# Presentation: 921122

## kT Asymmetry in Longitudinally Polarized        Collisions

- Douglas Fields
*University of New Mexico*
- for PHENIX

- Douglas Fields

- 10/7/2006

## What is the origin of jet kT?

- What is the origin of jet *k*T?

- Intrinsic (Confinement) *k*T  200 MeV/c

- Breaks collinear factorization

- Soft QCD radiation.

- An example  - J/ production.

- Extra gluon kick
- pTJ/ =1.80.230.16 GeV/c
*Phys. Rev. Lett. 92, 051802, (2004).*

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- 10/7/2006

## Another Possibility

- Spin-Correlated transverse momentum – partonic orbital angular momentum
- We can perhaps measure using jet kT
- Sivers Effect in single transverse spin
- Idea proposed by Boer and Vogelsang (Phys. Rev. D69 094025, 2004)
- Possible Effect in double longitudinal spin
- Idea proposed for the Drell-Yan process by M.Ta-chung et. al. (Phys. Rev. D40 p.769, 1989)
- Same idea for jets proposed by DF

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- 10/7/2006

## Like Helicity(Positive on Positive Helicity)

- Like Helicity(Positive on Positive Helicity)

- Integrate over b, left
- with some residual kT

- Measure jet

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- 10/7/2006

## Un-like Helicity(Positive On Negative Helicity)

- Un-like Helicity(Positive On Negative Helicity)

- Integrate over b, left
- with some *different*
- residual kT

- Douglas Fields

- 10/7/2006

## How does PHENIX measure jet kt?

- PHENIX doesn’t measure jets, so...
- 0 - h  azimuthal correlation functions

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## How does PHENIX measure kt?

- How does PHENIX measure kt?

- Zero kT
- Non-Zero kT

- Intra-jet pairs angular width :	near   jT
- Inter-jet pairs angular width : far  jT  kT

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## Jet Kinematics

- For details, see:
- Phys. Rev. D **74**, 072002 (2006)

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## π0 Identification

- Min photon energy *> *0.2 GeV (for both PbSc and PbGl).
- Photon probability *> *0.02.
- Two photon energy asymmetry *< *0.8.
- Gamma3 trigger check for higher energy photon in the pair.

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## Correlation Function

- Red – real (raw Δφ)
- Blue – background (mixed events)

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## Fit Function

- Black – real (raw Δφ)
- Blue – Fit from above equation

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## Fit Results

- Red     – Like helicity (++ & --)
- Blue    – Unlike helicity (+- & -+)

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## Need zt and xh

- Go from pout →
- Simple parameterizations of zt and xh taken from Phys. Rev. D 74, 072002 (2006)
- Our results are not sensitive to this parameterization – only needed to set the scale
- Use these parameterizations to estimate

- Douglas Fields

- 10/7/2006

## Preliminary Results

- Take the difference Like – Unlike helicities
- Normalized by beam polarizations
- jT asymmetry small (32 ± 24MeV/c out of ~580MeV/c for unpolarized)
- kT asymmetry not small (672 ± 387MeV/c out of ~3GeV for unpolarized)

- Douglas Fields

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## Summary

- Many more things to do:
- Can attempt to sort on “impact parameter” by looking at multiplicities in forward and central rapidities (Done, but not yet PRELIMINARY – very interesting...).
- Sort by hadron charge to change mix of interacting partons (PYTHIA MC).
- All of above with π0 in forward rapidities (MPC).
- Need theoretical guidance on how to interpret in terms of connection to orbital angular momentum.
- Look forward to Run6 data analysis (~ x3 in F.O.M.) soon!

- Douglas Fields

- 10/7/2006

## Backups

- Douglas Fields

- 10/7/2006

- Think of rotating (longitudinal) water balloons, or...

- Douglas Fields

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## From Meng Ta-Chung et al.Phys Rev. D40, p769, (1989)

- kTR

- kPR

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## From Meng Ta-Chung et al.Phys Rev. D40, p769, (1989)

- From Meng Ta-Chung *et al.**Phys Rev. D40, p769, (1989)*

- kTR

- kPR

- kTR

- kPR

- Like Helicity

- Un-like Helicity

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## From Meng Ta-Chung et al.Phys Rev. D40, p769, (1989)

- 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

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## Our Model

- Use different transverse density distributions to get pt kick from coherent spin-dependent motion:

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## 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.

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## SigmaNear and xzkt

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## Bunch Shuffling (σnear)

- σnear/ δσnear
- Mean consistent with zero and width consistent with 1.

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## Bunch Shuffling (pout)

- pout / δ pout
- Mean consistent with zero and width consistent with 1.

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## Bunch Shuffling Summary

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## pout as a Function of kT

- pout as a Function of kT

- Can see the trend of the far-side width becoming larger with input kT.
- At the largest kT, the method may become unreliable since the two gaussians begin to overlap.

- kT = 0 GeV

- kT = 1 GeV

- kT = 2 GeV

- kT = 3 GeV

- kT = 6 GeV

- pTt = 2.0 - 2.5 GeV

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## Compare to Data

- Plot of values of σF as kT varies. There are eight such plots, each for a different range of pTt.
- Below, a comparison of σF from the simulation to σF of run 5 data. The minimum corresponds to the input kT that best matches the data σF.

- pTt = 3.0 - 3.5 GeV

- σF

- Input kT

- (Data – Pythia)2

- Data

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## Compare to Data

- To find the minimum, each plot was fitted with a second order polynomial: a + bx + cx2
- Here the fit can be seen between values of kT = 2 GeV and kT = 3 GeV.

- pTt = 2.5 - 3.0 GeV

- Input kT

- σF

- (Data – Pythia)2

- Data

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## Comparison to Data Results

- The final results are eight minima, one for each range of pTt.
- The mean of these minima gives a kT of about 2.60 +/- .150 GeV, which is consistent with the kT result extracted directly from the data (ppg029).

- Pt bin	Minimum
- 2.0-2.5 	2.659
- 2.5-3.0	2.469
- 3.0-3.5	2.6164
- 3.5-4.5	2.414
- 4.5-5.5	2.5828
- 5.5-6.5	2.5408
- 6.5-7.5	2.646
- 7.5-9.0	2.8427
- Mean = 2.596 +/- * ~.150GeV
- Data mean ~ 2.68GeV (ppg029)

- * Estimated, not calculated

- Douglas Fields

- 10/7/2006