J/ Ψ TMD as a Sensitive Signature of QGP Pengfei Zhuang (Tsinghua University, Beijing)
Probing QGP by Heavy Flavors Santosh Kumar Das Theoretical Physics Division.
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Transcript of Probing QGP by Heavy Flavors Santosh Kumar Das Theoretical Physics Division.
Probing QGP by Heavy FlavorsProbing QGP by Heavy Flavors
Variable Energy Cyclotron Center, Kolkata-700064..
Santosh Kumar DasTheoretical Physics Division
Outline of my talk…………..
Introduction
Formalism
Heavy flavor as a probe of QGP.
Summary and outlook.
Gay D. Moore and D. Teaney, PRC, 71,064904(2005)
Heavy Quark (HQ)
Light Quark (LQ)
Gluon
τ HQ > τLQ , τ HQ ~ (M/T) τLQ
LQ thermalizes faster than HQ
The propagation of heavy quarks through the QGP can be treated as interactions between equilibrium and non equilibrium degrees of freedom.
Introduction
The FP equation provides an appropriate framework for such processes.
Water Light quarks and gluons
Heavy quarksPollen grain
Fokker-Planck equation is use to study the evolution of charm and bottom quark.
Just like evolution of pollen grain on the background of water molecule, where water molecule are in equilibrium and the pollen grains executes
Brownian motion in the water.
τLQ < τ < τHQThis time interval can be treated within the scope of Fokker Planck
Equation.
Why Heavy quark ??
Early Production
It does not decide the bulk properties of the system rather act as a probe to extract information about the system.
Boltzmann Kinetic equation
coltf
pxEP
t tpxf
,,.F
pfkpkpfkkpkdtftpR
col
,, 3
fPP
kkfp
kpfkpkpfkkpji
ji
2
21.)(,
colt
ftpft
,
kqkpqppqvqfqdgkp ,,,3
3
)()2(
),(
is rate of collisions which change the momentum of the charmed quark from p
to p-k
The plasma is uniform ,i.e., the distribution function is independent of x. Without application of any external force, i.e F=0
fpBpfpAptf
ijj
ii
i3
i k)k(pkdA ,
ji3
ij kk)k(pkdB ,
Where we have defined the kernels ,
Landau Kinetic equation.
→ Drag Coefficient
→ Diffusion Coefficient
kqkpqppqvqfqdgkp ,,,3
3
)()2(
),(
Non -equilibrium Equilibriumdistribution Function distribution
Function
Landau Kinetic Equation Fokker Planck Equation
reduced
replaced
fpBpfpAptf
ijj
ii
For Collision Process the Ai and Bij can be calculated as following :
ii
cpqqpi ppppqfqpqpM
Epd
Eqd
Eqd
EA
)(212222222
1 442
3
3
3
3
3
3
jiij ppppB )(21
Elastic processes
gcgc
qcqc
We have introduce a mass into the internal gluon propagator in the t and u-channel-exchange diagrams, to shield the infrared divergence.
B. Svetitsky PRD 37(1987)2484
2
022
0 Fkkdd
dnkddkn f
gg
The average energy loss per collision
220
2
2
kkF
kf /cosh
Where → dead cone suppression factor
and → the formation time
Yu.L. Dokshitzer and D.E.Kharzeev, PLB,519(2001)199 Em /0
ω → the energy of the emitted gluon.
Radiative Energy Loss
SKD, J. Alam and P. Mohanty ,PRC, 82,014908,2010
2222
2222
2222
2
22 )()(
)( D
DsA
D
sAg
mqkksmqqC
mqkkqC
dkddn
(Gunion and Bertsch results) Correction term
Source to the heavy quark radiative processes are cg → cgg and cq→ cqg
SKD and J. Alam PRD, 82,051502(R),2010
But we start with the common mass less process like gg → ggg , then we will generalized it for massive.
SKD and J. AlamPRD,83,114011,2011
.
raddXdE
The radiative energy loss per unit length for heavy quark is
Where
= 1/ interaction rate ( inverse of interaction time).
pdxdE
RadColleff
The drag acting on the heavy quark [Using Einstein's fluctuation-dissipation theorem ]
With this inputs we have solved the Fokker-Planks equation
Radiative Energy Loss (Contd.)
Collisional and radiative process are not independent from each other,
since collision contribution is less compare to the
radiative,we take it as a perturbation to the radiative
process.
TmD
Drag and Diffusion @LHC energy
At High temperature radiative loss dominate over collisional loss
SKD, J. Alam and P. Mohanty PRC, 82,014908,2010
Drag and Diffusion @LHC energy
At High temperature radiative loss dominate over collisional loss
SKD, J. Alam and P. Mohanty PRC, 82,014908,2010
Drag and diffusion @ finite baryonic chemical potential
For the process cg cgTemperature
Drag (γ) Diffusion (D)
140 MeV 8.42 * 10 -3 fm -1 1.42 * 10 -3 GeV2 fm -1
190 MeV 1.86 * 10-2 fm-1 4.31 * 10-2 GeV2fm-1
SKD, J. Alam, P. Mohanty and B. Sinha PRC,81,044912(2010)
Probability that a charm /bottom quark is produced at r is parametrized as:
where
cossin 222 rrRLCharm/bottom quark propagates a length:
Geometric average of drag coefficients:
R
rφ
φrcos φ
rsin
φ
L
222 RrsinrcosL
With the initial condition We solve the initial-value problem .
The full solution with an arbitrary initial condition follows as
Where is the Greens function for the Fokker-Planck equation
)(),0( 0 pfptf
00003 ,,, pfpptGpdtpf
0,, pptG
eXBDbc )()( C. Petersion et al PRD,27,105(1983)
SKD, J. Alam and P. MohantyPRC,80,054916(2009)
Nuclear Suppression Factor (RAA) :
pp
Tcoll
AuAu
TAA
dypddNN
dypddN
R
2
2
A direct measure of the energy loss
If RAA = 1 No medium
If RAA< 1 Medium
RAA @ highest RHIC energy
SKD, J. Alam and P. Mohanty PRC, 82,014908,2010
RAA @ Low Energy RHIC(Finite baryonic chemical potential )
√SNN (GeV) dN/dy Ti (MeV) μq (GeV)
39 617 240 62 27 592 199 70 17.3 574 198 100 7.7 561 197 165
Radiative loss is
neglected
SKD, J. Alam, P. Mohanty and B. Sinha PRC,81,044912(2010)
RAA @ LHC Energy
SKD, J. Alam and P. Mohanty PRC, 82,014908,2010
ddydpdNd
ddydpdNd
pv
T
TT
HF
)2cos()2cos()(2
.....)2cos(2)cos(212 21
vvdydpp
dNdyddpp
dN
TTTT
Overall shift
1+2v2
Elliptic Flow :
Major axis = 1+2v2Minor axis = 1-2v2
1-2v
2
Polar Plots :1+2v1cosφ 1+2v2cos(2φ)
px
pyy
x px
py
px
pyy
x
V2 @ highest RHIC energy
SKD and J. Alam arXiv-1008.2643
v 2
V2 @ LHC and Low Energy RHIC
LHCLow Energy RHIC
Hadronic Phase
S. Ghosh, SKD ,S. Sarkar, J. AlamPhys Rev D(R) 84,011503,2011
DDDKDKDD
BBBKBKBB
D (
GeV
2/fm
)
SKD, S. Ghosh ,S. Sarkar, J. Alam
arXiv:1109.3359 [hep-ph]
Summary & Outlook ……We have calculated the drag and diffusion coefficients for
both radiative and collisional energy loss with finite chemical potential.
Using drag, diffusion and initial distribution as input, we have solved the FP Equation.
Nuclear modification factor and elliptic flow has been calculated using the FP solution for partonic medium.
The effect of non zero baryonic chemical potential on nuclear modification factor is highlighted.
Comparison of the experimental data with the results is satisfactory.
Prediction for both LHC and low energy RHIC has been given.
RAA and V2 @ RHIC Energy
Where and → the energy fraction of the final state quark and anti-quark.sEx q /21 sEx q /22
Radiation from heavy quarks suppress in the cone from θ =0 (minima) to θ=2 √γ (maxima)
I) LPM effect : Suppression of bremsstrahlung and pair production. Formation length ( ) : The distance over which interaction is spread out 1) It is the distance required for the final state particles to separate enough that they act as
separate particles.
2) It is also the distance over which the amplitude from several interactions can add coherently to the total cross section.
As q┴ increase l f reduce Radiation drops proportional
(II) Dead cone Effect : Suppression of radiation due to mass
qfl
22
2
2
2
41~1
zC
dzdd s
F 212 xxz sm2
S. Klein, Rev. Mod. Phys 71 (1999)1501
where
and
2
222
2
2
1smq
dkddndkddn
R D
GB
g
g
c
218Tss
TTm sD 4
dtddt
dtddtt
22
ETMss HFHF 62 Das and Alam
PRD, 82,051502(R),2010
dtt
dtt
vyl
vlx
y
x
p
p
0
0
)(~
)(~
exp
exp