1. Strange Quark Contribution to the Proton Spin, from Elastic ep and p Scattering Stephen Pate New Mexico State University SPIN 2006 Kyoto, Japan, 3-October-2006 A combined analysis of HAPPEx, G 0, and BNL E734 data

2. Outline Initial indication of significant negative strange quark contribution to the proton spin came from SU(3)-based analysis of inclusive polarized DIS data from CERN (EMC); Similar experiments at SLAC and CERN supported this finding; An attempt to confirm this using neutrino-proton elastic scattering (BNL E734) was inconclusive; HERMES made first significant measurement of strange quark polarized p.d.f., using semi-inclusive DIS, for 0.03 < x < 0.2; suggests strange quark contribution to the proton spin is essentially zero! A combined analysis of BNL E734 p data with very recent HAPPEX and G 0 forward-scattering ep data show the Q 2 -dependence of the strange axial form factor for 0.45 < Q 2 < 1.0 GeV 2 ; suggests the strange quark contribution is negative… What to do now?

3.  s from polarized inclusive DIS Plan: Measure values of g 1 (x,Q 2 ), extrapolated to x=0 and x=1, and combine with axial charges from hyperon beta-decay data to extract a flavor decomposition of the quark axial charges. [E.g. see B.W. Filippone and X. Ji, Adv. Nucl. Phys. 26 (2001) 1 and references therein…] Surprise #1: Quarks contribute only about 20% of the proton spin. Surprise #2: Strange quarks make a negative contribution:  s ~  0.15 Problems: Need SU(3) flavor symmetry to bring in the hyperon data. Extrapolation to x=0 problematic. => Unknown theoretical uncertainties.

4.  s from p elastic scattering Plan: Measure absolute cross section for p elastic scattering, and extract the strange contribution to the proton axial form factor. Extrapolate to Q 2 =0 to obtain the strange quark axial charge. Note: Elastic p scattering and inclusive DIS both measure the sum of strange quark and strange anti-quark contributions. BNL E734 measured this cross section for both neutrinos and anti- neutrinos, but result for  s was inconclusive. Large uncertainty in cross sections. Lowest Q 2 point (0.45 GeV 2 ) not really low enough. Subsequent reanalyses (Garvey et al, Alberico et al.) came to similar non-conclusion.

5.  s from polarized semi-inclusive DIS Plan: Measure tagged structure function g 1 h (x,Q 2 ) by observing leading hadrons in coincidence with scattered lepton. Use leading- order analysis to extract separated polarized quark distributions  q(x). Integrate observed portion of  q(x) to get estimates of axial charges. [See HERMES PRD 71 (2005) 012003 and talk by Hal Jackson a few minutes ago…] Result: Advantages: No SU(3) assumption. No extrapolations to x=0. Can separate quark and anti-quark contributions. Disadvantages: Leading-order analysis. Some folks question validity of factorization at relatively low Q 2. Result contradicts SU(3)-based analysis of inclusive DIS data.

6.  s from combination of ep and p elastic scattering data [finally we come to the main point of this talk…] Plan: Combine existing p data from BNL E734 with recent parity- violating ep scattering data from HAPPEx and G0. Extract the strangeness contribution to the proton electromagnetic and axial form factors point-by-point. Observe Q 2 -dependence of these form factors for the very first time. [See SP, PRL 92 (2004) 082002, and SP et al., hep-ex/0512032] Advantages: No SU(3) assumption. Get total integral over x by using elastic scattering. Neutrino scattering is very sensitive to the axial form factor.

7. Features of parity-violating forward-scattering ep data measures linear combination of form factors of interest axial terms are doubly suppressed  (1  4sin 2  W ) ~ 0.075  kinematic factor  ” ' ~ 0 at forward angles significant radiative corrections exist, especially in the axial term à parity-violating data at forward angles are mostly sensitive to the strange electric and magnetic form factors

8. Full Expression for the PV ep Asymmetry Note suppression of axial terms by (  sin   W  and  ” ' 

9. Things known and unknown in the PV ep Asymmetry

10. Features of elastic p data measures quadratic combination of form factors of interest axial terms are dominant at low Q 2 radiative corrections are insignificant [Marciano and Sirlin, PRD 22 (1980) 2695] à neutrino data are mostly sensitive to the strange axial form factor

11. Elastic NC neutrino-proton cross sections Dependence on strange form factors is buried in the weak (Z) form factors.

12. The BNL E734 Experiment performed in mid-1980’s measured neutrino- and antineutrino-proton elastic scattering used wide band neutrino and anti-neutrino beams of =1.25 GeV covered the range 0.45 < Q 2 < 1.05 GeV 2 large liquid-scintillator target-detector system still the only elastic neutrino-proton cross section data available

13. Q 2 (GeV) 2 d  /dQ 2 ( p) (fm/GeV) 2 correlation coefficient 0.45 0.165  0.0330.0756  0.0164 0.134 0.55 0.109  0.0170.0426  0.0062 0.256 0.65 0.0803  0.01200.0283  0.0037 0.294 0.75 0.0657  0.00980.0184  0.0027 0.261 0.85 0.0447  0.00920.0129  0.0022 0.163 0.95 0.0294  0.00740.0108  0.0022 0.116 1.05 0.0205  0.00620.0101  0.0027 0.071 Uncertainties shown are total (stat and sys). Correlation coefficient arises from systematic errors. E734 Results

14. Combination of the ep and p data sets We use PV ep data in the same range of Q 2 as the E734 experiment. The original HAPPEx measurement: Q 2 = 0.477 GeV 2 [PLB 509 (2001) 211 and PRC 69 (2004) 065501] The recent G 0 data covering the range 0.1 < Q 2 < 1.0 GeV 2 [PRL 95 (2005) 092001] E734 Q 2 range

15. Combination of the ep and p data sets Since the neutrino data are quadratic in the form factors, then there will be in general two solutions when these data sets are combined. Fortunately, the two solutions are very distinct from each other, and other available data can select the correct physical solution. Intersections between electron and neutrino data. 1 2 Q 2 = 0.5 GeV 2

16. General Features of the two Solutions There are three strong reasons to prefer Solution 1: G A s in Solution 2 is inconsistent with all DIS estimates for  s G M s in Solution 2 is inconsistent with the recent HAPPEx result of G M s ~ 0 at Q 2 = 0.1 GeV 2 G E s in Solution 2 is inconsistent with the idea that G E s should be small, and conflicts with expectation from recent G 0 data that G E s may be negative near Q 2 = 0.3 GeV 2 GEsGEs Consistent with zero (with large uncertainty) Large and positive GMsGMs Consistent with zero (with large uncertainty) Large and negative GAsGAs Small and negativeLarge and positive Solution 1 Solution 2 I only present Solution 1 hereafter.

17. HAPPEx & E734 [SP, PRL 92 (2004) 082002] G0 & E734 [SP et al., hep-ex/0512032] First determination of the strange axial form factor.

18. HAPPEx & E734 [SP, PRL 92 (2004) 082002] G0 & E734 [SP et al., hep-ex/0512032] Q 2 -dependence suggests  s < 0 ! Strange Axial Form Factor from ep and p Elastic Scattering Data E734 data quality and Q 2 range again prevent a definitive conclusion, but the trend clearly suggests a negative strange quark contribution.

19. What if….? If these two results are both true, then the average value of  s(x) in the range x < 0.02 must be ~  5. That’s not impossible, as s(x) is ~20- 300 in the range x~10 -2 to 10 -3 (CTEQ6). But we would need a mechanism that would “turn on” the strange quark polarization suddenly at these low x values. Another more exotic possibility exists…

20. A topological “x  0” contribution to the singlet axial charge? Accessible in a form factor measurement “subtraction at infinity” term from dispersion relation integration [Steven Bass, hep-ph/0411005] Accessible in deep-inelastic measurements

21. What to do? The E734 data have insufficient precision and too narrow a Q 2 range to determine the strange quark contribution to the proton spin. Better neutrino data is needed, with smaller uncertainties and points nearer Q 2 = 0. A detailed understanding of the Q 2 -dependence of these form factors will not be possible until a more dense set of resolved data points are available. The semi-inclusive DIS data need to be extended to lower x and higher Q 2 to determine which of the two proposed explanations is correct, or perhaps to reveal some other explanation. A NLO analysis would also be a good idea. We need to approach the problem from the point of view of both kinds of data.

22. Better p elastic scattering data FINeSSE (B. Fleming and R. Tayloe) at BNL or FNAL A measurement of p elastic scattering is being considered for JPARC (NeuSpin, see talk by Y. Miyachi).

23. Better semi-inclusive DIS data Electron Ion Collider (EIC) The problem of the strange quark contribution to the proton spin is an explicit part of the physics program at this new facility. Improved version of HERMES semi-inclusive measurement will explore the quark polarizations to lower x and higher Q 2. [Figure is a simulation from Kinney and Stoesslein, AIP Conf. Proc. 588 (2001) 171.] HERMES

24. Conclusion Strange quark contribution to the proton spin remains a mystery. HERMES semi-inclusive DIS data suggests zero contribution. Inclusive DIS data with SU(3)-based analysis, and independent data from form factor measurements, suggest a negative contribution. None of these measurements are definitive. Better neutrino data are needed to improve the form factor picture for a clean determination of  s. => FINeSSE/NeuSpin Better semi-inclusive DIS data are needed to explore the low-x region to better understand the  s(x) distribution. => EIC [This work supported by the US DOE.]

25. More slides…

26. HAPPEx, SAMPLE & PVA4 combined (nucl-ex/0506011) FINeSSE (& G0) [exp. proposal: no nuclear initial or final state effects included in errors] HAPPEx & E734 [Pate, PRL 92 (2004) 082002] G0 & E734 [to be published] G0/HAPPEx/PVA4 Projected

27. An, Riska and Zou, hep-ph/0511223; Riska and Zou, nucl-th/0512102. determine a unique uudss configuration, in which the uuds system is radially excited and the s is in the ground state.

28. HAPPEx & E734 [Pate, PRL 92 (2004) 082002] G0 & E734 [to be published] Recent calculation by Silva, Kim, Urbano, and Goeke (hep-ph/0509281 and Phys. Rev. D 72 (2005) 094011) based on chiral quark-soliton model is in rough agreement with the data.