Path length dependence of jet quenching
(and quite a bit more)
Redmer Alexander Bertens
33rd Winter Workshop on Nuclear Dynamics
Redmer Alexander Bertens - January 11, 2017 - slide 1 of 27
Path length dependence of jet quenching
Jet quenching - what and why?
Tomography
‘imaging through modification of penetrating wave’
Redmer Alexander Bertens - January 11, 2017 - slide 2 of 27
Path length dependence of jet quenching
Jet quenching - what and why?
Tomography
‘imaging through modification of penetrating wave’
‘Motivation’ for jets in heavy-ion collisions is similar
How do you study the non-perturbative QGP ?
Use well-known (perturbative) probe (i.e. large Q 2 process)
Deduce medium properties from modification of the probe by the medium
nPDF j
hard scattering
QCD branching
hadronization
h1
=
⊗
⊗
⊗
⊗
h2
h3
Redmer Alexander Bertens - January 11, 2017 - slide 2 of 27
Path length dependence of jet quenching
jet reconstruction
nPDF i
Outline
... so when we talk about jets in heavy ions, we talk about ...
1 Understand interactions between the hard partons (quarks, gluons) and the QGP
(‘microscopic’)
2 Use this to deduce properties of the QGP (degrees of freedom, viscosity, density,
temperature, etc, ‘macroscopic’)
Redmer Alexander Bertens - January 11, 2017 - slide 3 of 27
Path length dependence of jet quenching
Outline
... so when we talk about jets in heavy ions, we talk about ...
1 Understand interactions between the hard partons (quarks, gluons) and the QGP
(‘microscopic’)
2 Use this to deduce properties of the QGP (degrees of freedom, viscosity, density,
temperature, etc, ‘macroscopic’)
A few questions for this morning
How-to: experimentally constrain QGP properties?
Which mechanisms contribute to parton energy loss, and
how can we model them?
What drives energy loss? Geometry or fluctuations?
Redmer Alexander Bertens - January 11, 2017 - slide 3 of 27
Path length dependence of jet quenching
Outline
... so when we talk about jets in heavy ions, we talk about ...
1 Understand interactions between the hard partons (quarks, gluons) and the QGP
(‘microscopic’)
2 Use this to deduce properties of the QGP (degrees of freedom, viscosity, density,
temperature, etc, ‘macroscopic’)
A few questions for this morning
How-to: experimentally constrain QGP properties?
Which mechanisms contribute to parton energy loss, and
how can we model them?
What drives energy loss? Geometry or fluctuations?
but let’s start with single tracks - to get a feeling of what we’re talking about
Redmer Alexander Bertens - January 11, 2017 - slide 3 of 27
Path length dependence of jet quenching
Chapter 1) RAA
‘nuclear modification factor’
of single tracks
.
.
and a few words on modeling
Nuclear modification factor RAA
‘Simplest’ probe: (high-pT ) particle production in vacuum vs. in medium
RAA =
d 2 N AA /dpT dη
QCD medium
≈
hTAA i· d 2 σpp /dpT dη
QCD vacuum
hTAA i ∝ hNcoll i = no. of binary nucleon-nucleon collisions
Possible scenarios
RAA > 1 (enhancement)
RAA = 1 (no medium effect)
RAA < 1 (suppression)
Assumption ...
... partons lose energy in the medium
RAA < 1
Redmer Alexander Bertens - January 11, 2017 - slide 5 of 27
Path length dependence of jet quenching
ALICE, Pb-Pb, sNN = 2.76 TeV
charged particles, |η|<0.8
1018
RAA
1022
1
norm. uncertainty
T
1/Nevt 1/(2π p ) (d2Nch) / (dη dp ) (GeV/c)-2
‘Convenient’ to measure ...
1012
RAA
T
10-1
106
1
70-80%
60-70%
50-60%
ALICE
Pb-Pb, sNN=2.76 TeV
charged particles, |η|<0.8
40-50%
30-40%
20-30%
1
10-1
16
10-12
10
50-60% (x10 )
8
60-70% (x102)
6
70-80%
0-5% (x10 )
20-30% (x10 )
5-10% (x1014)
30-40% (x10 )
10-20% (x1012)
40-50% (x10 )
pp reference (scaled by <T
AA
RAA
10-6
4
1
>)
1
10
Phys.Lett. B720 (2013) 52-62
... from spectra to RAA ...
p (GeV/c)
T
10-1
5-10%
10-20%
0
20
40
0
pT (GeV/c)
0-5%
20
40
0
pT (GeV/c)
Phys.Lett. B720 (2013) 52-62
Redmer Alexander Bertens - January 11, 2017 - slide 6 of 27
Path length dependence of jet quenching
20
40
pT (GeV/c)
RAA
... and qualitatively understand
1
More central collisions
longer average path length
denser medium
−→ stronger suppression
RAA
10-1
1
10-1
70-80%
60-70%
50-60%
ALICE
Pb-Pb, sNN=2.76 TeV
charged particles, |η|<0.8
40-50%
30-40%
20-30%
RAA
Suppression depends on centrality:
stronger for more central collisions
Strongest suppression around
7 GeV/c for all centralities
Suppression non-zero up to
high transverse momenta
norm. uncertainty
1
10-1
5-10%
10-20%
0
20
40
0
pT (GeV/c)
0-5%
20
40
0
pT (GeV/c)
Phys.Lett. B720 (2013) 52-62
Redmer Alexander Bertens - January 11, 2017 - slide 7 of 27
Path length dependence of jet quenching
20
40
pT (GeV/c)
RAA - from SPS to RHIC to LHC
Results from LHC and RHIC are
qualitatively similar
RAA < 1 points at energy
loss
Decrease
of RAA with increasing
√
s NN
Indicative of higher medium
density at the LHC compared
to RHIC
Data (and models) suggest
decrease of relative e-loss at high
pT
Prog. Part. Nucl. Phys. 70 (77) 2014
Redmer Alexander Bertens - January 11, 2017 - slide 8 of 27
so the RAA s a nice ‘educational’
tool - but let’s go a bit deeper
Path length dependence of jet quenching
How do parton’s lose energy?
in the ‘classic’ (vs. AdS/CFT) QCD picture energy loss is either
collisional or (induced) radiative
Redmer Alexander Bertens - January 11, 2017 - slide 9 of 27
Path length dependence of jet quenching
How do parton’s lose energy?
in the ‘classic’ (vs. AdS/CFT) QCD picture energy loss is either
collisional or (induced) radiative
both mechanisms have an explicit dependence on the length of the
parton’s tracjectory through the QGP (L, L2 ) and medium density
.
.
LPM interference - if parton and gluon are still in a coherent state
further radiation is suppressed
Redmer Alexander Bertens - January 11, 2017 - slide 9 of 27
Path length dependence of jet quenching
Modeling and the factorization theorem
Constraining QGP properties starts with comparing our data to models
factorization is the basis for all parton energy loss models
dN dN =
⊗
P(∆E )
⊗
D(pT /E )
dpT hadrons
dE jets
| {z }
| {z }
|
{z
}
| {z }
energy loss distribution fragmentation function
final state
pQCD, nPDF’s
or - in words
a parton is created in a hard scattering
it ‘travels’ through the QGP along a trajectory L
along its path it has a probability of scattering and/or radiating gluons
P(∆E ) ‘holds’ medium information (q̂, η/s, T , ...)
Redmer Alexander Bertens - January 11, 2017 - slide 10 of 27
Path length dependence of jet quenching
Modeling and the factorization theorem
Constraining QGP properties starts with comparing our data to models
factorization is the basis for all parton energy loss models
dN dN =
⊗
P(∆E )
⊗
D(pT /E )
dpT hadrons
dE jets
| {z }
| {z }
|
{z
}
| {z }
energy loss distribution fragmentation function
final state
pQCD, nPDF’s
or - in words
a parton is created in a hard scattering
it ‘travels’ through the QGP along a trajectory L
along its path it has a probability of scattering and/or radiating gluons
P(∆E ) ‘holds’ medium information (q̂, η/s, T , ...)
which brings us to the main point of these slides
.
.
to understand the nature of energy loss, experiments must get as close to partons as
possible, constrain the trajectory and measure the shape of the e-loss distribution
Redmer Alexander Bertens - January 11, 2017 - slide 10 of 27
Path length dependence of jet quenching
let’s move a bit closer to partons
.
.
.
Chapter 2) Jets
Jets in heavy-ion collisions in a nutshell
Hard scattering (Q2 > 1 (GeV/c)2 )
Parton travels through the QGP, scattering and
radiation of quarks and gluons
Hadronization into colorless spray: ‘jet’
Reconstructed jet: as close as one can experimentally
get to original parton
‘Removes’ ill-understood hadronization from modeling
Redmer Alexander Bertens - January 11, 2017 - slide 12 of 27
Path length dependence of jet quenching
Jets in heavy-ion collisions in a nutshell
Hard scattering (Q2 > 1 (GeV/c)2 )
Parton travels through the QGP, scattering and
radiation of quarks and gluons
Hadronization into colorless spray: ‘jet’
Reconstructed jet: as close as one can experimentally
get to original parton
‘Removes’ ill-understood hadronization from modeling
Out-of-cone radiation
R AA<1
Incoming
parton
In-cone radiation
Jet broadening
Redmer Alexander Bertens - January 11, 2017 - slide 12 of 27
Energy loss has two distinct effects on jets
Out-of-cone radiation: RAA < 1
In-cone radiation: RAA = 1,
fragmentation function changes
Of course, these are not exclusive ...
Path length dependence of jet quenching
Path-length dependence: di-jet systems
‘so to understand the nature of energy loss, we must get as close to partons as possible,
constrain the trajectory and measure the shape of the e-loss distribution’
Redmer Alexander Bertens - January 11, 2017 - slide 13 of 27
Path length dependence of jet quenching
Path-length dependence: di-jet systems
‘so to understand the nature of energy loss, we must get as close to partons as possible,
constrain the trajectory and measure the shape of the e-loss distribution’
Di-jet system: 2 −→ 2 process
Jets traveling in opposite direction with equal
initial transverse momentum pT1 = pT2
L1 6= L2
∆E1 6= ∆E2
Final state pT is not equal pT1 6= pT2
pT1 − pT2
pT1 + pT2
xj = pT1 /pT2
AJ =
J. Phys. G: Nucl. Part. Phys. 38 (2011) 035006
ET1
14 fm
Some caveats ... in all collision systems pT1 6= pT2
pp: recoil, out-of-cone radiation (vacuum
fluctuations)
AA: energy loss fluctuations, different
path-lengths
ET2<ET1
Redmer Alexander Bertens - January 11, 2017 - slide 13 of 27
Path length
Figure 2. Schematic illustration of the spatial embedding of a dijet e
In a central
collision, the overlap of the lead ions in the p
dependence
of jetPb+Pb
quenching
Di-jet imbalance xj = pT1 /pT2
Asymmetry quantified as
xj = pT1 /pT2
Fully unfolded
Direct comparison to theory
... and (eventually) other
experiments
Redmer Alexander Bertens - January 11, 2017 - slide 14 of 27
Path length dependence of jet quenching
Di-jet imbalance xj = pT1 /pT2
Asymmetry quantified as
xj = pT1 /pT2
Fully unfolded
Direct comparison to theory
... and (eventually) other
experiments
In pp
most probable dijet
configuration: xj ≈ 1
Redmer Alexander Bertens - January 11, 2017 - slide 14 of 27
Path length dependence of jet quenching
Di-jet imbalance xj = pT1 /pT2
Asymmetry quantified as
xj = pT1 /pT2
Fully unfolded
Direct comparison to theory
... and (eventually) other
experiments
In pp
most probable dijet
configuration: xj ≈ 1
In Pb–Pb
most probable configuration:
subleading jet has half as
much energy as leading jet
Strong centrality dependence
Redmer Alexander Bertens - January 11, 2017 - slide 14 of 27
Path length dependence of jet quenching
Di-jet imbalance xj = pT1 /pT2
Asymmetry: xj = pT1 /pT2
With increasing pT −→ xj goes towards 1
Redmer Alexander Bertens - January 11, 2017 - slide 15 of 27
Path length dependence of jet quenching
Di-jet imbalance xj = pT1 /pT2
Asymmetry: xj = pT1 /pT2
With increasing pT −→ xj goes towards 1
Prog. Part. Nucl. Phys. 70 (77) 2014
confirms sl. 6 ‘Relative loss decreases with pT ’
Redmer Alexander Bertens - January 11, 2017 - slide 15 of 27
Path length dependence of jet quenching
Di-jet imbalance xj = pT1 /pT2
In summary
RAA : moderate average energy loss
di-jets: wide variation in possible energy loss
So di-jet asymmetry very nicely illustrates
centrality dependence hints on path length
dependence
e-loss is a distribution
Redmer Alexander Bertens - January 11, 2017 - slide 16 of 27
Path length dependence of jet quenching
Di-jet imbalance xj = pT1 /pT2
In summary
RAA : moderate average energy loss
di-jets: wide variation in possible energy loss
So di-jet asymmetry very nicely illustrates
centrality dependence hints on path length
dependence
e-loss is a distribution
But it doesn’t tell what the balance is between
per-jet energy loss fluctuations? (analogous to
fluctuations in vacuum radiation)
average energy loss from kinematics, medium
compisition and geometry?
Redmer Alexander Bertens - January 11, 2017 - slide 16 of 27
Path length dependence of jet quenching
‘to understand the nature of energy loss, experiments
must get as close to partons as possible, constrain the
trajectory and measure the shape of the e-loss
distribution’
‘to understand the nature of energy loss, experiments
must get as close to partons as possible, constrain the
trajectory and measure the shape of the e-loss
distribution’
.
.
.
so let’s give that a go from both the experimental and
theory side
Experimentally fixing pangth length
event-plane dependence of jet
production
v2ch jet : ‘selecting’ path lengths
v2ch jet : comparing short to long L at fixed
medium density
hLin i ≈ hLout i
v2ch jet
≈ 0?
hLin i < hLout i
v2ch jet > 0?
so this is not hydro flow! the contribution of
vn to v2ch jet has been removed
Redmer Alexander Bertens - January 11, 2017 - slide 19 of 27
Path length dependence of jet quenching
v 2part, v 2jet
v2ch jet in semi-central collisions
0.3
ALICE
ch jet
Pb-Pb sNN = 2.76 TeV
R = 0.2 anti-k T, |η |<0.7
jet
v2
30-50%, Stat unc.
Syst unc. (shape)
Syst unc. (correlated)
calo jet
ATLAS v 2
0.2
30-50%
part
CMS v 2 {|∆η|>3} 30-50%
part
ALICE v 2 {|∆η|>2} 30-50%
0.1
hLin i < hLout i
v2ch jet >?
0
(b)
0
PLB 753 (2016) 511-525
p
50
T, track
> 0.15 GeV/c , p
T, lead
> 3 GeV/ c
100
150
part
jet
p , p (GeV/c )
T
T
Non-zero v2ch jet over full pT range - strong path length dependence
Good agreement between measurements of ALICE, ATLAS, CMS
Redmer Alexander Bertens - January 11, 2017 - slide 20 of 27
Path length dependence of jet quenching
‘Theorically’ fixing path lengths
.
.
.
generate di-jets with L1 = L2
compare to L1 6= L2
Briefly introducing the model: JEWEL
JEWEL (Jet Evolution With Energy Loss)
Radiative energy loss with LPM interference and elastic scatterings (plus
momentum exchange [recoil] with medium)
Glauber initial conditions + PYTHIA hard scatterings
Bjorken expanding medium
Redmer Alexander Bertens - January 11, 2017 - slide 22 of 27
Path length dependence of jet quenching
Briefly introducing the model: JEWEL
JEWEL (Jet Evolution With Energy Loss)
Radiative energy loss with LPM interference and elastic scatterings (plus
momentum exchange [recoil] with medium)
Glauber initial conditions + PYTHIA hard scatterings
Bjorken expanding medium
v 2ch jet
Very succesful in describing RHIC and LHC
ch jet
v2
0.2
ch jet
v2
ALICE
30-50%, JEWEL
30-50%, Stat unc.
Pb-Pb sNN = 2.76 TeV
R = 0.2 anti-k T, |η |<0.7
Syst unc. (shape)
jet
Syst unc. (correlated)
0.1
0
(b)
20
p
30
40
50
T, track
60
> 0.15 GeV/c , p lead > 3 GeV/ c
T
70
80 90 100
ch jet
p
(GeV/c )
T
Redmer Alexander Bertens - January 11, 2017 - slide 22 of 27
Path length dependence of jet quenching
Briefly introducing the model: JEWEL
JEWEL (Jet Evolution With Energy Loss)
Radiative energy loss with LPM interference and elastic scatterings (plus
momentum exchange [recoil] with medium)
Glauber initial conditions + PYTHIA hard scatterings
Bjorken expanding medium
v 2ch jet
Very succesful in describing RHIC and LHC
ch jet
v2
0.2
ch jet
v2
ALICE
30-50%, JEWEL
30-50%, Stat unc.
Pb-Pb sNN = 2.76 TeV
R = 0.2 anti-k T, |η |<0.7
Syst unc. (shape)
jet
Syst unc. (correlated)
0.1
0
(b)
20
p
30
40
50
T, track
60
> 0.15 GeV/c , p lead > 3 GeV/ c
T
70
80 90 100
ch jet
p
(GeV/c )
T
Especially interesting: agreement with CMS
di-jet imbalance
Redmer Alexander Bertens - January 11, 2017 - slide 22 of 27
Path length dependence of jet quenching
Fixing path lengths with JEWEL
‘Origins of the di-jet asymmetry in heavy ion collisions’
(26/12/2015, arXiv:1512.08107)
Study original of imbalance by using random (left) or fixed (right) di-jet production
points - fixed points: both jets ‘see’ same medium distance L
Redmer Alexander Bertens - January 11, 2017 - slide 23 of 27
Path length dependence of jet quenching
Fixing path lengths with JEWEL
(≈ verbatim) from the paper
Path-length difference plays no
significant role in generating di-jet
asymmetry
Increase w.r.t. pp due to fluctuations
in vacuum-like fragmentation and
medium related fluctuations
Amount of energy lost is determined
strongly by ratio of m/pT of original
parton
Redmer Alexander Bertens - January 11, 2017 - slide 24 of 27
Path length dependence of jet quenching
Path lengths dissected
≈ 35% of cases L1 > L2 (density weighted path-length)
Dependence of Aj on ∆Ln small compared to width (strong fluctuations)
Redmer Alexander Bertens - January 11, 2017 - slide 25 of 27
Path length dependence of jet quenching
Path lengths dissected
≈ 35% of cases L1 > L2 (density weighted path-length)
Dependence of Aj on ∆Ln small compared to width (strong fluctuations)
conflict with measurements? experimental answers ?
Redmer Alexander Bertens - January 11, 2017 - slide 25 of 27
Path length dependence of jet quenching
Event-plane dependence of di-jets
Distance traveled by di-jet depends
on orientation w.r.t. ΨEP, 2
hAj i smaller for dij-ets in
direction of ΨEP, 2
Redmer Alexander Bertens - January 11, 2017 - slide 26 of 27
Path length dependence of jet quenching
Event-plane dependence of di-jets
0.292
0.302
0.3
0.29
Centrality (20-30)%
0.28
0.296
0.294
0.292
0.286
0.284
0.275
0.282
0.27
0.29
0.28
cobs
2 =-0.0047± 0.0024
0.288
0
0.285
Centrality (10-20)%
0.288
0.298
〈 AJ 〉
〈 AJ 〉
Distance traveled by di-jet depends
on orientation w.r.t. ΨEP, 2
ATLAS Preliminary
Pb+Pb sNN=2.76 TeV
R=0.2 Centrality (0-10)%
〈 AJ 〉
0.304
0.5
1
1.5
2
2|φlead-Ψ2|
2.5
3
0
cobs
2 =-0.0030± 0.0028
0.5
1
1.5
2
2.5
3
0.265
0
2|φlead-Ψ2|
cobs
2 =-0.0083± 0.0035
0.5
1
1.5
2
2|φlead-Ψ2|
hAj i = A0J 1 + 2c2 cos(2(ϕlead − ΨEP, 2 ))
hAj i smaller for dij-ets in
direction of ΨEP, 2
Reasonably described by
cosine modulation
Anti-correlation is signficant
Redmer Alexander Bertens - January 11, 2017 - slide 26 of 27
Path length dependence of jet quenching
2.5
3
Event-plane dependence of di-jets
0.292
0.302
0.3
0.29
Centrality (20-30)%
0.28
0.296
0.294
0.292
0.286
0.284
0.275
0.282
0.27
0.29
0.28
cobs
2 =-0.0047± 0.0024
0.288
0
0.285
Centrality (10-20)%
0.288
0.298
〈 AJ 〉
〈 AJ 〉
Distance traveled by di-jet depends
on orientation w.r.t. ΨEP, 2
ATLAS Preliminary
Pb+Pb sNN=2.76 TeV
R=0.2 Centrality (0-10)%
〈 AJ 〉
0.304
0.5
1
1.5
2
2.5
3
0
cobs
2 =-0.0030± 0.0028
0.5
2|φlead-Ψ2|
1
1.5
2
2.5
0.265
0
3
2|φlead-Ψ2|
cobs
2 =-0.0083± 0.0035
0.5
1
1.5
2
2.5
3
2|φlead-Ψ2|
hAj i = A0J 1 + 2c2 cos(2(ϕlead − ΨEP, 2 ))
0.02
0.02
R=0.2
〈c2〉=-0.010 ± 0.004
R=0.4
〈c2〉=-0.015 ± 0.005
0
0
0
−0.02
0.02
0.02
0.04
0.04
c2
hAj i smaller for dij-ets in
direction of ΨEP, 2
Reasonably described by
cosine modulation
Anti-correlation is signficant
0.02
R=0.3
〈c2〉=-0.013 ± 0.004
−0.04
ATLAS Preliminary
Pb+Pb sNN=2.76 TeV
20
40
60
80
20
40
60
80
20
40
Centrality [%]
Points at small but significant(?) contribution to asymmetry from geometry
Redmer Alexander Bertens - January 11, 2017 - slide 26 of 27
Path length dependence of jet quenching
60
80
that’s all
.
.
.
How-to: experimentally constrain QGP properties?
Which mechanisms contribute contribute to parton energy
loss, and how can we model them?
What drives energy loss? Geometry or fluctuations?
BACKUP
Jets and parton energy loss
Out-of-cone radiation
R AA<1
Incoming
parton
In-cone radiation
Jet broadening
Two qualitative scenarios
1) Out-of-cone radiation: RAA < 1
2) In-cone radiation: RAA = 1, fragmentation function changes
Of course, these are not exclusive ...
Redmer Alexander Bertens - January 11, 2017 - slide 29 of 27
Path length dependence of jet quenching
Collisional energy loss - an incomplete picture
As a ‘back of the envelope’ thought, ingredients for collisional energy loss
where ω = E initial − E final is transferred one can write
−
dE
=
dz
Redmer Alexander Bertens - January 11, 2017 - slide 30 of 27
Path length dependence of jet quenching
Collisional energy loss - an incomplete picture
As a ‘back of the envelope’ thought, ingredients for collisional energy loss
where ω = E initial − E final is transferred one can write
X Z
dE
−
=
d 3k
dz
p=q,g
|
{z
}
sum over states
Redmer Alexander Bertens - January 11, 2017 - slide 30 of 27
Path length dependence of jet quenching
Collisional energy loss - an incomplete picture
As a ‘back of the envelope’ thought, ingredients for collisional energy loss
where ω = E initial − E final is transferred one can write
plasma density
X Z
dE
−
=
d 3k
dz
p=q,g
|
{z
}
z }| {
ρp (k)
sum over states
Redmer Alexander Bertens - January 11, 2017 - slide 30 of 27
Path length dependence of jet quenching
Collisional energy loss - an incomplete picture
As a ‘back of the envelope’ thought, ingredients for collisional energy loss
where ω = E initial − E final is transferred one can write
plasma density
X Z
dE
−
=
d 3k
dz
p=q,g
|
{z
}
z }| {
ρp (k)
flux
Z
z}|{
dq J
2
sum over states
Redmer Alexander Bertens - January 11, 2017 - slide 30 of 27
Path length dependence of jet quenching
Collisional energy loss - an incomplete picture
As a ‘back of the envelope’ thought, ingredients for collisional energy loss
where ω = E initial − E final is transferred one can write
plasma density
X Z
dE
−
=
d 3k
dz
p=q,g
|
{z
}
z }| {
ρp (k)
sum over states
Redmer Alexander Bertens - January 11, 2017 - slide 30 of 27
flux
Z
z}|{ dσ Qp→Qp
dq J ω
dq 2
| {z }
2
cross section
Path length dependence of jet quenching
Collisional energy loss - an incomplete picture
As a ‘back of the envelope’ thought, ingredients for collisional energy loss
where ω = E initial − E final is transferred one can write
plasma density
X Z
dE
−
=
d 3k
dz
p=q,g
|
{z
}
z }| {
ρp (k)
sum over states
flux
Z
z}|{ dσ Qp→Qp
dq J ω
dq 2
| {z }
2
cross section
with a lot of trickery that we’ll skip this can be integrated
2 X Z d 3k
qmax
dE
2
Cp
−
= παs
ρp (k) ln
2
dz
k
qmin
p
4παs2 T 2
Nf
cE
'
1+
ln
3
6
αs T
Redmer Alexander Bertens - January 11, 2017 - slide 30 of 27
Path length dependence of jet quenching
Radiative energy loss - an incompleter picture
The energy loss for radiative processes is directly connected to the energy
of the radiated gluon ω
Z
d2 I
h∆E i = dωdz ω
dωdz
Redmer Alexander Bertens - January 11, 2017 - slide 31 of 27
Path length dependence of jet quenching
Radiative energy loss - an incompleter picture
The energy loss for radiative processes is directly connected to the energy
of the radiated gluon ω
Z
d2 I
h∆E i = dωdz ω
dωdz
The difficulty enters here: gluons have a finite formation time during
which the parton and gluon are still a coherent object
τf '
Redmer Alexander Bertens - January 11, 2017 - slide 31 of 27
ω
2
k⊥
Path length dependence of jet quenching
Radiative energy loss - an incompleter picture
The energy loss for radiative processes is directly connected to the energy
of the radiated gluon ω
Z
d2 I
h∆E i = dωdz ω
dωdz
The difficulty enters here: gluons have a finite formation time during
which the parton and gluon are still a coherent object
τf '
ω
2
k⊥
if parton and gluon are still in a coherent state further radiation is
suppressed - this effect is known as LPM interference
Redmer Alexander Bertens - January 11, 2017 - slide 31 of 27
Path length dependence of jet quenching
LPM interference in radiative processes
Because of the finite τf the gluon spectrum has three distinct regimes
depending on mean free path λ and screening mass µ
 α
s

ω < ωBH


λ

r

2
d I
αs λµ2
ω
'
ωBH < ω < ωfact

dωdz
ω

 αλs


ωfact < ω < E
L
1
Low gluon energies: all constituents act as single sources of radiation
2
Intermediate energies: multiple constituents act as a coherent
scattering source (LPM interference)
3
Highest energies: the entire medium acts as one scattering center
µ2 L 2
h∆E i(L) ∼ c1 αs E + c2 αs
λ
Redmer Alexander Bertens - January 11, 2017 - slide 32 of 27
Path length dependence of jet quenching