1. Finding The Spin of the Proton
Douglas Fields
University of New Mexico

2. Outline Review of Problem Spin physics at RHIC
Brief Review of Deep Inelastic Scattering
Spin “Crisis”
Spin physics at RHIC
RHIC and PHENIX
Measurements of ΔG
“Measurements” of ΔL
PHENIX upgrades and future measurements
February 4, 2009 LANL P-25 Seminar

3. Motivation Hadron Physics: Standard Model Tests: Forget all of that
Understanding of the structure of the nucleon.
Understanding of nuclear interactions.
Tests of QCD.
Standard Model Tests:
Use spin as a tool to test Standard Model predictions.
Search for exotics (SUSY, PV…).
Forget all of that
Spin is as fundamental as charge or mass!
February 4, 2009 LANL P-25 Seminar

4. Spin Effects Polarized pp elastic scattering at 197MeV.
Ay ~ (NL – NR)/ (NL + NR)
Shows that the strong (nuclear) force depends strongly on the spin orientation. p NL NR
February 4, 2009 LANL P-25 Seminar

5. “Naïve Quark Model”
Protons are spin ½ objects composed of three spin ½ objects.
Since Quarks are fermions, total wavefunction must be antisymmetric
February 4, 2009 LANL P-25 Seminar

6. Strong Spin Dependence
Deltas are spin 3/2 objects composed of three spin ½ objects.
Mass is ~300MeV greater than proton!
February 4, 2009 LANL P-25 Seminar

7. Predictions
Baryon magnetic moments are well predicted by the Naïve Quark Model
mu = md ~ 1/3mp
ms given by L magnetic moment
(but mu=4MeV, md=7MeV)?
February 4, 2009 LANL P-25 Seminar

8. Caveat…
Quarks (and anti-quarks) only account for ½ of nucleon momentum and it is dependent on at what scale you observe.
I like the fractal analogy:
At low resolving power, one sees three quarks in the nucleon
At higher resolving power, one sees more and more detail of what a quark is, namely a collection of quarks, antiquarks and gluons.
Resolving power (smaller scales)
February 4, 2009 LANL P-25 Seminar

9. 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 (1995)
February 4, 2009 LANL P-25 Seminar

10. Probing the Proton EM interaction Strong interaction Weak interaction
Photon
Sensitive to electric charge2
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
February 4, 2009 LANL P-25 Seminar

11. Missing Ingredients Longitudinal momentum fraction (x)
Transverse position (b)
Intrinsic transverse momentum (kT)
Correlations of above (x┴ x kT)
P.H. Hägler, et. al.
February 4, 2009 LANL P-25 Seminar

12. Parton Distribution Functions
Quark Distributions
unpolarized distribution
q(x,Q2)= =
helicity distribution
Dq(x,Q2)=
g(x,Q2)=
Dg(x,Q2)=
No Transverse Gluon Distribution in 1/2
Gluon Distributions
transversity distribution
dq(x,Q2)=
February 4, 2009 LANL P-25 Seminar

13. Sum Rules Momentum Sum Rule Helicity Sum Rule:
ΔΣ measured in DIS experiments and found to be small (0.1 – 0.3)…
February 4, 2009 LANL P-25 Seminar

14. “Spin Crisis” “Not-so-Naïve” quark model and comparison to results
Predicted from EJSR
Measured in DIS
February 4, 2009 LANL P-25 Seminar

15. Not Really a Crisis… Remember the more complicated possibilities…
But Leptons don’t scatter off gluons (at first order)
How do we probe the gluons?
February 4, 2009 LANL P-25 Seminar

16. (longitudinal polarization)
RHIC Spin
BRAHMS & PP2PP
STAR
AGS
LINAC
BOOSTER
Pol. H- Source
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 flipper
PHENIX
February 4, 2009 LANL P-25 Seminar

17. PHENIX Detector Philosophy: High resolution at the cost of acceptance
High rate capable DAQ
Excellent trigger capability for rare events
Central Arms:
||<0.35, =2900
Charged particle ID and tracking; photon ID. EM Calorimetry.
Muon Arm:
1.2<||<2.4
Muon ID and tracking.
Global Detectors
Collision trigger
Collision vertex characterization
Relative luminosity
Local Polarimetry
February 4, 2009 LANL P-25 Seminar

18. “Measurements” of ΔG Example: choose channel with high statistics
p + p → π0 + X
Complicated mixture of
amplitudes
Compare with:
February 4, 2009 LANL P-25 Seminar

19. Solution Factorization between hard and soft physics Soft: Hard:
Example: q + g → π0 + X
Soft:
q(x), Δq(x), D(z)
Hard:
NLO pQCD cross-sections – spin dependent
Missing ingredients:
Δg(x)
beam polarization
Soft Physics
from universal
fits to data
Hard Physics
σ ~ momenta
and helicities D
February 4, 2009 LANL P-25 Seminar

20. Status of Ingredients Status of Pol. PDFs (2004)
Valence quark fairly well determined from DIS
ΔG and sea quarks poorly known
February 4, 2009 LANL P-25 Seminar

21. pQCD Check
pp0 X :
PRD76,051106
Next step: Measure cross-section as a test for perturbative QCD at
Run 6, pushes p0 cross-section to 20 GeV/c.
Agreement with pQCD over broad range of pT.
Does this mean that QCD works for spin sorted in this same range?
February 4, 2009 LANL P-25 Seminar

22. Where Are We So Far? Factorization between hard and soft physics Soft:
Example: q + g → π0 + X
Soft:
q(x), Δq(x), D(z)
Hard:
NLO pQCD cross-sections – spin dependent
Missing ingredients:
Δg(x), P – beam polarization ☺ ☺ ☺
Soft Physics
from universal
fits to data ☺
Hard Physics
σ ~ momenta
and helicities D ☺
February 4, 2009 LANL P-25 Seminar

23. π0 ALL
arXiv:
Put all ingredients into a NLO pQCD calculation with assumed values of ΔG, Monte Carlo the results with the detector acceptance, and compare to data to determine allowed values of ΔG.
February 4, 2009 LANL P-25 Seminar

24. From ALL to G (with GRSV model)
Generate g(x) curves for different (with DIS refit)
Compare ALL data to curves (produce 2 vs G)
arXiv:
Calculate ALL for each G
February 4, 2009 LANL P-25 Seminar

25. Update to Pol. PDFs
Using the π0 results from PHENIX, one can recalculate allowed values of the pol. PDFs.
Much improved limits on ΔG.
February 4, 2009 LANL P-25 Seminar

26. ΔL
ΔG is appearing to be small (although it may be enough to solve the Spin Crisis)
What is next?
ΔL…
Theory tells us it should be there anyway.
Anomalous magnetic moment
Sivers Effect
February 4, 2009 LANL P-25 Seminar

27. Sivers Effect
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). SP
kT,q p
FSI : SIDIS
ISI : Drell-Yan
February 4, 2009 LANL P-25 Seminar

28. How can you get a net kT?
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.
February 4, 2009 LANL P-25 Seminar

29. Sivers Effect No Sivers Effect without interaction with absorber.
February 4, 2009 LANL P-25 Seminar

30. Fields Effect Think of rotating (longitudinal) water balloons, or…
February 4, 2009 LANL P-25 Seminar

31. Origin of Jet kT Another Possibility:
Net transverse momentum of a di-hadron pair in a factorization ansatz
Di-hadron pT kT
initial – e.g., fermi motion of the confined quarks or gluons, initial-state gluon radiation…
hard – final-state radiation (three-jet)…
frag – fragmentation transverse momentum jT
Another Possibility:
Spin-correlated transverse momentum – partonic orbital angular momentum
Can examine the helicity dependence of each term:
February 4, 2009 LANL P-25 Seminar

32. Like Helicity (Positive on Positive Helicity)
Peripheral Collisions
Larger
Peripheral Collisions
Larger
Measure jet
Integrate over b, left
with some residual kT
Central Collisions
Smaller
February 4, 2009 LANL P-25 Seminar

33. Un-like Helicity (Positive On Negative Helicity)
Peripheral Collisions
Smaller
Integrate over b, left
with some different
residual kT
Central Collisions
Larger
February 4, 2009 LANL P-25 Seminar

34. Integrating over Impact Parameter
Drell-Yan pair production in polarized p+p collisions.
(Meng Ta-Chung et al. Phys. Rev. D 1989)
kTR
kPR
Like Helicity
Un-like Helicity
Averaging over D(b):
Integrating over impact parameter b:
February 4, 2009 LANL P-25 Seminar

35. Measuring jet kT – di-hadron correlation
o- h± azimuthal correlation
Trigger on a particle, e.g. o, with transverse momentum pTt. Measure azimuthal angular distribution w.r.t. the azimuth of associated (charged) particle with transverse momentum pTa. The strong same and away side peaks in p-p collisions indicate di-jet origin from hard scattering partons.
February 4, 2009 LANL P-25 Seminar

36. How does PHENIX measure kt?
near
Zero kT
Non-Zero kT
Intra-jet pairs angular width : near  jT
Inter-jet pairs angular width : far  jT  kT
far
Drawings by A. Zimmerman
February 4, 2009 LANL P-25 Seminar

37. Jet Kinematics For details, see: Phys. Rev. D 74, 072002 (2006)
February 4, 2009 LANL P-25 Seminar

38. Correlation Function Red – real (raw Δφ)
Blue – background (mixed events)
February 4, 2009 LANL P-25 Seminar

39. Fit Function Blue – real (raw Δφ) Red – Fit from above equation
February 4, 2009 LANL P-25 Seminar

40. Spin sorted dihadron correlations
Fit Results
Red – Like helicity (++ & --)
Blue – Unlike helicity (+- & -+)
February 4, 2009 LANL P-25 Seminar

41. Need <zt> and xh
<k2T> asymmetry results are not sensitive to this xh and <zt> values – only needed to set the scale. ^
xh and <zt> are determined through a combined analysis of the π° inclusive cross section and using jet fragmentation function measured in e+e- collisions. Ref. PRD 74, (2006) ^
February 4, 2009 LANL P-25 Seminar

42. kT results for unpolarized case
kT = / (stat) +/ (syst) GeV
jT = /- 0.8 (stat) +/- 0.3 (syst) MeV
February 4, 2009 LANL P-25 Seminar

43. Preliminary Results Take the difference Like – Unlike helicities.
Normalized by beam polarizations.
<j2T > asymmetry small (-6 ± 6 MeV out of ~607 MeV for unpolarized).
<k2T > asymmetry also small (-8 ± 90 MeV out of ~2.9 GeV for unpolarized).
February 4, 2009 LANL P-25 Seminar

44. Interpretation
The small asymmetry in jT verifies our assumption that the third term is suppressed.
The second term may be constrained from current knowledge of the π0 ALL.
February 4, 2009 LANL P-25 Seminar

45. Interpretation
The first term can be related in the “Meng conjecture” to partonic transverse momentum:
where cij give the initial state weights and Wij give the impact parameter weighting.
Since PYTHIA studies show that the final state studied here is dominated by gg scattering (~50%),
We can interpret this as a constraint on the gluon orbital angular momentum.
Consistent with previous (Sivers) measurements, and complimentary, since one naïvely needs no initial or final state interactions.
February 4, 2009 LANL P-25 Seminar

46. What Next?
February 4, 2009 LANL P-25 Seminar

47. PHENIX VTX Detector Upgrade
Main physics goal to discriminate heavy-flavor production via displaced vertices.
I would like to use it to better determine jet kT.
Needs simulation and study.
February 4, 2009 LANL P-25 Seminar

48. Summary
We have an analysis tool – di-hadron azimuthal correlations - that allows us to measure kT.
We are studying this in helicity-sorted collisions to see if there is a spin-dependent, coherent component of kT.
In our kinematic range, we find jT RMS = -6 ± 6 MeV, and kT RMS = -8 ± 90 MeV.
While this is consistent with other measurements related to gluon OAM, the connection to parton OAM needs theoretical guidance!
February 4, 2009 LANL P-25 Seminar

49. Summary
Our group has made significant contributions to the RHIC Spin program and to the PHENIX experiment.
We are currently leading the investigation of an interesting, albeit speculative, physics analysis.
We will continue significant contributions to the PHENIX upgrade plan with an eye on our research thrust.
I look forward to an invigorated nuclear/particle group with the addition of active theorists.
February 4, 2009 LANL P-25 Seminar

50. Backups
February 4, 2009 LANL P-25 Seminar

51. How do you measure the quark spins?
~ l-q elastic scattering k k/
Leading order diagram.
+ Radiative corrections
+ NLO corrections
+ Higher twist…
n, q X
February 4, 2009 LANL P-25 Seminar

52. eμ Elastic Scattering e-(p2,s2) m-(p4,s4) m-(p3,s3) e-(p1,s1)
Initial State
Potential
Final State
Probability to happen:
February 4, 2009 LANL P-25 Seminar

53. Feynman Prescription…
EM coupling strength e
EM coupling strength e
Electric interaction
Magnetic interaction
February 4, 2009 LANL P-25 Seminar

54. Now, for e-quark scattering
eq scattering
Now, assume:
So that,
Modified by the quark fractional charge
Modified by the quark mass
February 4, 2009 LANL P-25 Seminar

55. Step towards protons…
Sum over quark flavors and integrate over x weighted by f(x), the probability to have momentum fraction x:
Electric STRUCTURE Function
Magnetic STRUCTURE Function
February 4, 2009 LANL P-25 Seminar

56. Structure Functions Structure functions in the scaling limit
Spin independent
Spin dependent
(= 0 when sum over spins)
This is related to the elastic scattering off parton with momentum fraction p = xP
February 4, 2009 LANL P-25 Seminar

57. Nosecone Calorimeter
Main physics goals to measure γ-jet events and isolate muons from W-decay
I would like to use it to better determine jet kT.
Needs simulation and study.
Tungsten absorber
Pb absorber
Pad readout
Stripixel readout
Cu skin
15 mm
February 4, 2009 LANL P-25 Seminar