1. Measuring Orbital Angular Momentum through Jet kT
Douglas Fields
University of New Mexico/RBRC
Jan Rak, Rob Hobbs, Imran Younus
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

2. Douglas Fields RHIC-AGS User's Meeting
Outline
Spin dependent jet kT
Sivers function
Question…
Something new
How does PHENIX measure jet kT?
Correlation functions
PHENIX detector
Origin of jet kT
Summary
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

3. Douglas Fields RHIC-AGS User's Meeting
What is the origin of kT?
Intrinsic (Confinement) kT  200 MeV/c
Soft QCD radiation.
An example - J/ production.
Extra gluon kick
pTJ/ =1.80.230.16 GeV/c
Phys. Rev. Lett. 92, , (2004).
Breaks collinear factorization
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

4. Douglas Fields RHIC-AGS User's Meeting
Another Possibility
Spin-Correlated transverse momentum – Partonic orbital angular momentum
We can perhaps measure using jet kT
Sivers Effect in single (double?) transverse spin
Possible Effect in double longitudinal spin
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

5. Sivers Fcn from Back2Back Analysis
Boer and Vogelsang, Phys.Rev.D69:094025,2004, hep-ph/
Non-Zero Sivers function means that there is a left/right asymmetry in the kT of the partons in the nucleon
For a positive Siver’s function, there will be net parton kT to the left (relative to direction of proton, assuming spin direction is up).
Boer and Vogelsang find that this parton asymmetry will lead to an asymmetry in the  distribution of back-to-back jets
There should be more jets to the left (as in picture to the left).
Should also be able to see this effect with fragments of jets, and not just with fully reconstructed jets?
Take some jet trigger particle along ST axis (either aligned or anti-aligned to ST)
Trigger doesn’t have to be a leading particle, but does have to be a good jet proxy
Then look at  distribution of away side particles
See talk tomorrow ??
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

6. Douglas Fields RHIC-AGS User's Meeting
Sivers Effect
Recently, at the RBRC Single Spin Workshop, Denis Sivers gave a nice conceptual (no twist-anything) picture of how orbital angular momentum could cause a single transverse spin asymmetry.
“Quantum Fan” description (top view – spin down):
No Sivers Effect
without interaction
with absorber –
Higher twist effect
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

7. Douglas Fields RHIC-AGS User's Meeting
Sivers Effect
Night before last, I was thinking…
Why not double spin?
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

8. Similar Idea for “Fields” Effect
Idea came from me trying to understand Sivers effect.
I basically got the picture wrong – I couldn’t understand how single transverse spin effects could cause an asymmetry – so I started playing around with double longitudinal spin asymmetries.
Same idea of rotating partons around spin direction
Two classes of collisions:
Like helicity, i.e.,
Un-like helicity, i.e.,
Positive Helicity
Positive Helicity
Positive Helicity
Negative Helicity
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

9. Like Helicity (Positive on Positive Helicity)
Peripheral Collisions
Larger
Peripheral Collisions
Larger
Measure jet
Integrate over b, left
with some residual kT
Central Collisions
Smaller
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

10. Un-like Helicity (Positive On Negative Helicity)
Peripheral Collisions
Smaller
Integrate over b, left
with some different
residual kT
Central Collisions
Larger
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

11. Douglas Fields RHIC-AGS User's Meeting
“Fields” Function
Something like: bT bP
kTR
kPR
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

12. Douglas Fields RHIC-AGS User's Meeting
History
Talked to many people – Werner pointed me to a paper by Meng Ta-chung et al.
“Experiment B” – similar idea, only for Drell-Yan
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

13. From Meng Ta-Chung et al. Phys Rev. D40, p769, (1989)
Total transverse momentum squared
of partons
For a particular impact parameter, b, the average transverse momentum
kPR
kTR
Where, is the product of the Jacobian and the density profile of partons, and D(b) is the overlap region.
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

14. From Meng Ta-Chung et al. Phys Rev. D40, p769, (1989)
We can now helicity separate: b
Like Helicity
The constant terms in pt cancel and we have
kPR
kTR
Un-like Helicity
kPR
We can then average over the impact parameter
kTR
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

15. From Meng Ta-Chung et al. Phys Rev. D40, p769, (1989)
This paper makes the following assumptions:
Uniform spherical density F(b,θP,θT)
kPR~kTR~kR (no dependence on b, θP, θT.)
Then,
Evaluated numerically
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

16. Douglas Fields RHIC-AGS User's Meeting
Our Model
We first assume constant angular velocity of partons, pθ, regardless of distance to the proton center.
We set (arbitrarily) the maximum transverse momentum of the partons to be 300 Mev at the radius of the proton equal to 1.3 fm.
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

17. Douglas Fields RHIC-AGS User's Meeting
Our Model
Use different transverse density distributions to get pt kick from coherent spin-dependent motion:
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

18. Douglas Fields RHIC-AGS User's Meeting
Our Model Results
Basically independent of transverse density distribution.
Ranges from 0.3 to 0.6 times the initial momentum.
Very crude – would like suggestions to improve.
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

19. How Large an Effect Can We Expect?
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

20. Centrality Dependence
Would be nice to have experimental handle on impact parameter:
Multiplicity
Forward or central
Underlying event…
but, not explicitly necessary.
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

21. How does PHENIX measure kt?
0 - h azimuthal correlation functions
Trigger 0
Intra-jet pairs angular width : N  jT
Inter-jet pairs angular width : A  jT  kT
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

22. kT, jT “easy” measurement in p +p
fragmentation
jet * 
jT  N
jet fragmentation transverse momentum, jT-scaling.
kT  2F-2N
parton transverse momentum, intrinsic + NLO radiative corrections.
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

23. Douglas Fields RHIC-AGS User's Meeting
Jet Kinematics
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

24. PHENIX Detector Overview
East Arm
tracking:
DC, PC1, TEC, PC3
electron & hadron ID:
RICH,TEC/TRD,
TOF, EMCal
photons:
EMCal
West Arm
tracking:
DC,PC1, PC2, PC3
electron ID:
RICH,
EMCal
photons:
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

25. Douglas Fields RHIC-AGS User's Meeting
π0 Identification
PHENIX has central arm EMCal with electron rejection in RICH.
Used shower profile cut.
Good S/B at higher pt (>2GeV).
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

26. Douglas Fields RHIC-AGS User's Meeting
Charged Particles
Tracks in the Drift Chamber
Hits in the Pad Chambers
RICH veto for low momentum
Shower shape cut at high momentum
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Douglas Fields RHIC-AGS User's Meeting

27. Correlation Functions
dNreal Δφ distribution from particles in the same event
dNmixed Δφ distribution from particles in different events with similar vertex position
Norm =
Fit to two gaussians plus a constant term
1.5<pT<2.0
Fit = const + Gauss(0)+Gauss()
3.0<pT<4.0
Intra-jet pairs angular width : N  jT
Inter-jet pairs angular width : A  jT  kT
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

28. How accurately can we measure <kt>?
is extracted from , σF, and fragmentation functions (to get zt) which are extracted from inclusive and associated distributions.
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

29. Douglas Fields RHIC-AGS User's Meeting
Origin of kT
An example - J/ production.
Breaks collinear factorization
pTJ/ =1.80.230.16 GeV/c
Phys. Rev. Lett. 92, , (2004).
6/20/2005
Douglas Fields RHIC-AGS User's Meeting
Oct. 27, 2005 29

30. Douglas Fields RHIC-AGS User's Meeting
Hard Scattering kT
transverse
Longitudinal
jet
acoplanar in PL  PT space
acoplanar in PX  PY space
Longitudinal
transverse
acoplanar in PL  PT space
collinear in PX  PY space
6/20/2005
Douglas Fields RHIC-AGS User's Meeting
Oct. 27, 2005 30

31. Douglas Fields RHIC-AGS User's Meeting
Spin Sorted Analysis
Do exactly the same analysis sorted on same and opposite helicity bunch crossings, extract <zkt>RMS and look at the difference.
Same Helicity
Opposite Helicity
C(Δφ)
C(Δφ) Δφ
6/20/2005
Douglas Fields RHIC-AGS User's Meeting Δφ
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32. Douglas Fields RHIC-AGS User's Meeting
Run03 Data
Like sign
Unlike sign
trigger π0
1< pTt<3 Gev/c
3<pTt<7 Gev/c
Associated h
1< pTa<2.5 Gev/c
6/20/2005
Douglas Fields RHIC-AGS User's Meeting
Oct. 27, 2005 32

33. Douglas Fields RHIC-AGS User's Meeting
Systematic Check
RMS = 45
Helicity assignments are randomized, and then the kT difference calculated for each randomized set.
The width of the distribution for all the randomized sets should be the same as our statistical errors on the previous plot.
RMS = 90
6/20/2005
Douglas Fields RHIC-AGS User's Meeting
Oct. 27, 2005 33

34. Douglas Fields RHIC-AGS User's Meeting
Run03 Data
Its too early to make a definite statement about the apparent excess as the systematic uncertainties are being evaluated.
However, there is an ongoing analysis of 10x more stat. and 2x better polarization in run05  should yield a definite answer.
BS variance
6/20/2005
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Oct. 27, 2005 34

35. Douglas Fields RHIC-AGS User's Meeting
For Run5
~10-20 times more statistics than Run3
Statistical errors smaller by factor of 3-5
Polarization in Run5 ~55%
Effect larger by factor of ~5 (PY*PB) than Run3
6/20/2005
Douglas Fields RHIC-AGS User's Meeting

36. Douglas Fields RHIC-AGS User's Meeting
Summary
Jet kT can be extracted from di-hadron correlations using method developed by J. Rak and others.
Jet kT can be used to probe initial and final state contributions to transverse momentum distributions.
We can make a measurement of the spin dependence of jet <kT> in:
Single transverse spin asymmetries – Sivers Function.
Double-longitudinal spin asymmetry – Fields Function.
These may be sensitive to orbital angular momentum.
Need theoretical guidance…
6/20/2005
Douglas Fields RHIC-AGS User's Meeting