# Presentation: 752801

## Measuring Orbital Angular Momentum through Jet kT

- Douglas Fields
*University of New Mexico/RBRC*

- Jan Rak, Rob Hobbs, Imran Younus

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## Outline

- How do we measure jet kT?
- Correlation functions
- PHENIX detector
- Origin of jet kT
- Spin dependent jet kT
- Sivers function
- Something new
- Summary

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## How do we measure kt?

- Intra-jet pairs angular width :	N   jT
- Inter-jet pairs angular width : A  jT  kT

- 0 - h  azimuthal correlation functions

- Trigger 0

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## kT, jT “easy” measurement in p +p

*k*T, *j*T “easy” measurement in *p *+*p*

- fragmentation

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## Jet Kinematics

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## 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:
- EMCal

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## π0 Identification

- PHENIX has central arm EMCal with electron rejection in RICH.
- Used shower profile cut.
- Good S/B at higher pt (>2GeV).

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## Charged Particles

- Tracks in the Drift Chamber
- Hits in the Pad Chambers
- RICH veto for low momentum
- Shower shape cut at high momentum

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## 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

-  3.0<pT<4.0

- Fit = const + Gauss(0)+Gauss()

-  1.5<pT<2.0

- Intra-jet pairs angular width :	N   jT
- Inter-jet pairs angular width : A  jT  kT

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## How accurately can we measure <kt>?

-        is extracted from         , σF, and fragmentation functions (to get zt) which are extracted from inclusive and associated distributions.

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## What is the origin of kT?

- What is the origin of *k*T?

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

- Breaks collinear factorization

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## Another Possibility

- Spin-Correlated transverse momentum – Partonic orbital angular momentum
- We can perhaps measure using jet kT
- Sivers Effect in single transverse spin
- Possible Effect in double longitudinal spin

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## Sivers Fcn from Back2Back Analysis

**Boer and Vogelsang, Phys.Rev.D69:094025,2004, hep-ph/0312320**

- 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 M. Chiu’s talk tomorrow in the Spin Workgroup

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## 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

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## Idea came from me trying to understand Sivers effect about one year ago.
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.,

- 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.,

- “Fields” Effect

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## Like Helicity(Positive on Positive Helicity)

- Integrate over b, left
- with some residual kT

- Measure jet

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

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

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

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## 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

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

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

- kTR

- kPR

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## 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

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## 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

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## “Fields” Function

- Something like:

- bT

- bP

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## How Large an Effect Can We Expect?

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## Centrality Dependence

- Would be nice to have experimental handle on impact parameter:
- Multiplicity
- Forward or central
- Underlying event...
- but, not explicitly necessary.

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## How accurately can we measure Δ<kt>?

- How accurately can we measure Δ<kt>?

- ZT uncertainties should cancel in the difference
- Bunch Shuffling in Run3 (PHENIX)
- δ Δ<kt> ~ 80MeV

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## 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

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005

## 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...

- Douglas Fields                  RHIC-AGS User's Meeting

- 6/20/2005