6/2/2005Douglas Fields1 Measuring Orbital Angular Momentum through Jet k T Douglas Fields University of New Mexico/RBRC Jan Rak, Rob Hobbs, Imran Younus

6/2/2005Douglas Fields2 Idea came from me trying to understand Sivers effect –Quantum Fan Level Description –This is a double spin asymmetry –This is for longitudinally polarized protons Rotating partons around spin direction Two classes of collisions: –Like helicity, i.e., –Un-like helicity, i.e., Basic Picture Positive Helicity Negative Helicity

6/2/2005Douglas Fields3 Like Helicity (Positive on Positive Helicity) Central Collisions Smaller Peripheral Collisions Larger Integrate over b, left with some residual k T Measure jet Peripheral Collisions Larger

6/2/2005Douglas Fields4 Un-like Helicity (Positive On Negative Helicity) Peripheral Collisions Smaller Central Collisions Larger Integrate over b, left with some different residual k T

6/2/2005Douglas Fields5 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

6/2/2005Douglas Fields6 From Meng Ta-Chung et al. Phys Rev. D40, p769, (1989) For a particular impact parameter, b, the average transverse momentum Where, is the product of the Jacobian and the density profile of partons, and D(b) is the overlap region. Total transverse momentum squared of partons k TR k PR

6/2/2005Douglas Fields7 From Meng Ta-Chung et al. Phys Rev. D40, p769, (1989) The constant terms in p t cancel and we have We can now helicity separate: b We can then average over the impact parameter k TR k PR k TR k PR Like Helicity Un-like Helicity

6/2/2005Douglas Fields8 From Meng Ta-Chung et al. Phys Rev. D40, p769, (1989) This paper makes the following assumptions: 1)Uniform spherical density F(b,θ P,θ T ) 2)k PR ~k TR ~k R (no dependence on b, θ P, θ T.) Then, Evaluated numerically

6/2/2005Douglas Fields9 How Large an Effect Can We Expect?

6/2/2005Douglas Fields10 Pause For Feedback Need theoretical guidance! Would be nice to have experimental handle on impact parameter: –Multiplicity Forward or central Underlying event… but, not explicitly necessary.

6/2/2005Douglas Fields11 How do we measure k t ? Intra-jet pairs angular width : N j T Inter-jet pairs angular width : A j T k T 0 - h azimuthal correlation functions Trigger 0

6/2/2005Douglas Fields12 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

6/2/2005Douglas Fields13 π 0 Identification PHENIX has central arm EMCal with electron rejection in RICH. Used shower profile cut. Good S/B at higher p t (>2GeV).

6/2/2005Douglas Fields14 Charged Particles Tracks in the Drift Chamber Hits in the Pad Chambers RICH veto for low momentum Shower shape cut at high momentum

6/2/2005Douglas Fields15 Correlation Functions dN real Δφ distribution from particles in the same event dN mixed Δφ distribution from particles in different events with similar vertex position Norm = Fit to two gaussians plus a constant term 3.0<p T <4.0 Fit = const + Gauss(0)+Gauss( ) 1.5<p T <2.0 Intra-jet pairs angular width : N j T Inter-jet pairs angular width : A j T k T

6/2/2005Douglas Fields16 Jet Kinematics

6/2/2005Douglas Fields17 How accurately can we measure ? is extracted from and fragmentation functions which are extracted from the inclusive distributions.

6/2/2005Douglas Fields18 How accurately can we measure Δ ? Z T uncertainties should cancel in the difference Bunch Shuffling in Run3 (PHENIX) –δ Δ ~ 80MeV

6/2/2005Douglas Fields19 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 (P Y *P B ) than Run3

6/2/2005Douglas Fields20 Summary We can make a measurement of the double-longitudinal spin dependence of jet. This may be sensitive to orbital angular momentum. These effects (if really there) may also influence the double-longitudinal cross- section asymmetry. Need theoretical guidance…