A Monte Carlo for jet quenching: medium studies in ALICEgruppo3.ca.infn.it/cnfa08/cunqueiro.pdf ·...
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A Monte Carlo for jet quenching: mediumstudies in ALICE
Leticia Cunqueiro
Laboratori Nazionali di Frascati
Leticia Cunqueiro Palau, 29-9-2008
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Outline
At LHC a full unbiased jet reconstruction will be possible thanks to:
• The high rate of high energy jets (Ejet > 100 GeV) disentangled from the
background.
• New algorithms and background subtraction techniques.
• Detector properties.
New Accessible: Fragmentation functions, jet shapes, jet multiplicities, intrajet particle
correlations...that will allow for a much better characterization of the medium.
but to go beyond limited single inclusive measurements a Monte Carlo is needed.
We present Q-PYTHIA, a Monte Carlo for the Jet Quenching based on the ideas
described in [Armesto,Cunqueiro,Salgado,Xiang, JHEP 0802:048,2008]
Leticia Cunqueiro Palau, 29-9-2008
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Our framework: Medium-induced gluon radiation
Medium-Induced Radiation: In a QCD medium (QGP) a hard parton looses virtuality
by the induced emission of soft gluons. Their emission and their further (strong)
interactions with the medium are the dominant energy loss for high energy projectiles.
Y cuanto hemos podidio comprobar va desde
hasta
The hard parton looses virtuality from the initial scale t to the final hadronization one
t0 ' Λ2QCD. Hadronization happens outside the medium (for pT ≥ 7 GeV/c at RHIC)
The QCD vacuum radiation pattern is changed:
• energy loss of the leading parton( ∆E ' αSqL2)
• angular broadening of the jet cone (∆k2T >' qL)
• an increase and a softening of the shower multiplicity.
Leticia Cunqueiro Palau, 29-9-2008
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Medium-induced gluon radiation
The single inclusive distribution of medium induced gluons with energy
ω and kt from a parent parton of energy E was derived by Wiedemann (2000).
ωdI
dωdkT
=αSCR
(2π)2ω22Re
Z ∞
0
dyl
Z ∞
yl
dyl
Zdue
−ikTue−1
2
R∞yl
dζn(ζ)σ(u)×
∂
∂y
∂
∂u
Z u=r(yl)
y=0=r(yl)
Drei
R ylyl
dζω2 (r2−n(ζ)σ(r)
iω )
All the medium information is encoded in the product n(ζ)σ(r)
• n(ζ)=density of scattering centers.
• σ(r)=strength of the interaction.
BDMPS approximation (Brownian motion): n(ζ)σ(r) = 12q(ζ)r2
q(ζ) −→ < q2T > /λ .
(Transport coefficient, encodes information about the elementary interaction)
In this case→ numerically tractable expression for the spectra is obtained.
Leticia Cunqueiro Palau, 29-9-2008
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Medium Induced Gluon Radiation
-210 -110 1 10 210
0
0.5
1
1.5
2
2.5
3
3.5
4
]2κdω/[dmeddIω
2κ
-2=10cω/ω-1=10cω/ω
=1cω/ω=10cω/ω
ωTk
θ
p
Like in QED, the emission of a gluon has a phase
φ =k2T ∆z
2ω .
To strip the gluon out φ ∼ 1 → lcoh ∼ 2ω/k2t
D = average distance between the scattering
centers= L/N .
If lcoh < D → incoherent B-H limit.
If lcoh ≥ D → there is suppression of the radiation
due to LPM coherence.
Suppression happens at low k2t and/or great ω.
(κ2 =k2t
qL and ωc = 12qL2)
Leticia Cunqueiro Palau, 29-9-2008
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Medium-modified splitting functions
In vacuum: dIvac
dzdk2T
=αsP (z)vac
z−→12πk2
T
, P (z)vacz−→1 '
2CR1−z , z = 1− x
The ansatz is an extension of the former eq. to medium:
dI
dzdk2T
med=
αsP (z)medz−→1
2πk2T
, P (z)medz−→1 = 2πzt
qL F ( ωωc
, κ2) [Salgado-Polosa]
dIvac
dzdk2T
TOT= dIvac
dzdk2T
MEDIUM+ dIvac
dzdk2T
V ACUM
And the total splitting is taken to be the sum of vacuum + medium:
P TOTAL = P V ACUUM(z) + P MEDIUM(z, t, q, L)
Other approaches: [Borghini-Wiedemann] medium multiplicative factor, [Guo-Wang-
Majumder] higher twist corrections in DIS → P (z) = P (z) + δP (z).
Leticia Cunqueiro Palau, 29-9-2008
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Medium effects at the level of the Sudakovs
10 210 310 4100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 and t2 GeV4=102=E
maxProbability of no emission between t
)2t (GeV
lines/markers: with/without large x correct.
upper/lower curves: quarks/gluons
L=2 fm vacuum
/fm2=0.5 GeVq
/fm2=5 GeVq
Sudakov Form Factor: ∆a(t, ta0) = e
−P
a−cc′R tta0
dt′t′
R 1−zmin(t′)zmin(t′)
dzαS(t′,z)
2π Pca(z)
It gives the probability for a parton not to radiate while evolving from t0 to another scale
t.
When our total vacuum+medium splitting functions are supplemented the radiation
probability is very much enhanced.Leticia Cunqueiro Palau, 29-9-2008
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Medium Modified Fragmentation Functions
z-310 -210 -110 1
)2
(z,Q
gD
-910
-810
-710
-610
-510
-410
-310
-210
-110
110
210
310
410
510
610
=100 GeVjetE
/fm2=50 GeVq
/fm2=10 GeVq
/fm2=0 GeVq
z-310 -210 -110 1
)2
(z,Q
sM
/V
0
0.5
1
1.5
2
2.5
Solid/dashed=L=2,6 fm, Q = Ejet. Suppression (enhancement) of high (small) z par-
tons. These effects are enhanced with the medium lenght.
∂D(x, t)
∂t=
1
t
Z 1
x
dz
z
αS
2π(P (z) + ∆P (z, t, q, L))D(
x
z, t)
The medium accelerates the evolution.
Leticia Cunqueiro Palau, 29-9-2008
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Monte Carlo implementation
A Monte Carlo is a desireable tool: allows us to go beyond single inclusive production
and access more exclusive and differential observables → discriminate between energy
loss models.
Be aware that a probabilistic description of radiation in medium is not theoretically
proved: phenomenological assumptions are required.
Our approach: Q-PYTHIA (soon publicly avaliable)
1.Take final state showering routine PYSHOW in PYTHIA and correct vacuum split-
tings:
Ptot(z) = Pvac(z) → Ptot(z) = Pvac(z) + ∆P (z, t, q, L, E)
2.Consider the formation time of the radiated gluons to implement lenght evolution.
The interplay between gluon coherence and medium length is explored for the first time.
Leticia Cunqueiro Palau, 29-9-2008
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Monte Carlo implementation
A Monte Carlo is a desireable tool: allows us to go beyond single inclusive production
and access more exclusive and differential observables → discriminate between energy
loss models.
Be aware that a probabilistic description of radiation in medium is not theoretically
proved: phenomenological assumptions are required.
Other recent MC related approaches:
1. JEWEL [Zapp et al]: multiplicative increase of the soft splittings.
2. PYQUEN [I.P.Lokhtin]: radiation superimposed on other effects like collisional energy loss.
3. coucou[T.Renk]: enlargement of the QCD evolution by giving virtuality to the partons.
Leticia Cunqueiro Palau, 29-9-2008
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Monte Carlo implementation
A branching algorithm must solve this problem:
given a parton with coordinates (t1,z1), which are (t2,z2) at the next branching? Two
steps:
1. Sudakov Form Factor: ∆(t1) = e−
Pa−cc′
R t1t0
$dzαS(t′,z)
2π Pca(z)
gives the probability for a parton not to branch while evolving from an initial scale t0
to another scale t1.
∆(t2)
∆(t1) stands for the probability of evolving from t1 to t2 without branching.
Thus t2 can be generated by solving the equation (R is a random number)
∆(t2)
∆(t1) = R
2. And z2 can be diced down by solving the equation:
R z2zmin
dzαS2π P (z) = R
R zmaxzmin
dzαS2π P (z).
Leticia Cunqueiro Palau, 29-9-2008
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Monte Carlo implementation in medium
A branching algorithm must solve this problem:
given a parton with coordinates (t1,z1), which are (t2,z2) at the next branching? Two
steps:
1. Sudakov Form Factor: ∆(t1) gives the probability for a parton evolving from an initial
scale t0 to another scale t1.
∆(t2)
∆(t1) stands for the probability of evolving from t1 to t2 without branching.
Thus t2 can be generated by solving the equation (R is a random number)
∆(t2)
∆(t1) = R medium change P (z) → P (z) + ∆P
2. And z2 can be diced down by solving the equation:
R z2zmin
dzαS2π P (z) = R
R zmaxzmin
dzαS2π P (z).
In medium change P (z) → P (z) + ∆P
Leticia Cunqueiro Palau, 29-9-2008
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Implementing the longitudinal and energy evolution ofthe shower
1. In our DGLAP approach each kernel is evaluated at the same L and energy E: evolution
in virtulality but not an evolution in length nor in energy.
2. However, not every fragmenting gluon “feels” the same L as the shower developes. And
the energy is reduced at each branching.
3. Use this: each gluon travels a length before it becomes real (before it decoheres from
the hard parton wave function ):
The gluon phase: φ =k2T ∆z
2ω
To strip it out from the parton: φ ∼ 1 → lcoh = 2ω
k2T
P(L)
1cohl
2cohl
)1coh
P(L-l
)2coh-l1
cohP(L-l
4. First branching: P (L, E). Next branching: P (L− l1coh, zE) and so on.
Leticia Cunqueiro Palau, 29-9-2008
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Litmus check, intrajet distributions 0
0 1 2 3 4 5 6 7 8 9 10
0
0.5
1
1.5
2
2.5
3
3.5
=100 GeVjetEξd
partondN
/p)jet
=ln(Eξ0 5 10 15 20 25 30 35 40
−310
−210
−110
1
PYTHIAQ−PYTHIA
)−1 (GeVT
dp
partondN
(GeV)T
p0 0.5 1 1.5 2 2.5 3
0
2
4
6
8
10
12
14
16
18
20
θd
partondN
θCompare Q-PYTHIA with q = 0 and PYTHIA. Small differences mainly due to:
PYTHIA: P (z → 1), Q-PYTHIA: P (z).
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Medium in Pythia, intrajet distributions I
0 1 2 3 4 5 6
0
0.5
1
1.5
2
2.5
3
3.5
4
=10 GeVjetE
ξd
partondN
/p)jet
=ln(Eξ0 1 2 3 4 5 6
−310
−210
−110
1
10
)−1 (GeVT
dp
partondN
(GeV)T
p0 0.5 1 1.5 2 2.5 3
0
1
2
3
4
5
6
7
=100 GeVjetE
θd
partondN
=acos(pz/p)θ
vacuum/fm2=1 GeVq
/fm2=10 GeVq
The spectra are softened. Suppression/enhancement of large/low z values. High pT
suppression. pT broadening? → not clear due to energy conservation in PYTHIA. Clear
angular broadening. (L = 2 fm)
Leticia Cunqueiro Palau, 29-9-2008
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Medium in Pythia, intrajet distributions II
0 1 2 3 4 5 6 7 8 9 10
0
1
2
3
4
5
6
7
8
9
10
ξd
partondN
/p)jet
=log(Eξ0 2 4 6 8 10 12 14
−210
−110
1
10
=100 GeVjetE
)−1 (GeVT
dp
partondN
(GeV)T
p0 0.5 1 1.5 2 2.5 3
0
5
10
15
20
25
30
=100 GeVjetE
θd
partondN
/p)z
=acos(pθ
vacuum
/fm2=5 GeVq
/fm2=50 GeVq
The same but for Ejet = 100 GeV (L = 2 fm).
Leticia Cunqueiro Palau, 29-9-2008
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Medium in Pythia, intrajet distributions III
0 1 2 3 4 5 6
0
1
2
3
4
5
6
7
8
9
10
=10 GeVjetEξd
hadrondN
/p)jet
=ln(Eξ0 1 2 3 4 5 6
−310
−210
−110
1
10
210
)−1 (GeVT
dp
hadrondN
(GeV)T
p0 0.5 1 1.5 2 2.5 3
1
2
3
4
5
6
7
8
9
10
=100 GeVjetE
θd
hadrondN
=acos(pz/p)θ
vacuum/fm2=1 GeVq
/fm2=10 GeVq
Hadronization sweeps out soft effects. (L = 2 fm)
Leticia Cunqueiro Palau, 29-9-2008
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Medium in Pythia, intrajet distributions IV
0 1 2 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
35
40
=100 GeVjetEξd
hadrondN
/p)jet
=log(Eξ0 2 4 6 8 10 12 14
−210
−110
1
10
210 )−1 (GeVT
dp
hadrondN
(GeV)T
p0 0.5 1 1.5 2 2.5 3
10
15
20
25
30
35
40
45
50
=100 GeVjetE
θd
hadrondN
/p)z
=acos(pθ
vacuum
/fm2=5 GeVq
/fm2=50 GeVq
The same but for Ejet = 100 GeV (L = 2 fm).
Leticia Cunqueiro Palau, 29-9-2008
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Different effects in the shower
0 1 2 3 4 5 60
1
2
3
4
5
6
7
8
9
10
ξd
partondN
/p)jet
=ln(Eξ0 2 4 6 8 10 12 14
-210
-110
1
10
210
=100 GeVjetE
)-1 (GeVT
dp
partondN
(GeV)T
p0 0.5 1 1.5 2 2.5 3
0
5
10
15
20
25
30
35
θd
partondN
=acos(pz/p)θ
No evolution in energy (QW-like), no evolution in length
Evolution in energy, not in length
Our default: Evolution in energy, evolution in length
Leticia Cunqueiro Palau, 29-9-2008
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Caveats/Open issues
1. Our implementation assumes that there is an ordering variable in the medium. Is this
probabilistic interpretation valid?
2. There is no energy and momentum exchange with the medium. In an energy conserving
Monte Carlo this is of great importance.
3. Elastic energy loss not included: our BDMPS based implementation considers static
scattering centers → the recoil is not taken into account.
4. How does the Medium Induced Gluon Radiation affect jet hadroquemistry?
The medium causes color rotations and changes the color flow. The effects should
be tested by using different hadronization models.
An enhanced splitting probability is enough to change jet composition:
baryon/meson ratio is modified if just the number of splittings is increased.
Recombination, elastic scattering putting/taking particles in/from the jet etc.
5. our to-do list: Study these effects in a realistic nuclear envionment with current
background subtraction and jet reconstruction techniques. In a realistic detector envi-
ronment
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Comparison: QW vs our new approach
z-110 1
)2
(z,Q
ME
Dg
D
-710
-610
-510
-410
-310
-210
-110
1
10
2=2 GeV2Q2=300 GeV2Q
2=10000 GeV2Q
/fm, L=6 fm2=1GeVq=100 GeV jetEsoli/dashed=ours/QW
z-110 1
)2
(z,Q
VA
C
g)/
D2
(z,Q
ME
Dg
D
0
0.2
0.4
0.6
0.8
1
2=2 GeV2Q2=300 GeV2Q
2=10000 GeV2Q
/fm, L=6 fm2=1GeVq=100 GeV jetEsoli/dashed=ours/QW
For Q2 << E2jet QW overestimate suppression
At Q2 ' E2jet , it can be shown that this new method equals QW.
• good agreement in the relevant z range for inclusive particle production.
Leticia Cunqueiro Palau, 29-9-2008
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Nuclear Modification Factor
qt0 2 4 6 8 10 12 14 16 18 20 22
(qt,y=
0)AAR
0
0.2
0.4
0.6
0.8
1=200 GeVs
/fm2=0.33GeVq
/fm2=0.66GeVq
/fm2=1.GeVq
/fm2=1.33GeVq
/fm2=1.66GeVq/fm2=2.GeVq
/fm2=2.33GeVq
/fm2=2.66GeVq
/fm2=3.GeVq
L=6 fm
data0πdata points:PHENIX preliminary AuAu-
RAA = dσ(pdf + EKS + MMFF )/dσ(pdf + V ACFF ).
q ' 1 GeV2/fm at a fixed lenght of 6 fm. (the same as with the QW)
Tp
0 2 4 6 8 10 12 14 16 18 20 22
,y=0)
T(pAAR
0
0.2
0.4
0.6
0.8
1 /fm2=1 GeVq
/fm2=10 GeVq
solid/dashed=spherical/cylindrical geometry
Considering a path lenght distribution in a cylinder and in a sphere, the value of q grows
up to 10 GeV 2/fm.Leticia Cunqueiro Palau, 29-9-2008
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Reconstruction example
Leticia Cunqueiro Palau, 29-9-2008
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RHIC experimental results collage
partN100 150 200 250 300 350
b
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
200 GeV Au+Au
= 0.2η∆b |
= 1.8η∆b |
I.Akiba [QM2005]
D.J.Tarnowsky [STAR]
Leticia Cunqueiro Palau, 29-9-2008