1. JT , kT and the fragmentation in pp collisions at sNN=200 GeV
Jan Rak University of New Mexico
Jet kinematics from the angular width of the near and away-side correlation peak
Intrinsic transverse momentum kT
Jet transverse fragmentation momentum jT
Associated yield
Fragmentation function from the combined fit to the inclusive pT and and associated xE distributions
Conditional fragmentation - zt  pTa correlation
AuAu low pT correlation function
Distortions of back-to-back peak – Mach shock waves?
I am going to give you an overview on Exp…. Physics and I’ll try to cover CERN experiments at SPS and the most recent results from Rel. H. I. collider at Brookhaven.

2. Partonic jets as a probe of QCD medium
Particle RHIC s=200 GeV
dnch/dh |h=0 = 670, Ntotal ~ % of (15,000) all quarks from vacuum !
Scattered partons radiate energy in colored medium
suppression of high-pT particles
effective kT broadening
X.N. Wang nucl-th/
Medium induced fragmetation function softening
I will now concetrate on high-pt particle production
Jet spray of fin state part in relative narrow cone. What makes it different from vacuum? Induce rad.

3. kT, jT Partons have to materialize (fragment) in colorless world
jet
jet fragmentation transverse momentum
jT jet fragmentation transverse momentum - constant value independent on fragment’s pT is characteristic of jet fragmentation (jT-scaling).
kT (intrinsic + NLO radiative corrections) carries the information on the parton interaction with QCD medium.

4. o - h correlation functions
1.5<pT<2.0
Fit = const + Gauss(0)+Gauss()
3.0<pT<4.0
d+Au
Intra-jet pairs angular width : N  jT
Inter-jet pairs angular width : A  jT  kT

5. Jet kinematics
Feynman, Field, Fox and Tannenbaum (see Phys. Lett. 97B (1980) 163)
xE = two particle equivalent of the fragmentation variable z.
p2out =  p2Ta sin2  2 k2Ty z2a  2 k2Tyz2tx2h xh= pTa /pTt

6. Near and away-side angular width
1.4<pTa<2.4 GeV/c
Unlike N, the value of A is not vanishing for large values of pTt reflecting the fact that the magnitude of the away-side angle is driven by kT.

7. jT with associated and trigger pT
However, the  j2Ty analysis done at s=62 GeV explicitly neglected zt. This may explain the slightly larger value seen by CCOR collaboration.

8. ztkT “puzzle” 1.4<pTa<2.4 GeV/c
Assumption: For fixed pTt the parton momentum (jet energy) is fixed, pTa samples the different region of fragmentation at fix Q2  zt kT should be constant
THIS IS CLEARLY WRONG
1.4<pTa<2.4 GeV/c

9. Fragmentation Function from xE distribution
In order to understand the (anti)correlation of zt kT with pTt and pTa one has to explore the fragmentation under the condition of detection of an associated particle.
xE variable - two particle equivalent of the fragmentation variable z.
 Simple relation

10. xE in pp collisions 1/xE  -5.3 1/xE  -5.8 to –7.8
CCOR (ISR) s = 63 GeV
see A.L.S. Angelis, Nucl Phys B209 (1982)
Correct +-
1/xE  -5.3
1/xE  to –7.8

11. Is the z=xEzt valid assumption?
xE “scaling”
The shape of the xE distributions does not vary, unlike the pTa distributions, with pTt. This supports the the idea of D(z) =dn/dz  dn/dxE.
However, the scaling is not perfect ! It has nothing to do with pQCD scaling violation, but maybe it has something to do with the ztkT “puzzle” ?
Is the z=xEzt valid assumption?

12. Di-jet fragmentation zassoc ztrig
Monte Carlo
ztrig
zassoc
By selecting events with different passoc the probability distribution of mother parton is changing. 
Trigger parton distribution is affected as well !

13. Global fit to the inclusive and associated distribs.

14. Fragmentation function and z 
These are preliminary results from QM04 – final are under collaboration review.
QM04
PHENIX preliminary
pythia
The QM analysis did not account for “conditioanl fragmentation. The D(z)  exp(-z/z) assumption is also not well justified.

15. Azimuthal correlation function in AuAu
Two particle azimuthal correlation function
Unavoidable source of two particle correlations in HI – elliptic flow
“flow” pairs :
[1+2v22 cos(2)]
Intra-jet pairs angular width :
N  |jTy|
Inter-jet pairs angular width :
A  |jTy|  |kTy| z
CARTOON
flow
flow+jet N A

16. AuAu |jTy| and z |kTy| from CF
Phys.Rev.Lett.92:032301,2004
(3.0pTtrigg5.0)(1.5pTassoc3.0)
There seems to be significant broadening of the away-side correlation peak which persists also at somewhat higher pT range.
(2.5pTtrigg4.0)(1.0pTassoc2.5)
pp <z><|kTy|>
pp <|jTy|>

17. Jet correlation in Au+Au
h-h correlation
Intermediate pT correlation
Jet pair fraction is small
Jet shape is strongly distorted at away side
PHENIX preliminary

18. Away side is strongly distorted
Medium modification
Assume Zero jet yield at minimum
Systematics dominated by v2
Away side is strongly distorted
2 dip at .
Jet interact with flowing medium
hep-ph/ Shuryak
nucl-th/ , S. Voloshin
hep-ph/ Armesto,Salgado,Wiedemann

19. Novel behavior of away <pT>
Preliminary
<pT> more robust than correlation functions.
Novel dip structure observed in central AA.
Energy loss effect? Mach shock wave?

20. Summary
The angular width of the near and away-side correlation has been measured. Formulae for jT and kT we discussed. We found
j2T = 0.58 GeV/c by 15% small then at lower s measurement. This may be attributed to the neglecting the z.
Associated pTa and xE distributions were analyzed. The (anti)correlation between trigger z and pTa has been discussed. The method of extraction the D(z) parameters from the combined fit to the inclusive and associated pTa distributions was presented. Similar analysis of AuAu data is under way.
Intermediate pT ( 2 GeV/c) correlation function in AuAu data develops significant distortion of back-to-back peak with the dip around at 180 deg. Associated pTa reveals similar structure. Some speculation about Mach shock waves, however, there is no reasonable calculation supporting this interpretation.

21. CCOR j2T from |pout|2
CCOR coll. PL 97B (1980)
|pout|2 (GeV2/c2)

22. Inclusive fragmentation
= effective final state parton distribution
= 0 fragmentation function

23. associated “double” fragmentation
With the condition of seeing associated particle, the parton spectrum on the away-side is biased:
It is now evident why xE distributions do not scale perfectly! At fixed trigger pt the xE distribution is a folding of D(z)fq and not just D(z)!

24. kT-smearing
Associated parton distribution fa = kTft and the final formula for invariant cross section is
Correlation fcn between b2b parotns
gaussian for kt>0 or delta function for kT=0

25. STAR sees the same?
4 < pTtrig < 6 GeV/c
2.5 < pTtrig < 3 GeV/c
0.3<pTassoc<0.8 GeV/c
0.8<pTassoc<1.3 GeV/c
1.3<pTassoc<1.8 GeV/c
Shape varies with pT and becomes broader and double peaked at large pTa. Effect is more pronounced for lower pTt !
Vitev, hep-ph/ : should not have peak structure.