Download Direct photon production in heavy-ion collisions

A light-cone wavefunction
approach to heavy meson
dynamics in the QGP
Ivan Vitev
Credit goes to my collaborators
R. Sharma and B. W. Zhang
Phys. Rev. C 80, 054902 (2009),
Rishi Sharma, IV, Ben-Wei Zhang
• Phys. Lett. B 649, 139 (2007),
Azfar Adil, IV
•
Heavy Quark Production in Heavy Ion Collisions
Purdue, January 4-6, 2010
Outline of this Talk






Motivation, light particle quenching and the nonphotonic electron puzzle
An alternative mechanism for open heavy flavor
suppression
Heavy mesons near the phase transition
Distribution and fragmentation functions for open
heavy flavor at zero and finite T
Calculation of the in-medium heavy meson
dissociation probability (GLV approach).
Heavy flavor dynamics at RHIC and the LHC,
examples for inclusive D/B and decay e±
I. Light Particle Quenching

So far has worked very well
versus pT, root(s), centrality,
…
Gyulassy-Levai-Vitev (GLV) formalism
Gyulassy et al, (2001)
•
RAA: provides useful information for
the hot / dense medium
T [MeV]
RHIC
LHC
370
720
.75-1.
1.4-1.8
.75-.42
.39-.25
qˆ  0.35  0.85 GeV . fm
2
1
qφ  0.40  0.99 GeV 2 . fm1
IV 2005
I. Leading Particle Suppression
at the LHC
K. Amadot et al, (2011)
IV, (2005)


1
ET 
Observable
Observable ~ n , RAA
 1 
ET
ET 

n (2 m ')
I.V., M. Gyulassy (2002)
The pT dependence and magnitude of the ~ suppression
is consistent with predictions form 2002 and 2005
I. The Open Heavy Flavor
Quenching Puzzle


Calculations include Cronin effect,
coherent power corrections
(shadowing), IS energy loss, E-loss
in the QGP (FS)
The real problem comes form B
mesons that dominate at
intermediate / high pT
R. Sharma et al. (2009)
II. The Space-Time Picture of Hadronization
• Inside-outside cascade
• Outside-inside cascade
String models
Hadron
Parton
Bjorken (1984)
Bialas et al. (1987)
QGP extent
B
D
Perturbative
QCD
6
20 fm
1.5 fm
0.4 fm
II. The Mass and Momentum Dependence
of Particle Formation

Markert et al. (2008)
For particle masses ~ > 1 GeV
one has to consider their
formation and dissociation in
the medium
II. Collisional Dissociation of D / B Mesons
 An alternative
D-mesons, B-mesons
c
Simultaneous fragmentation and
dissociation call for solving a system
of coupled equations
• Example: radioactive decay chain
u
Time evolution
• Both emulate energy loss and lead to
suppression of the final observable
spectra
Adil, IV (2007)
dN i
 i 1 N i 1  i N i
dt
III. Quarkonia
Near the Phase Transition
The quark-antiquark potential can be extracted form the lattice
One particular
parametrization
•
Mocsy, Petreczky (2007)
Non-relativistic – Schroedinger
J/ψ
J/ψ can survive (color screening) to
~ 2 Tc. ϒ can survive to much higher
temperatures
ϒ
III. D and B Mesons
Near the Phase Transition
•
Relativistic – Dirac equation
M. Avila (1994)
Coulomb
Linear
1
4
V   ,    s
r
3
S  br
b 
 dG
 k 1




V
'
S
'
m
F





 G
 dr
r
2M

 dF  k  1
b 



 F    V ' S ' m G

r
2M
 dr
B, D can survive color screening to ~ 1.5 – 2 Tc depending
on the effective light quark mass
IV. Light Cone Wave Functions
• Expansion

P , P , S , S z 
2
in Fock components

n
n 2,3
i1
dxi d 2 k i

2xi 2 3 n
 
 


i, j,k  n
x,k , a 
i
i
i
i
 n
  n

   xi  1    k i 

 

i1
i1
r
r
r
a
a
...a (xi P  k i )...b j (x j P  k j )... d  k (xk P  k k )... 0
a
i
Composite hadron creation operator:
'
'

'2 '
'
z

2
P , P , S , S P , P , S , S z
  

r  r ' s s '
 2P 2  P  P  z z

3
3
r
a (P )
† sz
H
The normalization then becomes
1

1
 
2 2
3
n
 
n 2,3
i1
dxi d 2 k i
 
2xi 2
3


 n xi , k i , i ai 
2
 n
  n

   xi  1    k i 

 

i1
i1
IV. Parton Distribution Functions
at Non-zero T

Even though the physical situation of mesons in a co-moving plasma
is nor realized it is interesting to investigate theoretically the PDFs
and FFs at finite temperature
Distribution function
dy  ixP y
 a
a

q / P (x)  
e
P  (y , 0)  (0, 0) P
2
2
• Light cone gauge A+=0 , 0<x<1
 (k , x)
2
 k2  4mQ2 (1 x)  4mq2 (x) 
: Exp  

42 x(1 x)


Sharma, IV, Zhang (2009)
IV. Heavy Quark
Fragmentation Functions at Non-zero T
Fragmentation function
At tree level: #  (x  1). #  0
The leading contribution:
dy  iP  / z y 1
1
DH /q (z)  z 
e
Trcolor TrDirac
2
3
2


2
0  a (y  , 0)aH† (P  )aH (P  ) a (0, 0) 0
Ma (1993), Braaten et al. (1995)
•
Keep the leading qT dependence in
the meson wavefunction. Complexity
~10^3 terms
Sharma et al. (2009)
Includes:
3
S0 1 S0
The only calculation of “modified fragmentation functions”. The shape is the
same as in the vacuum. Quenching comes from energy loss - not universal.
IV. The Inapplicability of
Simple Mesons in Equilibrium Models
•
Incompatible with equilibrium
+ boost assumption AdS/CFT
 The J/ψ yield suggests that the LQCD based results with the equilibrium
dissociation
 Theoretically
•
 rmed  t form
. Leads to “instant” wavefunction approximation
It is not the screening, but the subsequent collisional dissociation
that reduce the rates of open heavy flavor and quarkonia
V. Calculating the Heavy Meson
Dissociation Probability

Calculate the kernel for the
system evolution in the GLV
approach
Opacity (mean # scatterings):  

L

One can resum the interactions in impact parameter space
Rutherford tail enhancement
Master equation

(  3  5)
V. The Physics of In-medium
Heavy Meson Scattering
k
m (1 x ) m2 x



 1
2
4 x(1 x )2
x(1 x ) 2


 i (k , x)   (K  )  Norm e
e


2
2
Initial condition:
2
2
2
  K2 
k2
m 2 (1 x ) m22 x 
2

 1
 e 4    
2
2
2
2
x(1  x)
2
 f (k , x)  
  Norm
e 4(    x(1 x ) ) e x(1 x ) 
2 
2
2
   x(1  x)

 4    



2
Result:

Two physics effects arise form meson broadening
• Heavy
meson
acoplanarity:
K
2


L 
 2  2 2  
q 

K
• Broadening
(separation)
the q-qbar pair:
k
 f (k , x)  a M (k , x)  (1  a) qq dissociated (k , x)
16
VI. Coupled Rate Equations
and Initial Conditions
t f Q ( pT ,t)  
1
 form ( pT ,t)
f Q ( pT ,t)
1
+
 diss ( pT / x ,t)
t f H ( pT ,t)  
+
1
 dx
0
1
 (x) f H ( pT / x,t)
2 Q/ H
x
1
f H ( pT ,t)
 diss ( pT ,t)
1
 form ( pT / z ,t)
1
 dz
0
1
DH / Q (z) f Q ( pT / z,t)
2
z
Adil, IV (2007)
•
•
•
The subtlety is how to include partonic energy loss
It cannot be incorporated as drag/diffusion
We include it approximately
as MODIFIED INITIAL
CONDITION
f Q ( pT ,t  0) 
d
Q
f
( pT ,QUENCHED)
2
dyd pT
f H ( pT ,t  0)  0
Sharma et al. (2009)
VI. Numerical Results for
D/B mesons at RHIC
•
D/B mesons (and non-photonic electrons): show similar suppression
Au+Au, Cu+Cu at RHIC
•
•
Cronin effect is very important.
Reduces the suppression at
intermediate pT
M. Aggarwal et al. (2010)
VI. RHIC Results
on Non-photonic Electrons
•
Employ a full simulation of the D and B meson semi-leptonic decay,.
PYTHIA subroutin.e
T. Sjostrand et al (2006)
•
•
•
The predicted suppression is
still slightly smaller than the
quenching of inclusive
particles
It is compatible with the
experimental data within the
error bars
Improved direct
measurements are needed
to pinpoint the magnitude
and relative contribution of
B/D
R. Sharma et al. (2010)
VI. Open Heavy Flavor
Suppression at the LHC
•
•
•
•
The main effect is the
increased suppression in the
intermediate pT range 5 GeV
to 30 GeV
At low pT the predicted D/B
(electron) suppression is
smaller than the one for light
particles
At pT > 40 GeV they become
comparable. (Residual
matching model
dependence)
LHC is critical to cover the pT
range needed for b-quark, Bmeson dynamics
Conclusions




Theoretical predictions of leading light particle
suppression in the GLV approach have worked very well
from SPS to the LHC
In contrast, the suppression of non-photonic electrons
is significantly underpredicted. The problem is in the B
mesons. Common to all e-loss approaches
Color screening by itself does not imply disappearance
of quarkonia to ~ 2Tc and heavy mesons to 1.5- 2 Tc
Presented first calculations of heavy meson distribution
and fragmentation functions at zero and finite
temperature (beyond the point like approximation)
There is no universal (T) medium modification of
fragmentation functions. Suppression comes from
processed that are/emulate energy loss
Conclusions (continued)





Theoretical and phenomenological considerations
suggest that for energetic mesons fragmentation may
not be affected by the thermal medium.
Calculated the dissociation probability of mesons
moving through the medium associated with its
collisional interactions
Partonic energy loss and meson dissociation are now
combined. This is not straightforward – as quenched
quark initial conditions
The main prediction remains equal and large B and D
meson suppression. Matches smoothly onto the
quenching region. Compatible with RHIC results.
Predictions for LHC presented
IV. QCD on the Light Front
The free theory
r
 (x  ) 
a
• Quarks
r
 (x  ) 
a
• Anti-quarks
• Gluons
r
A (x  ) 
a
dp  d 2 p
a r
ipx
†a r 
ipx
a
(
p
)u
(
p)e

b
(
p
)v
(
p)e





 2 p 2 3 

dp  d 2 p
a r
ipx
†a r 
ipx
b
(
p
)v
(
p)e

a
(
p
)u
(
p)e





 2 p 2 3 



|x   0
dp  d 2 p
a r
ipx
†a r 
*
ipx
d
(
p
)

(
p)e

d
 ( p )  ( p)e

 2 p 2 3  

|x   0

|x   0
Commutation relations and normalization of states
a
a'
'





r
r
r
r
3
( p  ' ), a† a ( p  )  2 p  2   3 p   p  '  aa '  '
b
a'
'



r
r
r
r
3
( p  ' ),b† a ( p  )  2 p  2   3 p   p  '  aa '  '
r
r
r
r
ba'' ( p ' ),b†a ( p )  2 p 2 3  3 p  p '  aa '  '
• States:
  a   
r
n, pn ,  n
n
r
r
r
... a†a,i ( pi)...b†a, j ( pj )...d†a,k ( pk ) 0
i, j,kn
• Implicit: quark flavor, (anti)symmetrization
• Normalization trivially obtained from above
I. High pT (ET) Observables

Understanding high pT particle suppression (quenching)
Power laws:
n  n( s, pT , system)
m-Particle Observable ~
Observable
RAA

ET 
 1 
ET 

d
A
A


d 2 pT pT  p0 n pT n
Quenching factor
correlated to spectra
1
ETn
n (2 m ')
• Some models’ RAA varies with the
underlying power law spectrum
• High pT suppression at the LHC can
be comparable and smaller than at
RHIC
• Complete absorption models produce
a constant RAA
24
I. The Open Heavy Flavor
Quenching Puzzle


Large suppression of nonphotonic electrons –
incompatible with
radiative/collisional e-loss
… one can fit heavy flavor
only (no doubt)
M. Djordjevic et al. (2006)
But it doesn’t work. Data favors B
meson suppression comparable to that
of D mesons
M. Aggarwal et al. (2010)
“Instant” Approximation
•
•
Compatible with measured
multiplicities
Full treatment of cold nuclear
matter effects
Results from the LHC
So far has worked very well
versus pT, root(s), centrality,
…


Advantage of RAA :
providing useful
information of the hot /
dense medium, with a
simple physics picture.
Gyulassy-Levai-Vitev(GLV) formalism
Gyulassy, Levai, IV, NPB 594(2001)371
Leading particles
Gluon Feedback to Single Inclusives
• Note that Nbin / (Npart/2) = 0.11
• The redistribution of the lost energy is
very important at the LHC. 100%
correction and pT<15 GeV affected
• Can quickly eliminate some models or
indicate very interesting new
possibilities for modeling
28
Calculating the Meson Wave
Function
• Relativistic Dirac equation
3 VS
m
S'  S 

V
2 MQ MQ
V'S
2
1 S
m

S
2 MQ MQ

 l  1,
l,


 
j  l 1/ 2
j  l 1/ 2
Reduces to:
• Radial density:
1
(r) ~ (F 2  G 2 )
D0 , D0 , D _ D , Ds ... The*, .... Same for B
S0 3 S1
Coulomb
Linear
S  br
1
4
V   ,    s
r
3
Reduces to:
b 
 dG
 k 1




V
'
S
'
m
F





G
 dr
r
2M 

 dF  k  1
b 



 F    V ' S ' m G

dr
r
2M

Boost with large P+ - end up at
the same longitudinal rapidity
 (k , x)
2
 k2  4mQ2 (1 x)  4mq2 (x) 
: Exp  

42 x(1 x)


M. Avila, Phys. Rev. D49 (1994)
29
Heavy Quark Production and
Correlations
D
D
• Fast convergence of the perturbative
series
• Possibility for novel studies of heavy
 , k, 
30
D
quark-triggered (D and B) jets: hadron
composition of associated yields
Quenching of Non-Photonic Electrons
• Full semi-leptonic decays of C- and B-
mesons and baryons included. PDG
branching fractions and kinematics.
PYTHIA event generator


RAAe ( pT ) 
• Similar to light
d AAe / dyd 2 pT

N coll d pp e / dyd 2 pT
 0, however, different
physics mechanism
• B-mesons are included. They give a
major contribution to (e++e-)
Note on applicability
D-, B-mesons to RAA (D)  RAA (B)
(e++e-) to 25 GeV
31
Light Front Quantization
• Advantages of light front quantization: simple vacuum, the only state with
p+=0
• Full set of operators, commuting:
M 2  2 p  p   p2 , p  , p
S 2 , Sz
S.Brodsky, H.C.Pauli, S.Pinsky, Phys. Rep. (1998)
32
From Low to High Fock
Components
• Perturbative generation of the
higher Fock states
 s d  2 d
dPa 
dzPa bc ( z )
2  2 2
At the QCD vertexes: conserve color, momentum, flavor, …
• The lowest lying Fock state (non-perturbative) – the most
important
Correct quantum #s carry over to higher states
33
Medium-Induced Radiation: Theory
• Includes
interference with
the radiation from hard scattering

d  el
d 2 q
1
 el 2 ( q )
2

1
 el 2 ( q )
2
φn  Vφn φn Dφn  V
Rφn  D

n
CR s  n L  ji1 z j d zi
k
 k
  2  
 2
 2
dk d k n 1 dk d k n 1   i 1 0
g ( zi )
dN g


dN n g

 
n

 -2C1...n    Bm1...n m...n  cos
m 1

Color current propagators
 1 d el

2
 d qi   el d 2 qi   (qi ) 

2
 
 k 2 k ...nzk  cos
m

Momentum transfers
Number of scatterings




 k 1k ...nzk 
m
Coherence phases
(LPM effect)
The Soft Medium
• Local thermal equilibrium
PHOBOS
• Local parton-hadron duality
• Gluon-dominated soft sector
• Bjorken expansion /
approximate boost invariance
Au + Au



2
g

g
T
,
g

2

2
.
5
(


0
.
3

0
.
5
)
D
s
4
2


1
g
g 9
s

2
,
g
g
g
2



D

 
w
h
e
r
e
#
D
o
F

2
(
p
o
l
a
r
i
z
a
t
i
o
n
)

8
(
c
o
l
o
r
)
,[

3
]

1
.
2

2
1
4
p
d
p
#
D
o
F 3
(
T
)

#
D
o
F
2 [
3
]

T
t
h
e
o
r
y
p
/
T
3

0
e
1
(
2
)

T [MeV]
RHIC
LHC
370
720
.75-1.
1.4-1.8
.75-.42
.39-.25