Measuring Orbital Angular Momentum through Jet k T

1. 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

2. 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 Douglas Fields RHIC-AGS User's Meeting

3. 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, 051802, (2004). Breaks collinear factorization Douglas Fields RHIC-AGS User's Meeting

4. 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 Douglas Fields RHIC-AGS User's Meeting

5. 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 talk tomorrow ?? Douglas Fields RHIC-AGS User's Meeting

6. 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

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

8. Positive Helicity Positive Helicity Positive Helicity Negative Helicity 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., Douglas Fields RHIC-AGS User's Meeting

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

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

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

12. 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

13. Total transverse momentum squared of partons 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. From Meng Ta-Chung et al.Phys Rev. D40, p769, (1989) kPR kTR Douglas Fields RHIC-AGS User's Meeting

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

16. 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. Douglas Fields RHIC-AGS User's Meeting

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

18. 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. Douglas Fields RHIC-AGS User's Meeting

19. How Large an Effect Can We Expect? 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. 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 Douglas Fields RHIC-AGS User's Meeting

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

23. Jet Kinematics Douglas Fields RHIC-AGS User's Meeting

24. PHENIXDetector 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

25. 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

26. 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

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 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. Douglas Fields RHIC-AGS User's Meeting

29. Origin of kT An example - J/ production. Breaks collinear factorization pTJ/=1.80.230.16 GeV/c Phys. Rev. Lett. 92, 051802, (2004). Douglas Fields RHIC-AGS User's Meeting Oct. 27, 2005 29

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

31. 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 Douglas Fields RHIC-AGS User's Meeting Δφ Oct. 27, 2005 31

32. 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 Douglas Fields RHIC-AGS User's Meeting Oct. 27, 2005 32

33. 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 Douglas Fields RHIC-AGS User's Meeting Oct. 27, 2005 33

34. 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 Douglas Fields RHIC-AGS User's Meeting Oct. 27, 2005 34

35. 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

36. 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