Transcript Resummed QCD Power Corrections to F2

Jets in Nuclear Collisions
Ivan Vitev
ISMD 2004, July 26 - August 1, 2004
Sonoma County, California, USA
July 28, 2004
1
Ivan Vitev, LANL
Outline of the Talk
 Measurements of jets in nuclear collisions:
 Determination of the jet properties from the near-side and
away-side di-hadron correlations.
 Baseline jet results in the vacuum:
 Quark and gluon jet widths
 Quark and gluon jet multiplicities
 Modification of jet properties in cold and hot
nuclear matter :
Elastic: Transverse momentum diffusion. Broadening of the
away-side correlation function. Acoplanarity
Inelastic: QCD radiative energy loss. Jet quenching
Modification of the jet multiplicities and the
back-to-back jet correlations
Coherent: Power corrections
 Conclusions:
July 28, 2004
2
Ivan Vitev, LANL
Clean Jets in DIS and e+, e-
C.C. example
Jets in DIS
Jets in p+p
(Single clean jet)
July 28, 2004
3
Ivan Vitev, LANL
Jets in A+A Reactions
The complication at the RHIC (STAR)
The complication in heavy ion reactions
Infinite multiplicities to deal with
Globally correlated underlying event (v2)
So far STAR uses a jet reconstruction algorithm
Jets in nuclear collisions
The complication at the Tevatron (D0)
July 28, 2004
4
Ivan Vitev, LANL
Di-hadron Correlations
G.Altarelli, R.K.Ellis, G.Martinelli, Phys.Lett. 151B (1985)
j y
k y
j y
Hadron 1
Hadron 2

• Vacuum: intrinsic, NLO corrections, soft gluon resummation
• Medium: transverse momentm diffusion
• Fragmentation: not collinear, a jT kick to the hadron
Di-hadron correlation function:
Relative to
 (   ) :
hh
1 dN 1 2 dijet ( y1  y2 ) ANear ( y1  y2 )  2 / 2 2 Near AFar ( y1  y2 )  (   )2 / 2 2Far
C2 ( ) 

e

e
Ntrig
d 
2 Near
2 Far
If AFar ( p  p)  1
then
AFar ( p  A, A  A)  Rh1h2 ( pT )
Relate the widths and the momentum measures
2

2

July 28, 2004
 Near 
jTy
pT assoc
1  xh2 , xh 
 1
 pT assoc

 Far  tan 1 
pT assoc
j y
pT trig
2
2 ztrig
kTy
2
xh2  1  xh2  jTy
5

2
1

j2
k y

1

k2

pT hadron
,
z


pT parton

Ivan Vitev, LANL
Analytic Multiplicity Results
Q
~ tp
2
k
Double ordering
tc

ki
 (t )
  log s p , zi  
0
 s (tc )
ki 1
2
 s (t ) 
See e.g. Field and Feynman,
Dokshitzer et al.
4
0 log(t /  2 )
8
aq , g  , 6
3
aq, g  n log n (1/ z0 )
n
Pn (tc , t p , z0 ) 
• The probability to emit n gluons:
 n P (t , t , z )    I (  )

 
,
P
(
t
,
t
,
z
)
2
I
(

)
 

n
• Average gluon number:
n !n !
c
p
0
n
Ng
1
n
c
p
n
0
  2 aq , g log(1/ z0 )
0
Experimentally 1.54 +/- …

lim z0 0 N g     aq , g log(1/ z0 )
2
Ng
Key
lim z0 0
Ng
result
Relative to naive
July 28, 2004
g  jet
q  jet

ag
aq
Ng
g  jet
Ng
q  jet


CA 3

CF 2
CA 9

CF 4
6
Z0 mass scale
Ivan Vitev, LANL
Angular Distribution
The LDLA
CR s 1
1 d
kT2
 CR s
2
2
2
2 
(
Q
,
k
)


2
log
exp

log
(
k
/
Q
)
T
T

 0 dkT2
2 kT2
Q2
 2

• The final kT distribution of the jet. Gives by momentum
conservation information for the distribution of gluons
• Definite shortcomings
1
kT2  0
(very broad)

0

 dk
2
T
0
1 d
(Q, kT2 )  1
2
 0 dkT
kT
Normalization and mean kT2
kT



1 d

2CR s
2

  dk k
(
Q
,
k
)

1

e
1  Erf
T
2


dk
2
C

0
T
0
R s


Q
2
2
2
d
dkT2
2



 2CR s
  2
CR s 2
2
Q
   Q , lims 0 kT 


  
• In the limit of small coupling
 g  jet
Key
lim 0
 lim 0
result
q  jet
s
s
The OPAL experiment:
Within 4% of the jet axis
July 28, 2004
kT
2
kT
2

g  jet
q  jet

CA 3

CF 2
17% of g-energy
30% of q-energy
7
Ivan Vitev, LANL
pT Diffusion in Nuclei
zn zn
zn
+
qn , an qn , an
qn , an
†ˆ
†
ˆ
ˆ
ˆ
ˆR  D
n
n Dn  Vn  Vn
zn
+
qn , an
qn , an
qn , an
n = c = L/ l
¥
dN ( p) =
f
¥
å
dN ( p) =
n
n= 0
å
n= 0
n
cn - c
1 d s el - qi ^ .Ñ p ^
-q ¶
2
e ò Õ d qi
e
Ä e iP pP )dN i ( p)
(
2
n!
s el d qi
i= 1
Incoherent local Glauber. Elastic application
Additional approximation for a Gaussian form
dN
dN
i
d 2q
ö
mb
1 æ
m2b2
3 ÷
ç
=
K
(
m
b
)
»
1
x
+
O
(
b
)
÷
ç
÷
4p 2 1
4p 2 çè
2
ø
k2
-
Before the hard scatter
Summary
pair

July 28, 2004
k
D k 2 = 2c m2 x
x = log 2 / (1.08mb)
L
2
2
1 e cm x
dN (k ) =
,
2p c m2 x
i
k
d s el (b)
f
2
vac
1
2
  1  tanh 2 yi  k
i 2
kT
2
IS
2
 2
L
q, g
kT
2
FS
After the hard scatter

2
2
L

q , g


2
g
2 3CR s 1 dN ln L

2
A dy
0

Cold
Hot 1+1D
i nucl
8
Ivan Vitev, LANL
d+Au and Au+Au
J.W.Qiu, I.V., Phys.Lett.B 570 (2003); hep-ph/0405068
From: <z> = 0.75, <|kTy|>pp = 1.05 GeV
<|kTy|>pA = 1.25 GeV
p+A
• The vacuum broadening is large
• Cold nuclear matter – only a small effect
• Hot nuclear matter – seems insufficient
<z><|kTy|>AA = 1.25 - 1.45 GeV
A+A
2.5pTtrigg4.0, 1.0pTassoc2.5
Feedback?
pp: <z><|kTy|>
pp: <|jTy|>
J.Rak, hep-ex/0403038
P.Constantin, N.Grau
July 28, 2004
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Ivan Vitev, LANL
Medium Induced
Non-Abelian Energy Loss
Rˆ =
zn
qn , an
+
qn , an
qn , an
Iterative solution
M.Gyulassy, P.Levai, I.V., Nucl.Phys.
B594 (2001); Phys.Rev.Lett.85 (2000)
• Explicitly the Landau-
qn , an
+
qn , an
qn , an
Interplay of formation times and medium size

n1,2,...
z / l f
Pomeranchuk-Migdal
destructive interference
effect in QCD
• Incorporates finite
kinematics and small
number of scatterings
• Applicable for realistic
Inverse formation
times
systems
Color current
propagators
Also see R. Baier et al.,
B. Zakharov, U. Wiedemann,
X.N. Wang
July 28, 2004
zn
zn
zn
10
Ivan Vitev, LANL
Radiative Spectra
The basis for jet tomography – the extraction of the
density of the medium

E  I   dt t  (t , x0  vˆ(t  t0 ))
Isospin symmetry
Parton-hadron duality
t0
E
(1)
dN g 3 dN ch d

dy
2 d dy
CR  s 2L2
2E

Log 2
 ... ,
4
g
 (L)L

Static medium
3
E
(1)
9CR  s
1 dNg
2E

L
Log 2
 ... ,
4
A  dy
 (L)L

2 / 
dN g / dy
Small and finite
1+1D Bjorken
- transport coefficient
- effective gluon rapidity
density
B.Back et al., Phys.Rev.Lett. 88 (2002)
Estimate:
17 GeV
g
July 28, 2004
dN
dy
62 GeV 200 GeV
 550,
850, 1100
11
I.V., nucl-th/0404052
Ivan Vitev, LANL
The Basic pQCD Process
 A1/ 3 
 2 
 Q 
Extended to include
power corrections
N
J.Collins, D.Soper, G.Sterman, Nucl.Phys.B223 (1983)
J.W.Qiu, I.V., hep-ph/0405068
One way of implementing radiative
energy loss:
 : pc  pc (1   ), z 
 1
1
 d P( ) 1   D  1   z, Q
Deff ( z, Q2 )
2
X
P
ph
z

pc
1 



P’
d
pd
zd
{
xaP
Pd / zd
xbP’
Pc / zc
X
0
• Single inclusive hadron production
h1
d s NN
dy 1d 2 pT 1
=
å
abcd
1
1
a s2
ò dxa ò dxbf (xa )f (xb ) (xa x S )2 M
b
x min
x min
a
b
2
ab® cd
Dh
1
/c
(z 1 )
Pc
Pd
0
z1
• Double inclusive hadron production (most of what will be discussed)
d s Nh1Nh2
2
2
dy 1dy 2d pT 1d pT 2
July 28, 2004
d(D j - p )
=
å
pT 1pT 2 abcd
1
ò
dz 1
Dh
z1 min
12
1
/c
(z 1 )
Dh
z1
f (x a )f (xb ) a s2
(z 2 )
M
/d
2
xa xb
S2
2
ab® cd
Ivan Vitev, LANL
The E-loss Connection
The plasmon
frequency forces
radiation in fewer
semi-hard gluons
S.Pal, S.Pratt, Phys.Lett.B574 (2003)
25-40% increase
in the multiplicity
Factor of
2 in mult.
600 MeV
Poisson approximation
• Increase in the jet multiplicity
2 GeV
• In the approximations used the
medium induced multiplicity
scales as N g g  jet C 9
Ng

q  jet
A
CF

4
• One can hopefully establish the
subsequent rescattering and
thermalization of the gluons
July 28, 2004
13
Ivan Vitev, LANL
Jet Quenching and
Jet Tomography
d 2 AA / dpT d
RAA ( pT ) 
Nbin d 2 NN / dpT d
• Attenuation of the inclusive hadron spectra
• Extraction of the soft underlying parton
density (bulk matter)
• In jet algorithms – a need for hard pT cut
I.V., nucl-th/0404052
SPS relative to D.d’Enterria, nucl-ex/0403055
S.S.Adler, et al., Phys.Rev.Lett.91 (2003)
I.V., M.Gyulassy, Phys.Rev.Lett. 89 (2002)
July 28, 2004
14
Ivan Vitev, LANL
Centrality Dependence of
Jet Quenching
dN h pp
1
dN h AA
1

D
(
z
),

Dn / p ( z )
n/ p
neff
neff
2
dyd 2 pT
dy
d
p
pT
( pT  Z pT )
T
RAA 
E  N part , 1  1D
2/ 3
1
n
(1  Z pT / pT ) eff
central
peripheral
G.G.Barnafoldi et al., hep-ph/0311343
July 28, 2004
X.N.Wang, nucl-th/0305010
15
Ivan Vitev, LANL
Modification of the
Jet-like Correlations
RAA
h1h2
d 2 AA / dpT 1dpT 2 d1d2
( pT ) 
Nbin d 2 NN / dpT 1dpT 2 d1d2
hh
1 dN 1 2 dijet ( y1  y2 )
C2 ( ) 
Ntrig
d 

ANear ( y1  y2 )
2 Near
e
2
/ 2 2 Near

2
2
AFar
e (   ) / 2 Far
2  Far
In triggering on the near side all effects
are taken by the away side correlation
function
hh
h
R 1 2 / R 1 ~ 1.5
• The attenuation of the double inclusive
hadron production is between the two
naïve limits R h1h2 / R h1 ~ 1 , Rh1h2 / Rh1 ~ 2
• Attenuation (disappearance) of the away-side
correlation function
• Dependence relative to the reaction plane
July 28, 2004
Jet 2
16
Jet 1
Ivan Vitev, LANL
Conclusions
 Jet tomographic and jet quenching studies in heavy ion collisions
have rapidly developed as one of the most exciting and successful
directions in RHIC and LHC physics
Relate to: Spectra, jets and di-hadron correlations
 The propagation of jets through cold and hot and dense nuclear
matter results in calculable modifications to the pQCD factorization
approach
 A multitude of novel observable effects are predicted and
observed at RHIC and expected at the LHC:
- Strong suppression of the simple and double inclusive hadron
cross sections (4-5 times for single), (5-7 times double)
- Broadening and disappearance jet-jet correlations. Dependence
on centrality and orientation relative to the reaction plane
- Redistribution of the lost energy into the system
- Increase of the jet multiplicities by 30% to 100%
- Broadening of the jet cone (small)
July 28, 2004
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Ivan Vitev, LANL
A. Predictive Power of pQCD
•
Factorization theorem:
J.Collins, D.Soper, G.Sterman,
Nucl.Phys.B223 (1983)
Scale of hadron wave function:
 1/ fm 200 MeV
Scale of hard partonic collision: Q  1 GeV , 1/ Q  0.2 fm
Factorization:
 Hadron (Q)  Parton / hadron ()  Parton (Q)
Process-dependent:
Process-independent:
•
 Hadron (Q),  Parton (Q)
Parton / hadron ()
Predictive power: Universality of Parton / hadron ()
Infrared safety of  Parton (Q)
•
Systematically addresses the deviations:
Power corrections
Radiative energy loss
July 28, 2004
18
(dynamical nuclear shadowing)
(jet quenching)
Ivan Vitev, LANL
Basic pQCD Processes (I)
•
DIS:
All orders
1
F1 ( x, Q )   Q 2f  d 0eix0
2 f
2

J.Collins, D.Soper, G.Sterman,
Nucl.Phys.B223 (1983)
p  (0) E (0)
1
Q 2f  f ( x, Q 2 )  O ( s )

2 f

2p
E † (0 )  (0 ) p

k
xP
P
F2 ( x, Q2 )  2xF1 ( x, Q2 )
Eikonal line.
Disappears in A+ = 0
Extended to
 A1/ 3 
 2 
 Q 

k
’
X
…
N
• Drell-Yan:
corrections in e()+A
All orders
J.W.Qiu, I.V., hep-ph/0309094
X
P

G.Bodwin, Phys.Rev. D31 (1985)
DY
d s NN
dq 2
1
=
å ò
f
xa min
( B orn )
ds
dq2
July 28, 2004
1
ò
dx adx b f (x a )f (x b )
d s ( Born ) (x a p, x b p ¢, q 2 )
x aP
dq 2
xbP’
xb min
2
= Q f2
4p a
2
2
¢
d
q
(
x
p
+
x
p
)
(
)
a
a
3N cq2
19
P’


X
Ivan Vitev, LANL
Basic pQCD Processes (II)
•
Hadron production in N+N:
2
Q
ln 2

1
Q2
Factorization: at leading power
and leading power corrections
A 
 2 
Q 
1/ 3
Extended to
X
P
J.Collins, D.Soper, G.Sterman, Adv.Ser.Dir. 5 (1988)
J.W.Qiu, G.Sterman, Nucl.Phys.B353 (1991)
N
P’
in p+A corrections
d
pd
zd
{
xaP
Pd / zd
xbP’
Pc / zc
0
J.W.Qiu, I.V., hep-ph/0405068
X
• Single inclusive hadron production
h1
d s NN
dy 1d 2 pT 1
=
å
abcd
1
1
a s2
ò dxa ò dxbf (xa )f (xb ) (xa x S )2 M
b
x min
x min
a
b
2
ab® cd
Pc
Dh
1
/c
Pd
0
(z 1 )
z1
• Double inclusive hadron production (most of what will be discussed)
d s Nh1Nh2
2
2
dy 1dy 2d pT 1d pT 2
July 28, 2004
d(D j - p )
=
å
pT 1pT 2 abcd
1
ò
dz 1
Dh
z1 min
20
1
/c
(z 1 )
Dh
z1
f (x a )f (xb ) a s2
(z 2 )
M
/d
2
xa xb
S2
2
ab® cd
Ivan Vitev, LANL
Particle Production
• Fragmentation:
natural near-side and away-side correlations
• Relativistic hydrodynamics:
Cooper-Frye formula
After solving
From an uncorrelated evolved fluid
• Coalescence models:
Folding the quark Wigner
functions and the meson
or baryon wave functions
E
dN M
P u
  d
dx w ( R, xP  ) w ( R,(1  x) P  ) M ( x)
3
3 
d P  (2 )  , 
E
2
dN B
P u




d

dx
dx
'
w
(
R
,
xP
)
w
(
R
,
x
'
P
)
w
(
R
,
(1

x

x
')
P
)

(
x
,
x
'
)




B
d 3 p  (2 )3  ,  , 
• Saturation gluon fussion models:
2
Folding two gluon
distributions into
one gluon (particle)
These mechanisms don’t have natural don’t have natural correlations
July 28, 2004
21
Ivan Vitev, LANL
L
L  0
 R  M D
R
M DT 

MR 
The Fragmentation
Seesaw Analogy
SM + right handed neutrino with
large Majorana mass
Gell-Mann, Slansky, Yanagida
M  M DT M R1M D
A much simpler analog of the interplay between
light and heavy, small and large
To lowest order and leading twist
pT 1
z1

pT 2
z2
Provides a new way of testing the
fragmentation picture, the factorization
approach and the deviations
July 28, 2004
22
Ivan Vitev, LANL
LO pQCD Example
Calculated as in: J.W.Qiu, I.V., hep-ph/0405068
• Perturbative unbiased calculation
• Clear anti-correlation between
pT assoc and ztrig .
(Not the naïve
expectation that triggering fully fixes
the near side.)
• Novel way of studying the pQCD
2 to 2 hadron production mechanism.
Distinguish from the alternatives
July 28, 2004
23
Ivan Vitev, LANL
B. Motivation: Deviations
from Hard Scaling
Examples:
200, 62 GeV Au+Au;
200 GeV d+Au
d 2 N AA / dpT d
RAA ( pT ) 
TAAd 2 NN / dpT d
AA
<Nbinary>/inelp+p
nucleon-nucleon
cross section
• Quenching
• Shadowing
Rapidity dependence,
centrality dependence
July 28, 2004
• Acoplanarity
24
Ivan Vitev, LANL
Acoplanarity
• Consider di-hadron correlations associated with hard
(approximately) back-to-back scattering
 (   )  0
Vacuum: intrinsic, NLO corrections, soft gluon resummation
Medium: transverse momentm diffusion
j y
Di-hadron correlation function
hh
1 dN 1 2 dijet ( y1  y2 )
C2 ( ) 
Ntrig
d 

ANear ( y1  y2 )
2 Near
e
2
/ 2 2 Near
2
2
AFar
e (   ) / 2 Far
2  Far

Relate the widths and the momentum measures
2

2

 Near 
 Far
j y
July 28, 2004
jTy
pT assoc
1  x , xh 
2
h
 1
 tan 
 pT assoc

1

1

j2
2
trig
2z
k y
pT assoc
pT trig
2
kTy

1

x  1  x
2
h
2
h
k2
25

jTy
2


 If
K
k y
AFar ( p  p)  1
AFar ( p  A, A  A)  Rh1h2 ( pT )
Ivan Vitev, LANL
Experimental Results
(Approximate representation of the
theoretical calculation in the Figures)
• Qualitative and somewhat quantitative agreement
• Indicates the need for a possibly stronger
Cronin effect
• Systematic error bars should be taken seriously
• Beware of baryon/meson ratios (I wouldn’t attempt
to fit baryons below 4-5 GeV)
Similar results: (h+,h-) by PHOBOS and STAR. (BRAHMS?)
July 28, 2004
26
DIS Coherence
Hard part
Matrix element
d lh 4 em 1  y 2
mN xy 

2
2 

2
x
F
(
x
,
Q
)

1

y

F
(
x
,
Q
)
1
2


dxdy
Q 2 xy  2
2E 



1
xp  
( xi p  q)  i
i
2 p  xi  x  i
Q2
Factorization approach: separate the short
sistance computable dynamics from the long
distance matrix emenets.
Final state effect
• Lightcone gauge:
• Breit frame:
2D lightcone dynamics
A  n  A  0
First coherent calculation
n  [1,0,0 ], n  [0,1,0 ]
Q2
Q2

q   xp n 
n, p  np , xp  q 
n
2 xp 
2 xp 

July 28, 2004
27
Pole – on-shell, long distance
No pole – contact, short distance
J.W.Qiu, Phys.Rev. D42 (1990)
Ivan Vitev, LANL
Resummed
Power Corrections

n 1
PA  (0)   (0 )  Fˆ 2  0    d i  (i ) Fˆ 2 (i ) PA
2p
i 1
Oˆ j
ˆ
O
i
ˆ
O
0
Dynamical generation of a parton’s
mass in the final state
x
(pole-separated, long-distance)
 3 s (Q 2 ) 
ˆ 2 ( ) p
 
p
F

i
2
8
r
0


2
1
lim x 0 xG  x, Q 2 
2
Scale of power corrections (geometric and
vertex factors, two gluon correlation function)
U-quark, CTEQ5 LO
Simple analytic formula:
n
A   2 ( A1/ 3  1)  n d n FT( LT ) ( x, Q 2 )
x 2 ( A1/ 3  1) 2 
A
2
( LT ) 
FT ( x, Q )   
x
 A FT  x 
,Q 

2
n
2
Q
d x
Q
n 0 n ! 
2


4
FLA ( x, Q2 )  A FL( LT ) ( x, Q2 )  2 FTA ( x, Q 2 )
QM shift operator
Q
N
July 28, 2004
28
Ivan Vitev, LANL
Numerical Results
Generated by the
multiple final
state scattering
of the struck quark
Q2 dependence,
Longitudinal SF
 L FL ( x, Q2 )
R( x, Q ) 

 T F1 ( x, Q2 )
2
• For Q2  0 we impose Q  mN .
(discussion of O( sn ) corrections will follow)
2
2
• Compares well to the EKS98 scaledependent shadowing parameterization.
J.W.Qiu and I.V., hep-ph/0309094
July 28, 2004
29
Ivan Vitev, LANL
+A Reactions
and Mass Corrections


mN xy  W 
d  , cc  y 2
y2  W 

W
2
2
2
  2 xF1 ( x, Q )  1  y 
 F2 ( x, Q )   y   xF3 ( x, Q ) 
dxdy
2
2
E
2 





- Axial and vector part (weak current)
Special propagator structure:
- Similarly for the neutral current
( xp  q)  i
- Helps us understand charm and
bottom in heavy ion collisions
xB  
p 
p
Q2
xB xM p    (Q 2 / 2 xB p  )   M
i 2
Q
x  ( xB  xM )  i
  p  M      p  M   0
  p      p   0
• Equations of motion - nuclear enhanced power corrections and mass corrections
commute


( W )
2
2
2
F1,3 ( xB , Q )  2 A   | VDU | D ( xB  x 2  xMU )   | VUD | U ( xB  x 2  xM D )  ,
U ,D
 D,U



( W  )
F1,3 ( xB , Q2 )  2 A   | VUD |2 U ( xB  x 2  xM D )   | VDU |2 D ( xB  x 2  xMU )  ,
D ,U
 U ,D


July 28, 2004
30
M2
xM  xB 2
Q
x 2  xB
 2 ( A1/ 3  1)
Q2
Ivan Vitev, LANL
F2(x,Q2) and xF3(x,Q2)
QCD Sum Rules
Valance quark shadowing and QCD sum rules: examples where dipole models will fail
J.W.Qiu, I.V., Phys.Lett.B 587 (2004)
Testable at the Fermilab
NuMI facility
J. Morfin, J.Phys.G 29, (2003)
sea ( x)  x , sea 1.0
val. ( x)  x , val. 0.5
1
1
SGLS   dx
0

3
10
Q2
20

1
N
N
xF3 ( x, Q2 )  xF3 ( x, Q2 )  3(1  GLS )
2x
sea
D.J.Gross and C.H Llewellyn Smith ,
Nucl.Phys.
14 (1969) 587 (2004)
J.W.Qiu,
I.V.,BPhys.Lett.B
val .
 2  0.09  0.12 GeV 2
July 28, 2004
31
Ivan Vitev, LANL
p+A Collisions
Resum the multiple final state scattering
of the parton “d” with the remnants of
the nucleus
( )
A
p
Starting point: LO pQCD
• Maximum coherent rescattering of the small x b parton in the

h1
d s NN
dy 1d 2 pT 1
nucleus
• Other interactions: less coherent (elastic) and sppressed at
forward rapidity by a large scale 1/u, 1/s
+,1
=
å ò
abcd z min
1
h1h2
d s NN
dy 1dy 2d 2 pT 1d 2 pT 2
dz 1
Dh
/c
1
(z 1 )
z 12
d(D j - p )
=
å
pT 1pT 2 abcd
1
f (x a )
1
a s2
ò xa xa x aS + U / z S
1
x min
ò x d(x
a
1
ò
z1 min
dz 1
Dh
1
/c
z1
32
b
f (x a ) a s2
(z 2 )
/d
2
xa S 2
F (xb ) =
f (xb )
xb
b
- x b ) F (x b )
0
(z 1 )
Dh
Isolate all the xb dependence of the integrand:
July 28, 2004
1
1
ò x d(x
b
b
- x b ) F (x b )
0
M
2
ab® cd
Ivan Vitev, LANL
Numerical Results
  dx  ( x
N  0, 
b
b
• Similar power corrections
modification to single and double
inclusive hadron production
 xb ) F ( xb ) 


 2 1/ 3
dx

(
x

x
)
F
x

x
C
(
A

1)

 b b b  b b d t

- increases with rapidity and centrality
- disappears at high pT in accord with
the QCD factorization theorems
J.W.Qiu, I.V., hep-ph/0405068
July 28, 2004
33
Ivan Vitev, LANL
Conclusions (II)

This talk is only an introduction to the morning
session – the details will be given by the experts:
Jets and di-hadron correlations:
 Experimental:
K. Filimonov, “Di-hadron correlations at high pT”
J. Jia, “Jets in PHENIX”
C. Mironov, “Charged kaons correlations”
J. Rak, “Measurement of jet properties and their modification
in heavy ion collisions at RHIC”
Y. Guo, “Correlations of high-pT particles produced in Au+Au
collisions at 200 GeV”
 Theoretical:
J. Jalilian-Marian, “Two particle production in proton
(deuteron) nucleus collisions”
A. Majumder, “High pT hadron-hadron correlations”
July 28, 2004
34
Ivan Vitev, LANL
The Single Inclusive Spectra Revisited
I. Arsene et al., nucl-ex/0403050
Power corrections
~ 0.4 – 0.5
GCG
GCG
It makes no sense to try and fit the charded hadrons at low pT and these rapidities
• Data is for qualitative
comparison
(pions versus baryons)
• The power corrections
modify the ratio from low
pT to high pT
(not vice versa)
Looks like 0.5!
July 28, 2004
35
Ivan Vitev, ISU
The Technology of Power Corrections
Hard part
Matrix element
...   ...   ...
Only one contributing uniquely defined sequence:
   

i ( xi  xi 1 ) i
d i e
x 1
 2
Vertex: 2
2 (4 s ) 

Q 2 Nc
2 xi  xi 1  i    
 2

1/ 3
Note: it is  d i that gives A  enhancement
d
p Fˆ 2 (i ) p   i
2
iFˆ 2 (i )
, Left of cut
xi 1  x  i
iFˆ 2 (i )
, Right of cut
xi  x  i

p F  (i ) F (i ) p
( p  )2
 (i  i )  lim x0
1
xG( x, Q 2 )
2
The small-x limit of the leading twist gluon distribution function
July 28, 2004
36
Ivan Vitev, ISU
Lowest Order Contributions to FL ( x, Q )
2
 4 2 s
FL ( x, Q )  4 
2
 3Q
2
1

ix0
2
p (0)  (0 ) Fˆ0 p
  Q f  d 0e
2p
2 f


d

d

F
(n ) F (0 )
n
0
Fˆ0  
 (n ) (0  0 )
2
( p  )2
(Twist 4)
• Genuinely new higher twist contribution
Short distance, not A1/3-enhanced
The old and known Leading Twist contribution

Bremsstrahlung
diagram


Box
diagram
kT

kT
1
1
 x  x 
s
d
2
2  8 x  s 
2  d
FL ( x, Q )   Q f   f ( , Q )      Q f   g ( , Q 2 )  2 1  
2 f

 3   2  f
    
x 
x
2
July 28, 2004
G.Altarelli and G.Martinelli,
Phys.Lett. B76 (1978)
37
M.Gluck and E.Reya,
Nucl.Phys. 145 (1978)
Ivan Vitev, ISU
Color Glass Inspired Calculations
RdAu = 0.3-0.5
J.Jalilian-Marian, nucl-th/0402080
Y=2,3,4
RdAu = 0.5
Forward d-A
Discuss problems
Evolves very quickly
Kharzeev, Kovchegov, Tuchin,
High pT workshop at RHIC
RdAu = 0.4
The effect never disappears
R.Baier et al., Phys.Rev.D 68 (2003)
July 28, 2004
Violate factorization!
38
Ivan Vitev, ISU
Motivation: pQCD in Nuclear Collisions
• Universal nuclear dependence:
from nuclear wave functions
K.Eskola,V.Kolhinen and C.Salgado,
Eur.Phys.J. C9 (1999)
M.Hirari,S.Kumano and M.Miyama,
Phys.Rev. D64 (2001)
Shadowing
• Process-dependent nuclear
effects:
● Initial-state:
● Final-state:
(Will be discussed)
• Nuclear PDF’s versus
medium-induced nuclear effect
Data from: NMC
Ivan Vitev, LANL
Power Correction
Contributions to LO pQCD
1. Recall that the two gluon ladder generates
the scale of higher twist -  2
c
2. For a fixed number of interactions (2N) we
take all possible t   cuts
d
d 
New contributions to
the cross section
N

m
  ( xm  xb ) 
m0
 i 1

1   N m
1

 
xi 1  xm   j 1 xm j  xm 
 1  ( N ) ( x  x )
b
b
N
 d 
xi  xb
N!
3. Sum over all possible N
The results look like LO pQCD with the substitution:
N
I.B.P


1 ( N )

C2 
 2 1/ 3

2
1/ 3
dx

(
x

x
)
x

(
A

1
)
F
(
x
)

dx

(
x

x
)
F
x

x
C
(
A

1
)


  b N!
b
b  b
b
b
b d

 b b b
t
t
N
N  0,




• Driven by the Mandelstam invariant (-t) the resulting suppression will be
sensitive to pT and rapidity y.
Cd = 1 for quarks, CA/CF = 9/4 for gluons
J.W.Qiu, I.V., hep-ph/0405068
July 28, 2004
40
Ivan Vitev, ISU
Observing the Acoplanarity
and the Power Corrections
• Consider di-hadron correlations associated with hard
(approximately) back-to-back scattering
0
hh
1 dN 1 2 dijet ( y1  y2 )
C2 ( ) 
Ntrig
d 

ANear ( y1  y2 )
2 Near
k

2
pair
e
k
2
/ 2 2 Near
2
vac
Before the hard scatter
kT
2
IS
 2

L
q, g
July 28, 2004
2
kT
2
FS

i

2
2
AFar
e (   ) / 2 Far
2  Far
1
2
1  tanh 2 yi  k

2
i nucl
After the hard scatter

2
2

L


q,g


2
g
2 3CR s 1 dN ln L

2
A dy
0

Cold
Hot 1+1D
41
K
If AFar ( p  p)  1
AFar ( p  A)  Rh1h2 ( pT )
Ivan Vitev, ISU
Dijet Acoplanarity in d+Au and Au+Au
Estimate from:
J.W.Qiu, I.V., Phys.Lett.B 570 (2003); hep-ph/0405068
From: <z> = 0.75, <|kTy|>pp = 1.05 GeV
j y 
1

2

j
k y

1

k2
<|kTy|>pA = 1.25 GeV
<z><|kTy|>AA = 1.25 - 1.45 GeV
p+A
A+A
(2.5pTtrigg4.0)(1.0pTassoc2.5)
Feedback?
pp: <z><|kTy|>
pp: <|jTy|>
J.Rak, hep-ex/0403038
P.Constantin, N.Grau
July 28, 2004
42
Very interesting!
Ivan Vitev, ISU
Nuclear Effects in Inclusive Deeply
Inelastic Lepton-Nucleus Scattering
d lh 4 em 1  y 2
mN xy 

2
2 

2 xF1 ( x, Q )  1  y 
 F2 ( x, Q ) 

2
dxdy
Q xy  2
2E 


F1 ( x, Q2 ), F2 ( x, Q2 )
k
P

-
the DIS structure functions
k’
1
FT ( x, Q )   Q 2f  d 0 eix0
2 f
2
xP
…
X
Convenient to calculate in a 
basis of polarization stares of
July 28, 2004
Used to determine the parton distribution
functions (PDFs)

p  (0)

2 p
 (0 ) p
1
Q 2f  f ( x, Q 2 )  O ( s )

2 f
FL ( x, Q2 )  0
FT ( x, Q2 )  F1 ( x, Q 2 ),
4x 2 mN2
F2 ( x, Q2 )
2
FL ( x, Q ) 
 F1 ( x, Q ), if
1
2x
Q2
43
Ivan Vitev, ISU
2
The Reaction Operator Approach to
Multiple Elastic and Inelastic Scatterings
zn zn
qn , an
+
zn
qn , an qn , an
†ˆ
†
ˆ
ˆ
ˆ
ˆR  D
n
n Dn  Vn  Vn
zn
+
qn , an
qn , an
qn , an
n = c = L/ l
For the elastic scattering
Reaction Operator = all possible
t=¥
on-shell cuts through a new Double Born case illustrated here by
iteration:
interaction with the propagating system
¥
dN ( p) =
f
å
n= 0
dN i
¥
dN ( p) =
n
å
n= 0
n
cn
1 d s el - qi ^ .Ñ p ^
- qi P¶ pP
2
d
q
e
Ä
e
- 1)dN i ( p)
(
Õ
2
ò
i
n ! i= 1
s el d qi
dN
f
d s el (b)
d 2q
ö
mb
1 æ
m2b2
3 ÷
ç
=
K
(
m
b
)
»
1
x
+
O
(
b
)
÷
ç
÷
4p 2 1 k 2 4p 2 çè
2
ø
-
2
1 e cm x
dN (k ) =
,
2p c m2 x
D k 2 = c m2 x
x = log 2 / (1.08mb)
Mandelstam s,t,u
July 28, 2004
kT kick that helps
44
Ivan Vitev, ISU
Dihadron Correlation
Broadening and Attenuation
Midrapidity and moderate pT
J.Adams et al., Phys.Rev.Lett. 91 (2003)
• Only small broadening
versus centrality
• Looks rather similar at
forward rapidity of 2
• The reduction of the area
is rather modest
Forward rapidity and small pT
• Apparently broader
distribution

• Even at midrapidity a small
reduction of the area
• Factor of 2-3 reduction of the
area at forward rapidity of 4
Trigger bias can also affect:
AFar
July 28, 2004
(t ) ~ 1/ z1
J.W.Qiu, I.V., Phys.Lett.B 570 (2003); hep-ph/0405068
45
Ivan Vitev, ISU
The Gross-Llewellyn Smith
and Adler Sum Rules

1

1
N
N
xF3 ( x, Q2 )  xF3 ( x, Q2 )  3(1  GLS )
2x
SGLS   dx
0
D.J.Gross and C.H Llewellyn Smith ,
Nucl.Phys. B 14 (1969)
SGLS  #U  # D  3 • To one loop in s (Q2 )
GLS  s (Q2 ) / 
• Nuclear-enhanced power corrections
are very important
• Leading twist shadowing does not
contribute to GLS
1
S A   dx
0


1
n
n
F2 ( x, Q2 )  F2 ( x, Q2 )  1   HT
2x
S.Adler , Phys.Rev. 143 (1964)
July 28, 2004
1
3
Q2
10
20
Compatible with the trend in
the current data
• Can set a limit on the 4-point parton
correlation function
46
Ivan Vitev, ISU
Modifications to the Structure
Functions in   A Scattering
Motivation
Based on:
 ( N   X )
v
R

,

• 3 deviation from the Standard Model
 ( N  l X )
2
sin W (SM )  0.2227  0.0004
 ( N   X )

2
R

sin W ( NuTeV )  0.2277  0.0013  0.0009  ...
 ( N  l  X )
• Asymmetric strange sea and violation of the isospin symmetry
The NuTeV experiment claims:
G.P.Zeller et al., Phys.Rev.Lett 88 (2002)
G.P.Zeller et al., hep-ex/0203004
Beware: Monte Carlo with many effects taken on average


mN xy  W 
d  , cc  y 2
y2  W 

W
2
2
2
  2 xF1 ( x, Q )  1  y 
 F2 ( x, Q )   y   xF3 ( x, Q ) 
dxdy
2
2
E
2 





Axial and vector part (weak current)
Similarly for the neutral current
g  g (sym.)  g (asym.)
Recall the tensorial decomposition
July 28, 2004
47
Ivan Vitev, ISU
Power Corrections at Forward Rapidity
STAR
Preliminary:
L.Bland, [STAR Colaboration]
-4 and
What
author
• At x2 =the
2 x 10
pT =concluded
1.25 GeV hard
scattering is
Are
suppressed
in d+Au
similar
in p+p and
p+A
relative to p+p at small
<xF• >There
and <p
isn’t
T,>mono
jettiness
Spp-SdAu= or
(9.0g-fusion
± 1.5) %
25<E<35GeV
X2 = 1.94 x10-4
CGC logic
CGC
•Consistent
I think thatwith
the p+A
analysis picture
has under and
over estimated the
Are consistent in d+Au
away-side area
and p+p at larger <xF>
and <pT,>
• There may be room for
35<E<45GeV
July 28, 2004
X2 = 2.51 x10-4
Assuppression
expected bydue
some
to power
corrections
HIJING
Statistical errors only
48
Ivan Vitev, ISU
Analytic Limits For Energy Loss

E  I   dt t  (t , x0  vˆ(t  t0 ))
E(1) 
t0

 2 transport
a) Static medium:
g coefficient
Static medium
3
E
(1)
b) Bjorken expanding medium:
9CR  s
1 dNg
2E

L
Log 2
 ... ,
4
A  dy
 (L)L

1+1D Bjorken
M.Gyulassy, I.V., X.N.Wang, Phys.Rev.Lett. 86 (2001)
 1  dN

A
   dy
 0  ( 0 )   ( )  
CR  s 2L2
2E
Log 2
 ... ,
4
g
 (L)L
parton
 2  2 pl  T 2 ,   T 3 ,   T 4
Beyond average
 E: need ansatz
• Independent Poisson emission
Guaranteed to be violated
¥
• By simple kinematics
P ( e, E ) =
Usefulness
å
Pn ( e, E )
n= 0
P0 ( e, E ) = e
• Allows the system to adjust itself
• Minimizes the effect of energy loss
July 28, 2004
Npart
0
- Ng
DE
=
E
d( e), P1( e, E ) = e
400
¥
ò d e eP (e, E )
0
- Ng
r ( e, E ), ...
R.Baier et al., JHEP (2001)
M.Gyulassy, P.Levai, I.V., Phys.Lett.B538 (2002)
49
Ivan Vitev, ISU
New Contribution to FL ( x, Q )
2
On-shell paricle (M)
xB
 
2


(
x
p


(
Q
/
2
x
p
)

M)
M
B
2
Q
(Cuts fix kinematics)
  ( xi  xB  xM )
M2
xM  xB 2
Q
Cut  (2 )
• Even if one neglects c ( x, Q2 ), c ( x, Q2 ) mass
effects show up due to the mixing of electroweak
and mass eigenstates
• Along the way we will develop techniques that
may be useful in the discussion of charm
production at RHIC
xi
J.W.Qiu, I.V., Phys.Lett.B 587 (2004)
|V| - the CKM matrix elements
U  (u, c, t ), D  (d , s, b)
2
2
M
M
( W )
FL ( xB , Q2 )   | VDU |2 U2 D ( xB  xMU )   | VUD |2 2D U ( xB  xM D )
Q
Q
D ,U
U ,D
2
2
M
M
( W  )
FL
( xB , Q2 )   | VUD |2 2D U ( xB  xM D )   | VDU |2 U2 D ( xB  xMU )
Q
Q
U ,D
D ,U

July 28, 2004
50
Ivan Vitev, ISU
Discussion of Jet Quenching
at Intermediate RHIC Energies
• The result, if confirmed, would not be
•
•
unexpected
Follow from energy loss jet quenching
calculations
Naturally interpolate between the SPS
and the top RHIC energies
X.N.Wang, Phys.Lett.B579 (2004)
RAA=0.5 at pT=4 GeV
The nuclear modification ratio
dN h (b) / dyd 2 pT
RAA (b) 
TAA (b)d h / dyd 2 pT
Possible most interesting outcome
• Sensitively depends on the underlying
partonic spectrum
• In their power law behavior the 62 GeV
spectra are much closer to the 130 GeV
and the 200 GeV cross sections than
to the 17 GeV ones
July 28, 2004
• Strong deviation from the perturbative
prediction
• Strong nonlinearity of  E in dNg/dy
In a Polyakov loop model
A.Dumitru, R.Pisarski, Phys.Lett.B 525 (2002)
51
Ivan Vitev, ISU
Experimental Results at 62 GeV
(Approximate representation of the
theoretical calculation in the Figures)
• Qualitative and somewhat quantitative agreement
• Indicates the need for a possibly stronger
Cronin effect
• Systematic error bars should be taken seriously
• Beware of baryon/meson ratios (I wouldn’t attempt
to fit baryons below 4-5 GeV)
July 28, 2004
52
Experimental Results (Continued)
PHOBOS
(submitted)
• Charged behave differently: factor of 50%
enhancement in peripheral but suppression
develops at high pt, as expected, in central
May have twice
as many baryons
as pions!
STAR
preliminary
July 28, 2004
53
Conclusions (I)
 Dynamical nuclear shadowing from resummed QCD power corrections.
Results consistent with its x-, Q2- and A- dependence. Neutrino-nucleus
DIS. Modification of the QCD sum rules.
 First calculations of dynamical power corrections for hadronic collisions,
p  A . Results for the centrality and rapidity dependent suppression of
single inclusive spectra and the dihadron correlations.
 The power corrections disappear at high pT. They are small at 62 GeV and
would not affect the extraction of RAA
 In central Au+Au collisions at C.M. energy of 62 GeV neutral pions were
found to be suppressed by a factor of 2-3 by jet quenching. Relatively
weak pT dependence of RAA
 Interpretation of the rapidity density dN g / dy  650  800 in 1+1D Bjorken
expansion: at  0  0.8 1 fm the energy density  0  6  8 GeV / fm3 already significantly above the current critical value.
 Charged hadrons, especially baryons, are expected to be less suppressed
and are beyond the reach of the current perturbative techniques
July 28, 2004
54
Ivan Vitev, ISU
Conclusions (II)
 In d+Au collisions midrapidity and moderate pT the dominant effect is
small broadening of the correlations.
 At very forward rapidity (y=4) and small pT the power corrections give a
factor of 2-3 reduction of the area of the away side correlations.
 If the preliminary STAR results at forward y correlations persist – there
isn’t
monojettines or high density gluon fusion effects at x=2x10-4 (following
saturation logic) in Au.
 Will be interesting to measure neutral pions at forward y and compare the
suppression effect (RAA) to the suppression for charged
 Given the results of correlation analysis one can go back and rethink their
favorite d+Au suppression scenarios
July 28, 2004
55
Ivan Vitev, ISU
July 28, 2004
56