Nuclear modification and Azimuthal anisotropy of
heavy flavour decay muons in ultra relativistic
heavy-ion collisions
2nd Heavy Flavour Meet
- 2016,
February
02 - 05, 2016
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Outline:
Motivation.
Initial distribution of production of heavy quarks.
Energy loss of heavy flavour.
Initial conditions and evolution of plasma.
RAA of muons from heavy flavour at forward rapidity at
LHC.
Azimuthal anisotropy of heavy flavour decay muons at
LHC.
Summary.
Motivation
At extremely high energy densities, QCD
predicted formation of a new form of
matter (QGP), consisting of deconfined
(anti)quarks and gluons.
Heavy quarks (charm and bottom, M>1 GeV) are widely recognized as
the excellent probes of QGP:
 Heavy flavours can be produced
only during the early stage of
collision. Produced mainly during the
time t=1/2MQ << 0.1 fm/c. Means it is
nearly negligible at later times.
Early stage
t=1/2MQ << 0.1 fm/c
No heavy quark
production
 Due to their large mass, the
production of heavy quarks is small
making them special as a probe for QGP.
 Experimentally easy to observe, through Semi-leptonic decays.
Heavy flavours produced at the initial time of system evolution will pass
through the QGP, colliding with quarks and gluons and radiating gluons. Thus
the heavy flavours will loose energy while passing through the QGP.
Initial distribution
0
10
Charm @ 2.76 ATeV
Charm @ 5.5 ATeV
Charm @ 39 ATeV
Bottom @ 2.76 ATeV
Bottom @ 5.5 ATeV
Botom @ 39 ATeV
Pb+Pb, y = 2.5
-1
2
-2
dNd pTdy (GeV )
10
-2
10
FONLL calculation.
M. Cacciari, S. Frixione, N. Houdeau,
M. L. Mangano, P. Nason and G.
Ridolfi, JHEP 1210 (2012) 137
-3
10
-4
10
-5
10
-6
10
-7
10
0
5
10
15
pT (GeV)
20
25
UJ and Dinesh K Srivastava , J. Phys. G:
Nucl. Part. Phys. , 37 (2010) 085106
30
Collisional energy loss for heavy quarks:
Peigne and Peshier (PP) formulation
 In Braatan and Thoma formalism, it was assumed that the momentum exchange
q<<E. PP pointed out that this is not reliable in the energy regime E>>M2 /T , and
corrected it in the QED case while calculating the collisional energy loss of a muon in
the QED plasma. This work in QED is then used to calculate the collisional energy loss
of a heavy quark through QGP.
 A fixed coupling approximation is used.
dE 4s 2T 2


dx
3
 n f
1 
6


ET 2
ET

 log 2  log 2  c(n f )
9


M

 n 
 2  4s T 2 1  f  , cn f   0.146n f  0.05
6 

Stephane Peigne and Andre Peshier,
PRD 77 (2008) 114017
Small-angle/collinear gluon emission
There are couple of model implementations in the literature viz., DGLV, ASW-SH, HT,
AMY, that aim to quantify jet quenching and energy loss (mainly radiative) related
phenomena within perturbative QCD.
All this generally used formalisms currently available for energy loss of a high
momentum parton through gluon radiations, have few common technical approximations.
One of the main approximations that involved at the level of
single emission kernel calculations and related to kinematics is:
Small-angle/collinear gluon emission :
Energy of the emitted gluon is much larger than its transverse momentum k ┴ i.e. w >> k ┴
and w  k||. For the process qQ  qQg, without loss of generality, one can take k ┴ = w sin q
and k|| = w cos q , where q being angle between direction of propagation of leading partons
and direction of emitted gluons. This particular approximation therefore implies q  0.
In the Present (AJMS) formalism, We DO NOT have taken this approximation.
Raktim Abir, UJ, Munshi G. Mustafa, Dinesh K. Srivastava, Physics Letters B 715 (2012) 183
Energy Loss of Heavy Flavour
Present (AJMS) radiative energy loss formalism

dE
1
1 1 
 24  3s q  g 
dx
g


1
log 1  1
1 1 

1 / 2

1 F  

æ 1+ M 2 e 2 d / s ö
1
(M 2 / s)cosh d
F (d ) =2 d - log ç
,
÷2 -2 d
2
4
2
2
è 1+ M e / s ø 1+2(M / s)cosh d + M / s
 log  1 
1/ 2


1
1



1
1
  log 
1 1

1 1 / 2
2
 1   1 
log

1



s  E 1  0 
2
2

2 
 
 
 
g2 T
M2
,1
,  0  1 2
C E
E
 M 2  6 E T 1   0  
3 M2
M4
C 

log 

2
2
2
2 4 E T 48 E T  0


M

6
E
T
1



0 

Raktim Abir, UJ, Munshi G. Mustafa,
Dinesh K. Srivastava
Physics Letters B 715 (2012) 183
K. Saraswat, P. Shukla, V. Singh, Nuclear Physics A 943 (2015), 83
Energy Loss of Heavy Flavor
Radiative energy loss for heavy quarks:
Djordjevic, Gyulassy, Levai, and Vitev (DGLV) formulation
 For massless case Gyulassy, Levai and Vitev (GLV) computed the induced
radiation to an arbitrary order in opacity χn (χ=L/λ) of the plasma .
 DGLV generalize the GLV opacity expansion method to compute the first
order induced energy loss including the kinematic effect due to heavy quark
mass.
Wicks et al. present a simplified form of the DGLV formalism for the average
radiative energy loss of heavy quarks.
S. Wicks et.al, Nuclear Physics A 784(2007)426
1
ΔE CF α s L

E

λg
M
E p

mg
E p

dx
4 μ 2 q3 dq
  4 E x 2
0

L

2
2
  q β

2
A logB  C 
Energy Loss of Heavy Flavor
Initial conditions and evolution of plasma.
The initial conditions:
The energy loss depends on:
Path length of the heavy quarks in the plasma.
Temperature evolution of the plasma and
The energy and mass of the heavy quark.
Neglect the transverse expansion of the plasma.
Bjorken cooling is assumed to work locally.
1
3
 π2
ρ(τ) 
Tt   
 1.202 9 n f  16 



y2
ρ τ  
Quantity
2
dN dN

e 2 σ dN /dη at η = 0
ch
dy dy y 0
Total Nch
1 dN g
πR 2 τ dy
S. Wicks et.al, Nuclear Physics A
784 (2007) 426
Pb–Pb 2.76 ATeV
Pb–Pb 5.5 ATeV
Pb–Pb 39 ATeV
1600
2000
3600
17000
23000
50000
N. Armesto et. al, Nuclear Physics A 00 (2014);
K. Aamdot et al. (ALICE Collaboration) 105 (2010) 252301
 The critical temperature Tc for existence of QGP is taken as 170 MeV.
Initial conditions and evolution of plasma.
Average path length:
The distance covered by the heavy
quark will vary from 0 to 2R.
 For central collisions the results for
<L> will not depend on f
Lf, r   R 2  r 2 sin 2 f  r cos f
2
R
L 

r dr
0
 L(f, r) TAA (r, b  0) df
0
2
R

0
r dr

TAA (r, b  0) df
0
 For non-central collisions the results
for <L> will depend on the azimuthal
angle
L(f,
r)
f
r
F
R
Initial conditions and evolution of plasma.
Average path length:
Now, vT =pT /mT  tL = <L>/vT .
If tc ≥ tL
If tc < tL the heavy quark would be inside
QGP only while covering the distance vT × tc.
We approximate <t> = <L>eff / 2, where
<L>eff =min [<L>, vT × tc ].
tL
tL
tc
Nuclear modification factor
The nuclear modification factor
at impact parameter b is:
dNAA dp T dy
R AA b  
TAA b  dσ NN dp T dy
TAA is calculated using Glauber model.
Suppression
=
Final momentum distribution of heavy quarks/Initial momentum distribution of
heavy quarks
 We perform the calculations in the frame in which the rapidity of the heavy
quark is the same as the fluid rapidity.
So, energy of the heavy quark
2
E  mT  MQ
 p 2T
2
After loosing energy ∆E, the heavy quark new energy: E  E - E  mT  MQ
 pT2
 The fragmentation of heavy quarks in to mesons is governed by Peterson
fragmentation function. The parameters used are ec = 0.06 and eb = 0.006.
Comparison of energy loss predicted by radiative and collisional energy loss formalisms.
14
10
Black colored lines represent 2.76 ATeV
Red colored lines represent 5.5 ATeV
Green colored lines represent 39 ATeV
DE (GeV)
8
10
8
6
Bottom quark
y= 2.5
Solid lines represent DGLV (rad.)
Dashed lines represent Present (rad.)
Dotted lines represent Peigne and Pesher (coll.)
y= 2.5
Black colored lines represent 2.76 ATeV
Red colored lines represent 5.5 ATeV
Green colored lines represent 39 ATeV
12
DE (GeV)
12
Charm quark
Solid lines represent DGLV (rad)
Dashed lines represent Present (rad)
Dotted lines represent Peigne and Pesher (coll)
16
6
4
4
2
2
0
0
5
10
15
20
25
E (GeV)
30
35
40
45
50
0
0
5
10
15
20
25
E (GeV)
30
35
40
45
50
RAA at LHC
RAA of D mesons at 2.76 ATeV and 5.5 ATeV.
Raktim Abir, UJ, Munshi G. Mustafa,
Dinesh K. Srivastava
Physics Letters B 715 (2012) 183
RAA at LHC
RAA of muons at forward rapidity
at 2.76 ATeV.
Pb+Pb Collision
@ 2.76 ATeV
muon RAA (2.5 < y < 4)
0.6
ALICE data (0-10% Centrality)
Present
DGLV
PP+Present
PP+DGLV
0.5
0.4
0.3
0.2
0.1
0
3
4
5
7
6
Pb+Pb Collision
muon RAA (2.5 < y < 4)
Comparison of RAA of muons at forward
rapidity at 2.76, 5.5 and 39 ATeV.
9
10
ALICE data (0-10% Centrality)
2.76 ATeV
5.5 ATeV
39 ATeV
Present
0.6
8
pT (GeV)
0.5
0.4
0.3
0.2
ALICE Collaboration, Phys. Rev. Lett. 109, 112301
(2012).
0.1
3
4
5
6
7
pT (GeV)
8
9
10
0.3
Pb+Pb@2.76 ATeV, 20 - 40 % Centrality
2.5 < y < 4
ALICE (Preliminary) data
DGLV
v2 (Heavy flavour decay muons)
Presention
ken as indicat ive of anisotropy which can arise due t o medium modificat
PP+present
0.25
t ionThe
funct
ion
due
t
o
energy
loss
of
partons.
PP+DGLV
differential azimuthal
0.2
anisotropy
in is measured in terms of t he parameter v2(pT ),
erent
ial azimutis
halmeasured
anisot ropy
termsFourier
of the parameter
0.15
T) : azimut hal
second
coefficient Vof2 (pt he
dist ribut ion of hadrons in t he
0.1
ne:
2π
0
v2 (Heavy flavour decay muons)
0.05
dφ cos(2φ)dN/ d2pT dy
v2(pT ) =
.
(19)
2π
2
0
0 dφdN/ d pT dy
-0.05
e calculated t he azimuthal anisotropy coefficient
7 ral 8 pions
3
4 v2(p
9
10
11
5T ) of
6 neut
pT (GeV)
√
GeV/ c for Au+ Au collisions at sNN = 200 GeV for t he six cent ralit ies
Pb+Pb collision, 20 - 40 % Centrality
ALICE (Preliminary) data
V2earlier
(pT) of muons
at forward
arlier.
energy
loss per collision
is taken from t he
analysis
and φ
<y<4
0.3 The2.5
39 ATeV
Present Formalism
2.76 ATeV
rapidity
2.76 ATeV. And
st ribution
of the pions is calculat
ed by incorporat ing
the φatdependence
of
0.25
prediction for 39 ATeV at FCC.
gth L.
0.2
Grazia Luparello for the ALICE Collaboration,
ult s0.15of our calculat ions are displayed in arXiv:1411.2442v1
Fig. 12 along wit
h the10data
[nucl-ex]
Nov 2014
m PHENIX
collaboration [33]. We show t he theoretical result s only over
0.1
ow where
t he corresponding mechanism wasALICE
foundCollaboration,
t o describe t he nuclear
0.05
arXiv:1507.03134v1 [nucl-ex] 11 Jul 2015
dat a,0 earlier (see Fig. 6).
g that t he BH mechanism was found t o provide a good descript ion of t he
-0.05
7
3
4
8
9
10
11
5
6
ression, up to pT equalp (GeV)
t o 5–6 GeV/ c, while the mechanisms for t he LPM
T
Summary
 The nuclear modification factor RAA predicted by present(AJMS) and DGLV formalisms are
quite different. But in case of elliptic flow we observe that both shows similar trend.
 We have noted that the suppression of muons at LHC is well supported by the
present(AJMS) formalism.
 The nuclear modification factor of muons at 0-10% centrality predicted by the present
formalism has shown very good agreement with the ALICE data. However the
prediction shows more suppression while we take account the collisional energy loss.
 We expect that the consideration of Wood-Saxon density distribution for the colliding
nuclei will improve the scenario.
 It is necessary to obtain both radiative and collisional energy loss from the same
formalism to minimize the various uncertainties.
 Moreover, data at high pT region with improved statistics are required to remove
prejudice on different energy loss and jet quenching models.