1. Recent results from high-energy longitudinal polarized proton-proton collisions at 200GeV at RHIC
Tai Sakuma
MIT

2. The gluon contribution to the proton spin, G, is poorly constrained.
Polarized DIS found
that quarks carry
only a small fraction
of the proton spin  - q p
G is only loosely
constrained from
polarized DIS data.
≈0.2
quarks
gluons
orbital motions
proton spin
The spin of the proton is carried by the quarks, gluons, and the orbital motions of quarks and gluons inside the proton.
Polarized deep inelastic scattering experiments found that delta sigma is small.
pDIS data can only loosely constrain delta g.
In polarized proton-proton collision p g
polarized pp 2

3. One of the goals of RHIC-Spin is to determine G with polarized pp collisions.
In proton-proton collisions,
gluons are in the initial states at lowest order.
polarized pp 3

4. In polarized pp collisions, ALL is the most important quantity to measure to determine G.
the double spin asymmetry in polarized pp collisions
- sensitive to G
As an example of ALL, this is one of the early results from STAR.
PRL 97 (2006)
In polarized pp collisions, A_LL is what is primarily measrued to study delta G.
As an example, this is the first A_LL result from STAR.
The result is comparted with four theory predicitions. p g
polarized pp

5. ALL is sensitive to G
The result is compared with theory predictions from GRSV working group.
As an example of ALL, this is one of the early results from STAR.
PRL 97 (2006)

6. ALL is sensitive to G
GRSV xG(x)
The result is compared with theory predictions from GRSV working group.
PRL 97 (2006)
GRSV polarized pdf
PRD 63 (2001)
GRSV - std
GRSV - max
GRSV - min
GRSV - zero
Each prediction has different polarized gluon distribution inputs.
Those are the four distribtuions.
They are provided by a global fit working group called GRSV.
They perform global fit to polarized deep inelastic experiments and provide polarized parton distrituion.
They provide four polarized gluon distributions.
Best fit to pDIS
Large uncertainty
3 extreme scenarios

7. ALL is predicted for various final states with different G models
GRSV xG(x)  
jet 

8. ALL is measured for various final states
jet
J/      

9. STAR inclusive jet ALL systematics 2006 RHIC Run 4.7 [pb-1]
Polarization ~60%
Jet Patch Trigger
Energy in a patch of calorimeter
towers (x  = 1 x 1) > 8.3 GeV
Midpoint Cone Algorithm
Cone Radius = 0.7
PARTICLE jet pT
Corrected measured jet pT to true jet pT
with Pythia MC sample
systematics
ALL systematics
(x 10-3)
Jet Reconstruction
+ Trigger Bias
[-2, +5] (pT dep)
Non-longitudinal
Polarization
~0.03 (pT dep)
Relative Luminosity
0.94
Backgrounds
0.5 (1st bin), 0.1(else) 15

10. STAR inclusive jet ALL
The results are compared with the GRSV ALL predictions. 16

11. STAR inclusive jet ALL The series of G spanning G-min and G-max
To quantify the impact on G 17

12. STAR inclusive jet ALL ALL predictions based on the series of G
The series of G spanning G-min and G-max
To quantify the impact on G 18

13. STAR inclusive jet ALL
Comparison of the results with the series of the ALL predictions
allowed region
GRSV STD
ALL predictions based on the series of G
Confidence Levels from the comparison
For example, the C.L. for G = 0.3 is about 0.1%. This means that if G = 0.3 is true, the probability that we observe ALL that is in worse agreement than the ALL we actually observed is 0.1 percent. 19

14. Confidence Levels from the comparison
STAR inclusive jet ALL
allowed region
Impact on G
GRSV STD
The 2006 results excluded G < -0.7 and G > 0.2 with C.L. 90% within the GRSV framework.
The results are consistent with pDIS data.
Confidence Levels from the comparison
For example, the C.L. for G = 0.3 is about 0.1%. This means that if G = 0.3 is true, the probability that we observe ALL that is in worse agreement than the ALL we actually observed is 0.1 percent. 20

15. PHENIX Inclusive π0 ALL    highly segmented EMCal
x  = 0.01 x 0.01
Run 5
3.5 [pb-1]
Polarization ~ 50%
Run 6
7.5 [pb-1]
Polarization ~ 60%
Final scaling error will be ~10%
Soft physics contribution
~ 10% at 2 GeV
Corrected for the background ALL

16. ALL predictions based on the series of G
PHENIX Inclusive π0 ALL
ALL predictions based on the series of G 22

17. PHENIX Inclusive π0 ALL Within the GRSV framework, 2min = 7/~7 NDF
Comparison of the results with the series of the ALL predictions
ALL predictions based on the series of G
Within the GRSV framework,
2min = 7/~7 NDF
2min + 3  -0.8 < G < 0.2 23

18. The constraints on G from the STAR and PHENIX results
inclusive 0
inclusive jets
The combined results constrain G
The Nuclear Science Advisory Committee (NSAC) Long-Range Plan (LRP)
STAR and PHENIX results are consistent and complementary
The analysis was done within the GRSV framework

19. The analysis was done within the GRSV framework
Beyond GRSV framework
The Nuclear Science Advisory Committee (NSAC) Long-Range Plan (LRP)
The analysis was done within the GRSV framework 25

20. The analysis was done within the GRSV framework
Beyond GRSV framework
The Nuclear Science Advisory Committee (NSAC) Long-Range Plan (LRP)
The analysis was done within the GRSV framework 26

21. The analysis was done within the GRSV framework
Beyond GRSV framework
The range of x probed is
0.02 < x < 0.3
The Nuclear Science Advisory Committee (NSAC) Long-Range Plan (LRP)
The analysis was done within the GRSV framework 27

22. The analysis was done within the GRSV framework
Beyond GRSV framework
Gehrmann-Stirling Set C (GS-C) has highly polarized gluon in low x and G = 1
The range of x probed is
0.02 < x < 0.3
The Nuclear Science Advisory Committee (NSAC) Long-Range Plan (LRP)
The analysis was done within the GRSV framework 28

23. ALL for GS-C is consistent with the results from RHIC Spin
Beyond GRSV framework
Gehrmann-Stirling Set C (GS-C) has highly polarized gluon in low x and G = 1
The range of x probed is
0.02 < x < 0.3
ALL for GS-C is consistent with the results from RHIC Spin
The Nuclear Science Advisory Committee (NSAC) Long-Range Plan (LRP) 29

24. Beyond GRSV framework
Gehrmann-Stirling Set C (GS-C) has highly polarized gluon in low x and G = 1
The range of x probed is
0.02 < x < 0.3
The Nuclear Science Advisory Committee (NSAC) Long-Range Plan (LRP)
G = 1 is ruled out within the GRSV framework but is still possible for much different shape of xG(x) 30

25. The low-x region needs to be measured.
500 GeV
Forward
, +jet
The range of x probed is
0.02 < x < 0.3
The Nuclear Science Advisory Committee (NSAC) Long-Range Plan (LRP)
Forward Meson Spectrometer (FMS) 31

26. New global analysis is starting at BNL.
G(x) models
ALL predictions  - q p
pDIS data
ALL measurements p g
constrains on G

27. New global analysis is starting at BNL. - q p
New global analysis at BNL
include both pDIS and RHIC Spin data for global fits of the polarized pdf.
started at BNL in the Fall 2007.
collaborative effort of
theorists from GRSV, DNS
and
experimentalists from
STAR and PHENIX.
pDIS data
ALL measurements p g

28. Summary
ALL for various final states in polarized pp collisions is measured at 200 GeV at RHIC.
ALL from RHIC is constraining G to -0.8 < G < 0.2 with 90% C.L. within the GRSV framework and the probed x range of 0.02 < x < 0.3.
Significant measured sensitivity is expected at RHIC with , +jet channels and 500 GeV run with access to lower x.
A global analysis of the polarized parton distributions with pDIS and RHIC data is starting at BNL.