1. 6/21/2006Douglas Fields UNM/RBRC1 Spin and the Lattice - Experimental Overview ???? Douglas E. Fields University of New Mexico/Riken-BNL Research Center

2. 6/21/2006Douglas Fields UNM/RBRC2 What value can I add?  Share some experimental details –Delivering a “Measureable”, a few selected details RHIC Spin “lattice” Polarimetry Analysis  Share insight into my ignorance –What does the proton look like? –What can we do in experiment?

3. 6/21/2006Douglas Fields UNM/RBRC3 What are the deliverables? = Gluon polarization from DIS from pQCD Experiment

4. 6/21/2006Douglas Fields UNM/RBRC4 RHIC Spin Collider Overview BRAHMS & PP2PP STAR PHENIX AGS LINAC BOOSTER Spin Rotators (longitudinal polarization) Solenoid Partial Siberian Snake Siberian Snakes 200 MeV Polarimeter AGS Internal Polarimeter Rf Dipole RHIC pC Polarimeters Absolute Polarimeter (H  jet) AGS pC Polarimeters Strong AGS Snake Helical Partial Siberian Snake PHOBOS Spin Rotators (longitudinal polarization) Spin flipper Siberian Snakes Installed and commissioned during FY04 run Commissioned during FY05 run Installed and commissioned during FY05 run

5. 6/21/2006Douglas Fields UNM/RBRC5 Continuous Progress

6. 6/21/2006Douglas Fields UNM/RBRC6 Polarimetry The problem of high energy polarimetry was not solved when RHIC spin began. Choices included a pion spectrometer a la E704… Or a proton-carbon polarimeter, yet to be designed and with unknown analyzing power…

7. 6/21/2006Douglas Fields UNM/RBRC7 Coulomb-Nuclear Interference Momentum transfer Extremely forward scattering Recoil carbon: Very low kinetic energy

8. 6/21/2006Douglas Fields UNM/RBRC8 E950 ADC distribution TDC distribution Carbon ribbon targets 6mm wide 3.7mg/cm2 thick 3cm long

9. 6/21/2006Douglas Fields UNM/RBRC9 Polarimeters in the C-AD LINAC 200 MeV –inclusive production proton from p-Carbon interactions 50% analyzing power, Fast a 2% in about 1 min. –pd elastic scattering slow, used to calibrate the above polarimeter Booster –none, however measure in AGS just after injection AGS –p-p quasi-elastic scattering on HydroCarbon and Carbon targets 3-5% analyzing power, good to Gγ ∼ 12 slow at higher energies, 10% measurement in ½ hour –p-Carbon CNI polarimeter 1-2% analyzing power at 24 GeV, fast 5% in 5 min. analyzing power known to 30% at 22 GeV ramp measurements RHIC –p-Carbon CNI polarimeters in Blue and Yellow beams analyzing power known at 22 GeV to 30% fast, a 2% measurement in about 30 sec. ramp measurements polarization profile measurements spin tune measurements Thanks to Alessandro Bravar

10. 6/21/2006Douglas Fields UNM/RBRC10 RHIC and AGS CNI Polarimeters Ultra-thin Carbon target 5  g/cm 2 600  m width beam direction 1 3 4 5 6 AGS RHIC 2 50cm 30cm x 2 rings Si strip detectors (TOF, Ec)

11. 6/21/2006Douglas Fields UNM/RBRC11 AGS Ramp Polarization Measurements resonances: intrinsic: G  = imperfection: G  = n 12+ 36- 36+ GG

12. 6/21/2006Douglas Fields UNM/RBRC12 A N for p  C  pC @ 100 GeV no hadronic spin-flip with hadronic spin-flip “forbidden” asymmetries systematic uncertainty best fit with hadronic spin-flip Kopeliovich – Truemann model PRD64 (01) 034004 hep-ph/0305085 r 5 pC  F s had / Im F 0 had preliminary statistical errors only spread of r 5 values from syst. uncertainties 1  contour

13. 6/21/2006Douglas Fields UNM/RBRC13 Beam Scan

14. 6/21/2006Douglas Fields UNM/RBRC14 p  p  pp and p  p   pp with a Polarized Gas Jet Target RHIC polarized Proton beams polarized gas JET target Need calibration of the RHIC p-C polarimeter (association with a known polarization). Gas jet target, with precisely measured jet polarization. Goal of 5% calibration.

15. 6/21/2006Douglas Fields UNM/RBRC15 A N for p  p  pp @ 100 GeV no need of a hadronic spin – flip contribution to describe these data no hadronic spin-flip Re r 5 = -0.001  0.009 Im r 5 = -0.015  0.029 in the simplest assumption: spin-flip prop. to non-flip ampli. source of systematic errors: 1  P TARGET = 2 % 2 from backgrounds & event selection <  0.0016 3 false asymmetries: small similar to statistical errors  2 ~ 13 / 14 d.o.f. (11 / 12) hep-ex/0601001

16. 6/21/2006Douglas Fields UNM/RBRC16 Transverse Spin Asymmetries Neutron asymmetry observed in IP12 while testing a local polarimeter designed to look for  0,  asymmetries: “Left-Right” asymmetry measured for different slices in phi:

17. 6/21/2006Douglas Fields UNM/RBRC17 Phi Asymmetry Successful measurement of forward neutron asymmetry. Understood (?) in terms of single pion exchange. Large asymmetry gives good figure of merit for local (PHENIX) polarimetry. Y. Fukao et al., "Proceedings of the 15th International Spin Physics Symposium (SPIN2002) Run-02

18. 6/21/2006Douglas Fields UNM/RBRC18 Local Polarimeter at PHENIX Spin Rotators OFF Blue Yellow Spin Rotators ON, Current Reversed Yellow Blue Yellow Yellow Spin Rotators ON, Almost… Spin Rotators ON, Correct! |P|=30%, P T =0%  P L =30%) |P|=37%, P T =24%  P L =28%) P B =35.5% PB=37% Run-03

19. 6/21/2006Douglas Fields UNM/RBRC19 Measurement of Transverse Component LR UD X F >0 X F <0  2 /NDF = 68.1/97 p0 = -0.00226±0.00069  2 /NDF = 119.3/97 p0 = 0.00727±0.00060 = 10.25±2.05(%) = 99.48±0.12±0.02 (%)  2 /NDF = 82.3/97 p0 = -0.00067±0.00064  2 /NDF = 83.0/97 p0 = -0.00089±0.00061 Run 5

20. 6/21/2006Douglas Fields UNM/RBRC20 Relative Luminosity In order to investigate our ability to measure the relative (++ vs. +-) luminosity: – look at ratio of 2 detector scalers crossing-by-crossing: a(i) = N A (i)/N B (i) –Ratio should be the same for all crossings (constant) if: N A (i) = L * ε and N B (i) = L * ε –B is always the counts from the beam-beam counter (BBCLL1), A is one of the other scalers. –Fit this by the expected pattern: a(i) = C[1+A LL P 1 (i)P 2 (i)] C, A LL are the fitting parameters. –Precision of relative luminosity can be estimated by:  C/C –If  2 of the fitting is bad, look for other factors in N(i). Ratio of Zero-Degree Counter scalars to Beam-Beam Counter scalers, sorted by bunch crossing and fit to a constant.

21. 6/21/2006Douglas Fields UNM/RBRC21 Correction factors What other factors could play a role in the determination of the scaler rate besides the luminosity? –Vertex width Vertex width also measured crossing by crossing. Look for a correlation of the scalers ratio with the vertex width: –Good correlation Can correct ratio for this factor.

22. 6/21/2006Douglas Fields UNM/RBRC22 Limit on Relative Luminosity Measurement After correction for (measured) vertex width, the ratio of counts in the two detectors is consistent with constant up to our level of statistics This means that if we apply correction for this the precision on R goes from: 0.11%  0.06% (syst. limited) (stat. limited)

23. 6/21/2006Douglas Fields UNM/RBRC23 Cross-section Next step: Measure cross- section as a test for perturbative QCD at Run-05, pushes  0 cross- section to 20 GeV/c. Agreement with pQCD over broad range of p T. Does this mean that QCD works for spin sorted in this same range?

24. 6/21/2006Douglas Fields UNM/RBRC24 Calculating A_LL Divide data into odd/even bunches for each fill. Calculate A LL (  °+BG) and A LL (BG) separately. Get background ratio (w BG ) from fit of all data. Subtract A LL (BG) from A LL (  °+BG): A LL (  °+BG) = w  ° · A LL (  °) + w BG · A LL (BG) Recombine even and odd.  +BG region : ±25 MeV around  peak BG region : two 50 MeV regions around peak

25. 6/21/2006Douglas Fields UNM/RBRC25 Put it all together Run5 results show a small asymmetry. Compare to NLO calculation. Excludes GRSV-max. Still consistent with GRSV-std and Δg=0.

26. 6/21/2006Douglas Fields UNM/RBRC26 Nice Picture from Naohito EM interaction –Photon Sensitive to electric charge 2 Insensitive to color charge Strong interaction –Gluon Sensitive to color charge Insensitive to flavor Weak interaction –Weak Boson Sensitive to weak charge ~ flavor Insensitive to color

27. 6/21/2006Douglas Fields UNM/RBRC27 Missing Ingredients Longitudinal momentum fraction Transverse position (x ┴ ) Transverse momentum (k T ) Correlations of above (x ┴ x k T ) P.H. Hägler, et. al.

28. 6/21/2006Douglas Fields UNM/RBRC28 3D Parton Distributions (From Harut Avakian) PDFs f p u (x,k T ), g 1, h 1 FFs F 1p u (t),F 2p u (t).. d2kTd2kT  =0,t=0 dx Measure momentum transfer to quark Measure momentum transfer to target Analysis of SIDIS and DVMP are complementary TMD PDFs f p u (x,k T ), GPDs H p u (x, ,t)..

29. 6/21/2006Douglas Fields UNM/RBRC29 What Does the Proton Look Like The distribution of partons in the proton was not very well understood 10 years ago Today, the picture is different… J.D. Bjorken, Collisions Of Constituent Quarks At Collider Energies SLAC-PUB-95-6949 (1995)

30. 6/21/2006Douglas Fields UNM/RBRC30 Nice conceptual picture from D. Sivers (talk given at UNM/RBRC Workshop on Parton Orbital Angular Momentum). Summary: –Sivers effect requires orbital motion (?). –Is process dependent. I would like to just follow this conceptual picture to see where it may lead.

31. 6/21/2006Douglas Fields UNM/RBRC31 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 k T of the partons in the nucleon For a positive Siver’s function, there will be net parton k T 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 S T axis (either aligned or anti-aligned to S T ) 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

32. 6/21/2006Douglas Fields UNM/RBRC32 Two of the possible sources of asymmetry: –Left vs. Right –Front vs. Back

33. 6/21/2006Douglas Fields UNM/RBRC33 Nucl.Phys.B107:1,1976 Hadronic matter current distribution inside a polarized nucleus and a polarized hadron T. T. Chou a a Chen Ning Yang b, a Physics Department, University of Georgia, Athens, Georgia 30602, USA b Institute for Theoretical Physics, State University of New York, Stony Brook, N New York 11794, USA Received 26 January 1976. Available online 22 October 2002. b Abstract The concept ofnucleonic current density (or velocity profile) inside a polarized nucleus and the concept of hadronic matter current density inside a polarized hadron are introduced. Utilizing the increasing opaqueness of hadrons relative to each other at increasing relative velocities, these current densities can be obtained from a measurement of the R(t) parameter in elastic hadron-nucleus and elastic hadron-hadron scattering. For very high energies, the spin dependence in elastic hadron-hadron scattering will be solely due to this non-vanishing R(t) parameter. Measurements of R(t) and therefore the nucleonic current or hadronic matter current thus provide powerful probes for the structure of polarized nuclei and hadrons. The results can be used to check nuclear theory and models of hadron structure. Estimates of the magnitude of R are given by assuming the proportionality between the hadronic matter density-current distribution and the electric charge-current distribution. This proportionality hypothesis which is heuristic is shown to be dependent on the concept of homogenization and the principle of minimum electromagnetic interactions for the basic constituents of hadrons. In the appendix it is shown that the spin of a Dirac particle does involve motion (currents).

34. 6/21/2006Douglas Fields UNM/RBRC34 Sivers Effect Front vs. Back animation of single spin asymmetry –“Quantum Fan” description (top view – spin down): No Sivers Effect without interaction with absorber.

35. 6/21/2006Douglas Fields UNM/RBRC35 Sivers Effect in Double Spin Front vs. Back – Effect adds (?) Spin Down Spin Up

36. 6/21/2006Douglas Fields UNM/RBRC36 Sivers Effect in Double Spin Left vs. Right Spin Down Spin Up

37. 6/21/2006Douglas Fields UNM/RBRC37 Sivers Effect in Double Spin But!!!! Spin Down Spin Up Impact parameter dependence that reduces the effect on average Can double spin asymmetries differentiate pictures?

38. 6/21/2006Douglas Fields UNM/RBRC38 Idea came from 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., Similar Idea for Longitudinal Effect Positive Helicity Negative Helicity

39. 6/21/2006Douglas Fields UNM/RBRC39 Like Helicity (Positive on Positive Helicity) Central Collisions Smaller Integrate over b, left with some residual k T Measure jet Peripheral Collisions Larger Can also have an affect on

40. 6/21/2006Douglas Fields UNM/RBRC40 Un-like Helicity (Positive On Negative Helicity) Peripheral Collisions Smaller Central Collisions Larger Integrate over b, left with some different residual k T

41. 6/21/2006Douglas Fields UNM/RBRC41 History Meng Ta-chung et al. “Experiment B” – similar idea, only for Drell-Yan

42. 6/21/2006Douglas Fields UNM/RBRC42 References

43. 6/21/2006Douglas Fields UNM/RBRC43 Impact Parameter Dependence Would like to follow Ta- Chung’s calculation to determine if effect remains when the impact parameter is undetermined. We first assume constant angular velocity of partons, p θ, 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. R. Hobbs, PhD Thesis, UNM (2006).

44. 6/21/2006Douglas Fields UNM/RBRC44 Trivial Model Use different transverse density distributions to get p t kick from coherent spin-dependent motion:

45. 6/21/2006Douglas Fields UNM/RBRC45 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.

46. 6/21/2006Douglas Fields UNM/RBRC46 Centrality Dependence Would be nice to have experimental handle on impact parameter: –Multiplicity Forward or central Underlying event… but, not explicitly necessary.

47. 6/21/2006Douglas Fields UNM/RBRC47 Summary RHIC Spin program has made much progress, and has great promise in the near future. Deliverables are not “easy”, but so far we have been successful in overcoming difficulties. Jet k T may probe partonic orbital angular momentum… –In single transverse spin (Sivers). –In double transverse spin??? Could be tested with existing data from RHIC. –In double longitudinal spin? Some data have been shown, more coming. These may be sensitive to orbital angular momentum. Need theoretical guidance…