Transcript Rapidity Asymmetry in d+A Collisions

Jet Quenching and Its effects
in Strong Interaction Matter
Enke Wang
(Institute of Particle Physics, Huazhong Normal University)
I. Jet Quenching
II. Modification of Hadron Fragmentation
Function
III. Jet Tomography of Strong Interaction
Matter
IV. An explanation of heavy quark energy
loss puzzle
V. Summary and Discussion
I. Jet Quenching
Rutherford experiment
a  atom
discovery of nucleus
SLAC DIS experiment
e  proton
discovery of quarks
Hard Probes of Quark Matter:
QGP
penetrating beam (jet)
absorption or scattering pattern
A-A collisions: Naturally provides jet and the QGP
Jet (hard probe) created by parton scattering before QGP is formed
– high transverse momentum
– calculable in pQCD
27 YEARS AGO
Brief History of Theoretical Research about Jet
Quenching
1982: J. D. Bjoken: Fermilab-pub-82/59-THY
Energy loss in elastic scattering
1992/1995: X.-N. Wang, M. Gyulassy:
PRL68(92) 148, PRD45 (92)844, NPB420(94)583, PRD51(95)3436
Energy loss is dominated by gluon radiation
1995/1997: BDMPS (R. Baier, Yu. L. Dokshitzer, A. Mueller, S. Peigue,
D.Schiff) :PLB345(95) 277, NPB478(96)577,NPB483(97)291,NPB484(97)265
Gluon multiple scattering and gluon radiation
2000: GLV(M. Gyulassy, P. Levai, I. Vitev): PRL85(00)5535, NPB594(01)371
U. Wiedemann: NPB588(2000)303
Opacity expansion
2001/2002: E. Wang, X.-N. Wang: PRL87(01)142301, PRL89(02)162301
Detailed Balance; Jet Tomography
Basic Idea for Jet Quenching
Leading
particle
suppressed
leading
particle
hadrons
hadrons
q
q
q
hadrons
leading
particle
p-p collision
At RHIC:
• Hard/Semihard processes is important
• High- Pt parton (jet)
• Jet quenching
• Jet production dominates particle yields
at high Pt
q
hadrons
leading
particle
suppressed
A-A collision
Suppression
of high Pt
hadron
spectra
Jet quenching and Observation
Jet Quenching:
Leading
particle
suppressed
hadrons
q
E
q
hadrons
leading
particle
suppressed
E '  E  E
A-A collision
Modification of Fragmentation Function:
0
2
Dq
(
z
,
Q
)
h
h
zh  (1  z) z'h
ph
( zh   ,
p
ph
z 'h   )
p'
~
Dqh ( zh , Q2 )  Dq0h ( zh , Q2 )  D( zh , Q2 )
Particle
Production:
p
ph
p'
d AA
d ~
 TAB  PDFs 
 Dqh
2
dpT dy
dtˆ
~
S
Jet Quenching in QCD-based Model
G-W (M. Gyulassy, X. –N. Wang) Model:
Static Color-Screened Yukawa Potential
First Order in opacity Correction
First Order in opacity Correction
Induced gluon number distribution:
Non-Abelian
LPM Effect
dN (1)
CRas L
2
2 
  2
x
d qv (q )(2C1  B1 ) 1  cos(1z1 )

2
 g
dxd k
Medium-induced radiation intensity distribution:
Induced radiative energy loss:
QCD: E (1)
L
(1)
QED: E  L
2
Higher order in Opacity
Reaction Operator Approach: (GLV)
Induced gluon number distribution:
Non-Abelian
LPM Effect
Radiated Energy Loss vs. Opacity
First order in opacity correction is dominant!
Jet Quenching with Detailed Balance
E. Wang, X.-N. Wang, Phys. Rev. Lett. 87 (2001) 142301
Temperature and Density QGP System
Gluon radiation:
E loss
Erad
Gluon absorption
E absorption Eabs
x0
Net energy loss of jet:
E  E －Eabs
(1)
rad
p
Detailed Balance
Final-state Radiation
k
x0
k
x0
p
p
Energy loss induced by thermal medium:
Eabs
(0)
 dp ( 0 ) dp ( 0 )
  d 

d
 d
=
Net contribution:
Energy gain


T 0 
a sCF T 2  4ET
6 ' (2) 
ln 2  2   E  2 

3 E 
 
Stimulated emission increase E loss
Thermal absorption decrease E loss
Energy Loss in First Order of Opacity
Energy loss induced by rescattering in thermal medium:
(1 )
(1 )
E (1)  Erad
 Eabs
Take limit:
EL  1
E  
Zero Temperature Part:
Erad
(1)
(0)
dp
  d
d

T 0
Temperature-dependent Part:
T

2
 L
2
 2E

a
C

s
F
2
L 4 ln  2 L  0.048
g

GLV Result
(1 )
( 1)


dp
dp
(1 )
Eabs   d 


d T 0 
 d
a sCF LT 2   2 L
6 ' (2) 

ln
1   E  2 

3 g E  T
 
Energy gain
Numerical Result for Energy Loss
• Intemediate large E,
absorption is important
•Energy dependence
becomes strong
•Very high energy E,
net energy gain can be
neglected
a S  0 .3
(0)
(1 )
(1 )
E  Eabs
 Eabs
 Erad
Parameterization of Jet Quenching
with Detailed Balance Effect
Average parton energy loss in medium at formation time:
dE
  0 ( E / 0  1.6)1.2 /(7.5  E / 0 )
dL 1d
Energy loss parameter
proportional to the initial gluon density
dN 1
0 
d  0RA2
Modified Fragmentation Function (FF)
Dh / c ( zc ,  2 , Ec )  (1  e
e
 L/
Dh0/ c ( zc' ,  2 )
 L/
z g' 0
zc' 0 ' 2
)[ Dh / c ( zc ,  )  L / 
Dh / g ( z g' ,  2 )]
zc
zc
(X. -N. Wang , PRC70(2004)031901)
zc'  pT /( pTc  Ec ), zg'  L /  pT / Ec ,
Light Quark Energy Loss
PHENIX,
Nucl. Phys. A757
(2005) 184
Theoretical results from the light quark energy loss
is consistent with the experimental data
II. Modification of Hadron Fragmentation Function
e-A DIS
e-
dW
dzh
   dx f ( x) H  ( x, p, q) Dqh ( zh )
q

dy ixp y  1
f q ( xB )  
e
p (0)  ( y  ) p
2
2
Frag.


1
H  ( x, p, q)  eq2 Tr   p    (q  xp )  2 (q  xp ) 2
2
 
zh dy  iph y / zh
Dqh ( zh )  
e
Tr 
0  q (0) ph , S

Func.
2 2
S
2

ph , S  q ( y  ) 0 

Modified Fragmentation Function
D( zh , Q2 )  D( zh , Q2 )  D( zh , Q2 )
Cold nuclear matter or hot QGP medium lead to
the modification of fragmentation function
Twist-four calculation
X.-N. Wang, X. Guo, NPA696 (2001); PRL85 (2000) 3591
e-
Modified Frag. Function in Cold Nuclear Matter
D( zh , Q2 )  D( zh , Q2 )  D( zh , Q2 )
a
Dq h ( zh , Q )  S
2
2
Q2

0
d
dz 
 zh 


(
z
,
x
)
D
L
q h 

z z 
 z 
h
2 1

4

Modified splitting functions
A
1  z 2 Tqg ( x, xL ) C A 2a S
 ( z, xL ) 

A
(1  z ) f q ( x)
Nc



(virtual)
Two-parton correlation:


 
dy

TqAg ( x, xL )  
dy1 dy2eixB p y A  (0) F ( y1 ) F  ( y2 ) ( y  ) A
2
2

 1 e
LPM
 ixL p  y2

1 e
ixL p  ( y1  y _ )

 ( y2 ) ( y   y1 )
Modified Frag. Function in Cold Nuclear Matter
Fragmentation function without medium effect:
0
Dh a ( z )
are measured, and its QCD evolution
tested in e+e-, ep and pp collisions
Fragmentation function with medium effect:
parton
E
hadrons
ph
D ( z)  Dh a ( z, E),
0
ha
Suppression of leading
particles
1
z
0
Dh a ( z, E ) 
D h a(
),
1  z
1  z
Heavy Quark Energy Loss in Nuclear Medium
B. Zhang, E. Wang, X.-N. Wang, PRL93 (2004) 072301; NPA757 (2005) 493
Mass effects:
1) Formation time of gluon radiation time become shorter
2 z (1  z )q
f  2
2
2
lT  (1  z ) M

LPM effect is significantly reduced for heavy quark
2) Induced gluon spectra from heavy quark is suppressed by
M
0  
“dead cone” effect
q
2
2
fQ/ q
lT
 0 4
4
[ 2
]  [1  2 ]
2
2
lT  z M

lT
 
q z
Dead cone Suppresses gluon radiation amplitude at    0
Heavy Quark Energy Loss in Nuclear Medium
~
2
2 ~
2
x
~
~
C
C
a
x
1

z
(
x

x
)
1
A
s
B
L
M
~
z gQ ( xB , Q 2 ) 
dz
d
x


L
~
N c Q 2 x A 0 z (1  z ) ~x
xL4

LPM Effect
M
1
~
{ c3 ( z, lT2 , M 2 )  (1  e  x
2
2
L
~
xL xB M 2
~
,
2
x A x AQ
1
xA 
mN RA
1) Larg x B or small Q 2 :
z gQ
~
CACa S2 xB
~
 RA
2
N c x AQ
2) Larg Q 2 or small x B :
z gQ
~
CACa S2 xB
2
~

R
A
N c xA2 Q 2
/ x 2A
)[c1 ( z, lT2 , M 2 )  c2 ( z, lT2 , M 2 )]}
Heavy Quark Energy Loss in Nuclear Medium
2
The Q dependence of
the ratio between charm
quark and light quark
energy loss in a large
nucleus
The x B dependence of
the ratio between charm
quark and light quark
energy loss in a large
nucleus
III. Jet Tomography of Strong Interaction Matter
E. Wang, X.-N. Wang, Phys. Rev. Lett. 89 (2002) 162301
Jet Tomography in Cold Nuclear Matter:
Quark energy loss = energy carried by radiated gluon
A
Q
Q
1
1
2
2
T
as
C
a
d 2T
1

(1

z
)
qg ( x, xL )
2
A s
zg   2  dz
z ( z, xL )   d T  dz
A
2
2
2
2

N
f
( x)

k
T
c
q
0
0
0
0
T
T
T
2
2


Energy loss
CA
1
2
E  Ca
mN RA 3ln
Nc
2 xB
2
s
E  A
2/3
Comparison with HERMES Data
~ 2
2
2
2
2
,
,
Q

3GeV
a
(
Q
)

0
.
33
C(Q )  0.0060GeV
s
HERMES Data: Eur. Phys. J. C20 (2001) 479
Expanding Hot Quark Gluon Medium


 
dy

TqAg ( x, xL )  
dy1 dy2eixB p y A  (0) F ( y1 ) F  ( y2 ) ( y  ) A
2
2

 1 e
 ixL p  y2

1 e
ixL p  ( y1  y _ )

y
~  dy  g  ( y ) 1  cos
A
f q ( x)
f

TqgA ( x, xL )
2
 2E 
E  a  d  ( ) ln  2 
  
0
R
3
s




 ( y2 ) ( y   y1 )
R. Baier et al
Initial Parton Density and Energy Loss
 2E 
E  a  d  ( ) ln  2 
  
0
R
3
s
2 0
E1d  E0
RA
jet1
E0 :
jet2
0
 ( )   0  ( R  r )

 0  0.1 fm
 dE 

  0.5 GeV/fm
 dx 1d
Initial energy loss in
a static medium with
density 0
RA 
15
2 0
 dE 
   14.6 GeV/fm
 dx  0
Initial parton density (Energy loss ) is
15~30 times that in cold Au nuclei !
Comparison with STAR data
STAR, Phys. Rev. Lett. 91 (2003) 172302
Tomography of Jet quenching in QGP Medium
in NLO
1) Single jet  Single hadron spectra
2) Dijet  Hadron-triggered away-side hadron spectra
3) Gamma-jet  Photon-triggered away-side hadron spectra
Single jet
Dijet
Gamma-jet
Surface Emission of Single Hadron Production
H. Zhang, J. F. Owens, E. Wang and X.-N. Wang , Phys. Rev. Lett. 98 (2007) 212301
y
Single hadron
x
emission surface
parton jet
 0  1.68GeV / fm
y  0 fm
completely suppressed
corona
thickness
Surface Emission + Punch-through jet in Dihadron Production
y
triggered hadron
x
associated hadron
 0  1.68GeV / fm
x  0 fm
partonic di-jet
tangential
Color strength = dihadron yield from
partons in the square
punch-through jets
25% left
Prediction at LHC
Fixed  0  5.0GeV / fm At LHC
Surface emission bias
single hadron
dihadron
punch-jets
Gamma-jet by NLO pQCD parton model
d
AA
 TAB  PDFs d  FFs
LO (tree level):

pT

pT
Jet
T
NLO corrections: (e.g. 23)
Jet2
T
p
Jet1
T
p
p
pTJet  pT

Fix triger: pT
Jet
T
p
Jet
T
p

 pT ,

 pT
pTJet  pT
pTJet  One of ( pTJet1, pTJet2 )
pTh hadrons with transverse momentum
zT  
pT may be larger than that of the photon
Gamma-Hadron Suppressions Factor
I AA ( zT )  DAA ( zT ) / D pp ( zT )
1) NLO radiative
corrections lead to
hadrons with z_T>1,
surface emission,
2) z_T<0.6, volume emission,
more sensitive to \eps_0
3) 0.6<z_T<1.4, competition
of two mechanisms of
hadron emssions.
4) Similarity in value
between I_AA for
dihadron and Gamhadron.
H.Z. Zhang, J.F. Owens, E. Wang and X.-N. Wang , PRL 103 (2009) 032302
Tomography of surface and volume emissions
zT  0.9
zT  0.3
1) The spatial transverse
distribution of the initial
Gama-jet production vertexes
that contribute to the Gamahadron pairs with given values
of z_T.
2) The color strength : Gamahadron yield
3) Projections of the contour
plots onto y-axes .
At large z_T, jet emissions in the
outer corona, no energy loss.
At small z_T, jets emisions near the
center of the medium, energy loss.
IV. An explanation of heavy quark energy
loss puzzle
Flow
QGP system is not static, it is a expanding system
Y
Reaction
plane
Flow
X
QED:
QCD:
Static Charge: Coulomb electric field
Static Target: static color-electric field
Moving Charge: electric and magnetic field
Moving Target: color-electric and colormagnetic field
Puzzle for Heavy Quark Energy Loss
Heavy quark has less dE/dx due
to suppression of small angle
gluon radiation
“Dead Cone” effect
B. Zhang, E. Wang, X.-N. Wang,
PRL93 (2004) 072301
Y. Dokshitzer & D. Kharzeev
PLB 519(2001)199
a sCF d k2 dk2
dP0
dP 

2
2 2 2
  (k   0 ) (1  02 /  2 )2
0 
M
k
,  
E

J. Adams et. al,
PRL 91(2003)072304
M. Djordjevic, et. al.
PRL 94(2005)112301
No Significant Difference Between
Heavy Quark Jet and Light Quark Jet
Non-photonic electrons
from heavy quark decays
Charged hadrons from
Light quark fragmentation
STAR
Interaction Potential with Flow
' system fixed at target parton:

Static potential

V 'n  2 (q' )v(q'n )Tan (R) Tan (n)
0
n

A'n  0

4as
v ( q 'n )   2 2
q 'n  
 system for observer:
Lorentz boost from ' system
 
0
0
q ' n   ( qn  v  qn )

  1   
0
q 'n  qn  2 (v  qn )v  qn v
v

1
2
1 v
 
Vn   (V 'n v  A'n )

  1   

An  A'n  2 (v  A'n )v  V 'n v
v
New Model Potential with Flow
 

 iqn  xn
0   ~ 
V n(qn , xn )  2 (qn  v  qn )v (qn )e
Tan ( R)  Tan (n)

 

iqn  xn 
0   ~ 
An (qn , xn )  2 (qn  v  qn )v (qn )e
v Tan ( R)  Tan (n)

4as
~
v ( qn )   2   2
2
qn  (v  qn )  
 

Four-vector potential : Aflow  (Vn (qn , xn ), An (qn , xn ))

The features of the new potential:
1) Collective flow produces a color-magnetic field



An (qn , xn )  v
 
2) non-zero energy transfor: q  v  qn
0
n
Dead Cone Reduce Significantly with Flow
Dead Cone:
Reason: Collective flow changes the poles of the propagator
Energy Loss vs. Flow Velocity
Average Flow Velocity
and Effective Average Energy Loss
Average Flow Velocity:
3D ideal Hydrodynamic simulation for 0-10% central
events of Au-Au collisions at RHIC energy:
Effective Average Energy Loss:
Numerical Results of Effective Average Energy Loss
3D ideal Hydrodynamic simulation for 0-10% central
events of Au-Au collisions at RHIC energy
V. Summary and Discussion
1) Jet can be used as a hard probe to explore the QGP.
2) Jet quenching lead to modification of hadron fragmentation
function, which result in the suppression of high transverse
momentum spectra observed in experiment.
3) Different tomography picture of the QGP for single jet, dijet
and gamma-jet: surface vs. volume emission.
4) New potential for the interaction of a hard jet with the parton
target has been derived. Collective flow reduce significantly
the dead cone from mass effect for heavy quark jet. Heavy
quark energy loss increase obviously in the presence of
collective flow. An explanation of heavy quark loss puzzle is
given in the framework of jet quenching theory.
Discussion
1) Dihadron azimuthal correlations in head-on collisions in
AMPT :
Talk this afternoon by Qingjun Liu
2) Multiple parton scattering and modified fragmentation
function in medium :
Talk this afternoon by Weitian Deng
3) Gamma-jet tomography of high-energy nuclear collisions in
NLO pQCD :
Talk this afternoon by Hangzhong Zhang
Thank You