branching approx: Momentum broadening during the branching process is suppressed

tf � t� � k2f � k2

�

11

Broadening due to branchings logarithmically enhanced

Wu (2011) Mueller, Liou, Wu (2013) Blaizot, Iancu, Dominguez, MT (2013)

Blaizot, MT (2014)

@

@tD(!, ✓) =

Z 1

0dzK(z, q̂)

D(!/z, ✓)

t⇤(!/z)� D(!, ✓)

t⇤(!)

�� q̂

!2r2

✓ D(!, ✓)

q̂ ⌘ q̂0

✓1 +

2↵sNc

⇡ln2

k2?m2

D

◆

This large correction can be fully absorbed in a renormalization of the quenching parameter

Evolution of the gluon distribution• Coll. branching approx: Momentum broadening

during the branching process is suppressed tf � t� � k2

f � k2�

As a consequence to the renormalization of the quenching parameter, the DL’s not only enhance the pt-broadening but also the radiative energy loss expectation:

For large media (asymptotic behavior)

12

Universality of the double logs

�E ⇠ L3

To be compared to N=4 SYM (strong-coupling) estimate

�E / L2+� � =

r4↵sNc

⇡

anomalous dimension

[Gubser et al, Hatta et al, Chesler, Yaffe (2008)]

hk2?i / L1+�

13

Energy flow and wave turbulence

0.001 0.01 0.1 1

x0.0001

0.001

0.01

0.1

1

10

100

1000

D(x

,t)

t=0.01 t=0.5 t=1 t=1 1.5

Energy Flow

• Scaling solution in the soft sector

• Constant flow of energy down to the medium temperature scale

• Parametrically large angle with

� � T

E�jet

1

�2s

�c

D(�) � 1/�

�

�E � �s � �2s�c

�/E

Gluon distribution as function of time

� < �s � E

k2�� � q̂t���(�) � k��

�>

1

�2s

�c � �jet

Angular distribution

14

I — Leading particle 𝜔 ~ E

III — Multiple branching regime 𝜔 ≪ 𝜔s ≪ E

II — Rare BDMPS radiation: 𝜔s ≪ 𝜔 ≪ 𝜔c < E

𝜔

E

15

✓c

I — Leading particle 𝜔 ~ E

D(!, ✓) ⇠ D(!)P(✓,!) ⇠ !�(! � E)P(✓,!)

P(✓,!) ⌘ 4⇡

h✓i2 e�✓2/h✓i2• Broadening Probability

• Not sensitive to gluon radiation (or only via the renormalized quenching parameter)

The deflection of the jet is negligible!

1

↵2s

✓c

h✓i2 ⌘ q̂L

E2(⇠ 0.001)

16

✓c

II — Rare BDMPS radiation: 𝜔s ≪ 𝜔 ≪ 𝜔c < E

Single gluon radiation O(𝛼s). The broadening is determined by the diffusion of the radiated gluon

The typical angular broadening reads (the factor 1/2 comes from the time integral)

1

↵2s

✓c

D(!, ✓) ' ↵s

Z L

0dt P(✓,!, L� t)

rq̂

!

��2� � �k2��

�2=

q̂L

2�2> �2

c

17

✓c

Multiple branching + multiple scatterings

1

↵2s

✓c

III — Multiple branching regime 𝜔 ≪ 𝜔s ≪ E

Soft gluon cascades take place at parametrically large angle

✓ � 1

↵2s

✓c � ✓c

18

where ✓2⇤(!) =1

↵s

✓q̂

!

◆1/2

D(!, ✓) = D(!) ⌘(✓2/✓2⇤(!))

0.0 0.5 1.0 1.5 2.0 2.5 3.00.0

0.1

0.2

0.3

0.4

0.5

pz

angulardistribution

pz ⌘

exp

(z)

pz ⌘(z)

pz ⌘fit(z)

⌘(z) =

Z 1

0d� J0(2

pz�)

1X

n=0

(�1)n cn �2n

The normalized angular distribution (at all orders in opacity expansion)

z = ✓2/✓2⇤

III — Multiple branching regime 𝜔 ≪ 𝜔s ≪ EThe solution can be written in the factorized form

19

Partial decoherence of intrajet structure

20

• Consider two subsequent splittings

dP2 ⇠ ↵sd✓

✓

d!

!⇥(✓1 � ✓)

• Color coherence yields the angular ordering constraint on the second branching

✓1

✓

Partial decoherence of intrajet structure

21

✓1

✓

dP2 ⇠ ↵sd✓

✓

d!

![⇥(✓1 � ✓) +�med ⇥(✓ � ✓1)]

• The interaction with the medium alters angular ordering

�med ! 1�med ! 0coherence: decoherence:

decoherence parameter:

�med ⌘ 1� e�q̂L r2?/12

• Consider two subsequent splittings

r? ⇠ ✓1L

[MT, Salgado, Tywoniuk (2010-2011) Iancu, Casalderray-Solana (2011) ]

Partial decoherence of intrajet structure

22

How to treat Interferences between Vacuum and in-medium shower?

A multi-scale problem

Q ⌘ ✓jet E

Qmed ⌘ (q̂L)1/2

r�1? ⌘ (✓jetL)

�1

Q0 ⇠ ⇤QCD

Jet mass

pt-broadeding

Jet size

𝜃jet

QGP

0 L

r

Q-1med

𝜃jet

Transparency limit: Jets as coherent objets Q � r�1

? � Qmed � Q0

23

The medium interacts mostly with the total charge (original parton)

x

dN

dx⌘ D

coh(x) ⌘Z

1

x

dz

z

D

vac

(x/z,Q)Dmed

(z, p?)

In-cone parton dist: Convolution of in-medium and vacuum evolution

x =E

parton

E

Q ⌘ p? ⇥jet

Corrections due to partial decoherence of vacuum radiation ~ r2

Dtot ⌘ Dcoh +�Ddecoh

Theory vs. data

(I) Missing pT in asymmetric dijet events (II) Medium-modified Fragmentation Function

24

[MT, Tywoniuk, PLB744 (2015) Blaizot, MT, Torres, PRL114 (2015)]

25

• Selection of dijet events with large energy Imbalance pT1>120 GeV and pT2>50 GeV

E flow

CMS: energy is lost in soft particles at large angles

pT1pT2

pT1

pT2

( I ) Missing pT in dijet events

0.2 0.4 0.6 0.8 1Θ

-40

-30

-20

-10

0

Dije

t ene

rgy

imba

lanc

e (G

eV)

26

CMS DATAMomentum imbalance

Leading jet: L1= 1 fm, Subleading jet: L2= 5 fm,

IR-cutoff (200 - 800 MeV)

no-IR-cutoff

Cumulative Energy

with E = 120 GeV , q̂= 2 GeV2/fm, 𝛼s=0.3

( I ) Missing pT in dijet events

l = � lnx

• vacuum baseline (blue) • medium-induced energy loss

at large angles depletes energy inside the cone. responsible for dip in the ratio

• small angle soft radiation due to decoherence of vacuum radiation: possibly responsible for enhancement at large l = shift of humpbacked plateau!

27

0

1

2

3

4

5

dN

/

dℓ

0.5

1

1.5

2

0 1 2 3 4 5

Ratio

ℓ

CohCoh + Decoh

VacuumCMS Prelim.: medium, 0-10%

CMS Prelim.: vacuum

CohCoh + Decoh

CMS Preliminary, 0-10%

( II ) Fragmentation Functions

Nota: the different suppression of quark and gluon jets does not explain the soft enhancement [M. Spousta, B. Cole (2015)]

Dtot ⌘ Dcoh +�Ddecoh

28

• Jets in HIC are composed of a coherent inner core and large angle decoherent gluon cascades that are characterized by a constant energy flow from large to low momenta down to the QCD scale where energy is dissipated. Geometrical separation: The cascade develop at parametrically large angles away from the jet axis.

• Excess of soft particles within the jet cone might be a signature of color decoherence.

• Comparison with data: consistent picture, but need a Complete Monte Carlo Event Generator (to deal with experimental biases) and a realistic treatment of the geometry of the collision, particle content, hadronization, etc, for quantitative studies.

Summary and outlook

29

• Jet ~ parton produced in a hard process at high energy: large separation between short and large distance physics: pT ≫ Λ QCD (QCD-factorization)

• Experimentally jets are reconstructed by clustering particles, whose total energy is pt, within a given cone of size R. An approximate way of reversing the process of fragmentation and compare to theory

R pT

Jets in QCD

0

1

2

3

4

5

6

7

8

9

0 1 2 3 4 5 6

dN/dl

l

OPAL data, Q = 90 GeVALEPH data, Q = 130 GeV • Perturbative QCD prediction for

the distribution of hadrons in a jet • 2 scales: non-perturbative scale

Q0 = ΛQCD and the jet transverse scale = E 𝜃jet

• Angular Ordering (AO) ⇒ soft gluon emissions (large l ~ small x) are suppressed

30

[Dokshitzer, Khoze, Mueller, Troyan, Kuraev, Fong, Webber…80']

Fragmentation Function

l ⌘ ln1

x

x ⌘ Eh/Ejet

D(x) = x

dN

dx

Jets substructure in vacuum

q̂0 q̂1 q̂n

..

31

Renormalization Group Equation for the quenching parameter

First 𝛼s correction enhanced by a double log (DL) is resummed with strong ordering in formation time (or energy) and transverse mom. of overlapping successive gluon emissions

⌧0 ⇠ 1/T ⌧ L⌧0 ⌧ ⌧1 ⌧ L

⌧0 ⌧ ⌧1 ⌧ ... ⌧ ⌧n ⌧ L

@q̂(⌧, Q2)

@ ln(⌧/⌧0)=

Z Q2

q̂⌧↵̄(q)

dq2

q2q̂(⌧, q2) q̂(⌧0) ⌘ q̂0with initial

condition

32

The evolution equation may be solved in Fourier space (rT ~ uT/𝜔 ~ transverse dipole size)

D(!,u) ⌘Z

d2✓D(!,✓) e�iu·✓

Opacity Expansion: (order by order in elastic scatterings but all order in branchings)

D(!,u) =1X

n=0

Dn(!,u) ,

III — Multiple branching regime 𝜔 ≪ 𝜔s ≪ E

33

The general term reads

Dn(!,u) = cn [�(!,u) t⇤(!)]n D(!)

where the coefficients cn are solved recursively

dipole cross-section

Why t∗(𝜔) and not L? a gluon 𝜔 can not survive in the medium longer than t∗(𝜔) therefore, to be measured it must be produced close to the surface within the shell L - t∗(𝜔)

III — Multiple branching regime 𝜔 ≪ 𝜔s ≪ E

cn =n�

m=1

2��

�( 3m2 )

�( 3m+12 )

( I ) Nuclear Modification Factor

L = 2 - 3 fm q̂ = 2.5 - 6 GeV2/fm

RAA = dNAA / ( dNpp x Ncoll )

Solving the evolution equation for D convolved with an initial power spectrum p�n

?

0

0.2

0.4

0.6

0.8

1

1.2

50 100 150 200 250 300 350 400

Rjet

AA

p⊥ [GeV]

ωc = 60-100 GeV, ωBH = 1.5 GeV

ωc = 80 GeV, ωBH = 0.5-2.5 GeV

CMS Prelim.

34

dNAAjet

d2p?⌘ N

coll

Z1

0

dx

x

D

med

(x, p?/x)dNpp

jet

d2p?(p?/x)