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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)
CCNU Symposium 2019Y. Mehtar-Tani 4
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
CCNU Symposium 2019Y. Mehtar-Tani 5
Jet quenching
use jets to probe the “QGP”
but perhaps first…
use the QGP to investigate medium modification of jets
CCNU Symposium 2019Y. Mehtar-Tani 6
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)
CCNU Symposium 2019Y. Mehtar-Tani 7
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)
CCNU Symposium 2019Y. Mehtar-Tani 8
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
CCNU Symposium 2019Y. Mehtar-Tani 9
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
Relating to parton energy lossRAA
CCNU Symposium 2019Y. Mehtar-Tani 10
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)
Relating to parton energy lossRAA
The quenching weight
CCNU Symposium 2019Y. Mehtar-Tani 11
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
� 1<latexit sha1_base64="gRw3McCyOOhIqYHkwkwcjmT40vY=">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</latexit><latexit sha1_base64="gRw3McCyOOhIqYHkwkwcjmT40vY=">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</latexit><latexit sha1_base64="gRw3McCyOOhIqYHkwkwcjmT40vY=">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</latexit><latexit sha1_base64="gRw3McCyOOhIqYHkwkwcjmT40vY=">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</latexit>
CCNU Symposium 2019Y. Mehtar-Tani 12
Parton energy loss at NLO
• 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⊥
CCNU Symposium 2019Y. Mehtar-Tani 13
Parton energy loss at NLO
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)
CCNU Symposium 2019Y. Mehtar-Tani 14
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
CCNU Symposium 2019Y. Mehtar-Tani 15
• 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
tf = L In-medium: naive estimate
12
log2 pT R2L
MT, Tywoniuk 1706.06047, 1707.07361 Caucal, Iancu, Mueller, Soyez 1801.09703
Phase-space analysis (Lund diagram)
CCNU Symposium 2019Y. Mehtar-Tani 16
• 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
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
Phase-space analysis (Lund diagram)
CCNU Symposium 2019Y. Mehtar-Tani 17
• 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
Phase-space analysis (Lund diagram)
CCNU Symposium 2019Y. Mehtar-Tani 18
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)
CCNU Symposium 2019Y. Mehtar-Tani 19
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
CCNU Symposium 2019Y. Mehtar-Tani 20
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
CCNU Symposium 2019Y. Mehtar-Tani 21
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
CCNU Symposium 2019Y. Mehtar-Tani 22
• 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
CCNU Symposium 2019Y. Mehtar-Tani 23
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
CCNU Symposium 2019Y. Mehtar-Tani 24
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
CCNU Symposium 2019Y. Mehtar-Tani 25
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