Transcript Rapidity Asymmetry in d+A Collisions

Jet Quenching Physics
Enke Wang
(Institute of Particle Physics, Huazhong Normal University)
I. Jet Quenching in QCD-based Model
II. Jet Quenching in High-Twist pQCD
III. Jet Tomography of Hot and Cold Strong
Interaction Matter
IV. Modification of Dihadron Frag. Function
Fragmentation Function
d e e h (Q 2 )
dzh
1 e4
dW 

L
4 
2s q
dzh
   0qq (Q 2 )[Dqh ( zh , Q 2 )  Dqh ( zh , Q 2 )]
2 2
q
ph
4 eq
qq
2
zh  
 0 (Q )  N c
p
3Q 2
Dqh ( zh , Q2 ) 
2
Q Evolution: DGLAP Equation
Jet
Quenching:
E
Leading
particle
suppressed
leading
particle
hadrons
hadrons
q
q
q
hadrons
leading
particle
E '  E  E
q
hadrons
leading
particle
suppressed
A-A collision
p-p collision
Modification of Fragmentation Function:
Dqh ( zh , Q2 )
zh  zh  zh
ph
q
p
~
2
2
2



Dqh ( zh , Q )  Dqh ( zh , Q )  D( zh , Q )
~
S
28 YEARS AGO
I. Jet Quenching in QCD-based Model
G-W (M. Gyulassy, X. –N. Wang) Model:
Static Color-Screened Yukawa Potential
Opacity Expansion Formulism (GLV)
GLV, Phys. Rev. Lett. 85 (2000) 5535; Nucl. Phys. B594 (2001) 371
Elastic Scattering
Double Born
Scattering
First Order in opacity Correction
First Order in opacity Correction
Induced gluon number distribution:
Non-Abelian
LPM Effect
dN (1)
CRs 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
Radiated Energy Loss vs. Opacity
First order in opacity correction is dominant!
Detailed Balance Formulism (WW)
E. Wang & X.-N. Wang, Phys. Rev. Lett.87 (2001) 142301
B-E Enhancement Factor
Thermal Distribution Func.
1+N(k)
N(k)
k
k
x0
p
Stimulated Emission
x0
p
Thermal Absorption
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 
 sCF T 2  4ET
6 ' (2) 
ln 2  2   E  2 

3 E 
 
Stimulated emission increase E loss
Thermal absorption decrease E loss
First Order in Opacity Correction
Single direct rescattering:
k
y0
k
y1
p
y0
y1
p
y0
y1
p
k
Double Born virtual interaction:
k
k
y0
y0
y0
y1
y1
y1
y1
y1
y1
p
p
p
y0
y1
y1
k
Key Point: Non-Abelian LPM Effect—destructive
Interference!
p
k
Energy Loss in First Order of Opacity
Energy loss induced by rescattering in thermal
(1 )
(1 )
medium:
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


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
 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
 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 ,
Comparison with PHENIX Data
PHENIX,
Nucl. Phys. A757
(2005) 184
II. Jet Quenching in High-Twist pQCD
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
Jet Quenching in e-A DIS
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 )

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 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

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
~
CAC S2 xB
~
 RA
2
N c x AQ
2) Larg Q 2 or small x B :
z gQ
~
CAC 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 Hot and Cold Strong
Interaction Matter
E. Wang, X.-N. Wang, Phys. Rev. Lett. 89 (2002) 162301
Cold Nuclear Matter:
Quark energy loss = energy carried by radiated gluon
A
Q
Q
1
1
2
2
T
s
C

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  C
mN RA 3ln
Nc
2 xB
2
s
E  A
2/3
Comparison with HERMES Data
~ 2
2
2
2
2
,
,
Q

3GeV

(
Q
)

0
.
33
C(Q )  0.0060GeV
s
HERMES Data: Eur. Phys. J. C20 (2001) 479
Initial Parton Density and Energy Loss
 2E 
E    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
IV. Modification of Dihadron Frag. Function
A. Majumder, Enke Wang, X. –N. Wang, Phys. Rev. Lett. 99 (2007) 152301
Dihadron fragmentation:
h1
h1
h2
jet
h2
DGLAP for Dihadron Fragmentation
h1
h1
h2
h2
h1
h2
Dhq1h2 ( z1 , z2 , Q 2 )
 ln Q
2
1


z1  z2
1 z2


z1
dy
z1 z2 2
q
P
( y ) Dh1h2 ( , , Q )  ( g  h1h2 )
2 q  qg
y
y y
dy ˆ
z
z
Pq qg ( y ) Dhq1 ( 1 , Q 2 ) Dhg2 ( 2 , Q 2 )  (q  g )
y (1  y )
y
1 y
Evolution of Dihadron Frag. Function
Evolution of Dihadron Frag. Function
h1h2
q
D
( z1, z2 )  D ( z1 )D ( z2 )
h1
q
h2
q
Medium Modi. of Dihadron Frag. Function
Nuclear Modification of Dihadron Frag. Func.
A
2h
1
2h
N ( z2 )
R2h ( z2 ) 
N ( z2 )
e-A DIS
Hot Medium Modification
Thank You