in honor of jean-paul blaizot larry mclerran miklos gyulassy

In honor of

Jean-Paul Blaizot

Miklos Gyulassy

Larry McLerran

for their outstanding careers and their major contributions to the field of heavy ion collisions

Jet evolution in QCD media

Yacine Mehtar-Tani (BNL)

Symposium on Contemporary QCD Physics and Relativistic Nuclear Collisions @ CCNU, Wuhan, China October 10-11, 2019

In preparationIn collaboration with Konrad Tywoniuk

CCNU Symposium 2019Y. Mehtar-Tani 3

The world before Quark Matter 2019

• Model calculations and Monte Carlo event generators provides a quantitative description of jet observables, in particular, the nuclear modification factor

arXiv:1902.05934

RjetAA =

1Ncoll

NAA(pT)Npp(pT)


The world after Quark Matter 2019

• 16 Monte Carlo and model predictions for QM 2019: Models tuned at lower ( ) span the whole range form 0 to 1 at high and large

pT 100 − 300 GeV RAApT R


Jet quenching

use jets to probe the “QGP”

but perhaps first…

use the QGP to investigate medium modification of jets


Jet quenching, a rich problem

Non-equilibrium dynamics of QCD: thermalization, transport, wave turbulence, etc

Jets in HIC: jets are coherent and extended quantum systems in contact with a reservoir

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A

B

BA

J.P. Blaizot, E. Iancu, Y.MT PRL 111 (2013) J.P. Blaizot, Y. MT, M. Torrres PRL 114 (2015)


Jet quenching, a rich problem

Liu, Mueller, Wu (2013), Blaizot, Dominguez, Iancu, MT(2014) Iancu (2014)

Quantum corrections to energy loss and pt-broadening

Nucl. Phys. A929 (2014)


Relating to parton energy lossRAA

P (✏) ⇡ �(✏) +

Zd!

dI

d!

⇣�(✏� !)� �(✏)

⌘

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• A highly energetic parton passing through the QGP lose energy via multiple soft gluon radiation

• Energy loss prob.

dI

d!= ↵

r!c

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for

for

BDMPS-Z

GLV

ϵ =n

∑i

ωi

pT

Baier, Dokshitzer, Mueller, Peigné, Schiff (1996); Zakharov (1996)

Gyulassy, Levai, Vitev (2001)

ωc ∼ qL2


dσdpT

pT

pp

AA

pT + ϵpT

dσdpT

= ∫ dϵ P(ϵ)dσdpT

(pT + ϵ)

RAA

∼ ( pT

pT + ϵ )n

≈ e−ϵn/pT

Steeply falling spectrum (large approximation) em the effect of energy loss

n

The jet spectrum in AA corresponds to the pp spectrum shifted to lower pT by a small amount ϵ

Typical energy loss

ωs ∼ α2s qL2 ( ∼ 10 GeV)

n ∼ 5 − 8



10 100 10000

0.2

0.4

0.6

0.8

1

1.2

Q(pT) = ∫ dϵ P(ϵ) e−nϵ/pT

• Strong suppression of partons with

RAA

≈ Q(pT)

ωs ≪ nωs < pT• Large separation of scales:

pT ≪ nωs

• Generalization to particles in the final stateN σ(N) ∼ QN(pT)

Baier, Dokshitzer, Mueller, Schiff (2001); Salgado, Wiedemann (2003)


The quenching weight


Parton energy loss at NLO

• Building block for vacuum jet shower: leading order splitting function

• Large phase-space for multiple branching (require resummations of large soft or collinear logarithms)

θ

z

1 − z

↵s Pqq(z)d✓

✓dz

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Prob =↵

2log2

pTR

⇤QCD

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• Consider the decay of highly virtual quark in a QCD plasma

• QFT tells us the interactions are not point-like in general

t0 ∼ 1/pT

• The plasma introduces a new time scale

tf = ω/k2⊥



tf = ω/k2⊥

t0 ∼ 1/pT

• The plasma generates a new time scale: the decoherence time r⊥ ∼ θ t

k−1⊥ ∼ ( qt)−1/2

tdecoh ≡ ( qθ2)−1/3

• The offspring quark and gluon lose energy independently only after tdecoh

tdecoh

θ

MT, Salgado, Tywoniuk PRL (2010), PLB (2012), Casalderrey, Iancu JHEP (2011)


Phase-space analysis (Lund diagram)

• How is the leading logarithmic phase-space structure of vacuum modified in the presence of the plasma?

ln ω

ln1θ

ln pT

k⊥ = ΛQCD

ln1R

PS =12

log2 pT RΛ

QCDPS ≡ Area

MT, Tywoniuk 1706.06047, 1707.07361 Caucal, Iancu, Mueller, Soyez 1801.09703



ln ω

ln1θ

ln pT

k⊥ = ΛQCD

ln1R

tf = L In-medium: naive estimate

12

log2 pT R2L

MT, Tywoniuk 1706.06047, 1707.07361 Caucal, Iancu, Mueller, Soyez 1801.09703




ln ω

ln1θ

ln pT

k⊥ = ΛQCD

ln1R

In-medium: naive estimate

12

log2 pT R2L

tf = L

In-medium phase-space

2 logpT

ωclog

Rθc

+43

log2 Rθc

ln1θc MT, Tywoniuk 1706.06047, 1707.07361

Caucal, Iancu, Mueller, Soyez 1801.09703



• The modeling of phase space affects the leading logarithmic structure of jet evolution in the medium

logpT

ωc

θc =1

qL3

≪

• The jet loses energy as a single color charges when θc > R

logRθc

log2 pT R2L

• The plasma does not resolve individual color charges but sees effective charges of size θc



Back to vacuum: DGLAP evolution

• DGLAP evolution equation for inclusive jet spectrum • Resummation of large • Suppression of small radii compare to large jets

log RR

dfa(z,R)

d logR=

Z 1

0dz0 Pab(z

0) fa(z/z0, R)

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pT

z pT

R

Dasgupta, Dreyer, Salam, Soyez (2014-2016) Kang, Ringer, Vitev (2016)


Nonlinear evolution of quenching weights

• The quenching weights, the suppression of a high pT parton obeys a nonlinear evolution dynamics

dQa(pT , ✓)

d log ✓=

Z 1

0dz Pab(z) [Qb(zpT , ✓)Qc((1� z)pT , ✓)�Qa(pT , ✓)] ⇥in

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pT

1 − z

z

• A gluon and a quark lose more energy than a single quark


Nonlinear evolution of quenching weights

• Solution of the linearized equation:

Qa(pT, θ) ≃ Qpartona (pT)

Q(pT , R) ' Q(0)(pT )

⇥ exp

�2↵

✓log

pT!c

logR

✓c+

2

3log2

R

✓c

◆(1�Q(0)(pT ))

�

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10 100 10000

0.2

0.4

0.6

0.8

1

1.2

Qq(

p T,θ

)

pT

• Initial condition: quark quenching weight

The effect of quenching of multiple color charges reduces the RAA


Medium-modified DGLAP evolution

• DGLAP evolution equation for inclusive jet spectrum • Resummation of large log R

pT

z pT

R

θ

fjet,a(z, pT , ✓) = Qa(pT , R) �(1� z) +

Z ✓

R

d✓0

✓0

Z 1

0dz0 Pab(z

0)⇥in

⇥hQb((1� z0)pT , ✓

0)1

z0fjet,c(z/z

0, pT , ✓0)� fjet,a(z, pT , ✓

0)i

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Z 1

0dz z fjet,a(z, pT , ✓) = Qa(pT , ✓)

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Normalization of micro-jets distribution

Reflects the fact that energy is not conserved


• The jet spectrum reads

dσdpT

= ∫1

0

dzz

f(z, pT)dσdpT

(pT /z) ≈ ⟨zn−1⟩dσdpT

• In vacuum the solution is

⟨zn−1⟩ ≈ eα γqq(n) log R

⟨zn−1⟩ ≈ Qq(pT) eα γqq(n) Qq(pT) log R −2α (1−Qq(pT)) log pTωc log 1

θc

γqq(n) = ∫1

0dz

1 − zn−1

1 − z∼ log n

• In medium quenching effects suppress the jet spectrum

where

Understanding what drives jet RAA

• Accounts for jet substructure fluctuations to all orders in LLA


Understanding what drives jet RAA

RAA ≈ Qq(pT, R)

× exp α (1 − Qq(pT, R))(−γqq(n) log R −2α logpT

ωclog

1θc )

• Slower dependence in AA than pp • Suppression driven by the large phase space for in-medium

splitting • Mild dependence when

R

R Qq(pT, R) ∼ 1

10 100 10000

0.2

0.4

0.6

0.8

1

1.2

Qq


Theory to data comparison

• Orange curves: our predictions from medium-modified DGLAP

• as function of the jet cone size and pTRAA

MT, Tywoniuk (in preparation)

Talk by M. Taylor at QM 2019


Quality control

A. Parametric estimates B. Solvable toy models C. Numerical calculations

In order to reach a satisfactory understanding of complex physics problems

Many thanks to Jean-Paul, Miklos and Larry for your guidance and for inspiring

all of us in “trying to understand” the glue that binds us all

…and look forward to many more years of fruitful collaboration and discussions

in honor of jean-paul blaizot larry mclerran miklos gyulassy

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