1. Polarization of Hyperons Orlando Villalobos Baillie University of Birmingham SQM2008 Beijing September 2008

2. Plan of Talk Features of  production Decay channels Effect of different backgrounds Cross checks of sample purity Historical examples Conclusions

3. The Ω - is a baryon consisting of three strange quarks. Its position in the decuplet was one of the key features in establishing the quark model, yet its spin has never been definitively established (see below). In the Liang-Wang model of polarization in heavy ions, the Ω - is expected to have large polarization compared with other baryons Owing to its higher spin, measurement of polarization should be clearer than for ½ + baryons. Interest in Ω - Production

4. Liang-Wang Model The Liang-Wang model notes the large values of L y ~ΔxΔp z produced in non-central nucleus-nucleus collisions, and how these are redistributed by spin-orbit coupling to quark spin orientations in deconfined matter. These result in predictions for particle polarization. For Ω this gives where P s is the polarization of the strange quark. Note that here P Ω ~ ρ ½½. Tensor polarization is not treated.

5. History So Far Measurements of the angular distribution of the Ω - come mainly from K - p bubble chamber experiments, and, more recently from a BaBar measurement. –K - p (1970s) 8.25 GeV/c K - p (CERN 2m HBC) 10 and 16 GeV/c K - p (CERN 2m HBC) –BaBar (2006) Ξ 0 c → Ω - K + ; Ω - → ΛK -

6. Advantages of Ω - Production The Ω- decay is predominantly p-wave, and therefore easy to see. It has a characteristic 1+βcos 2 θ shape. In contrast, the angular distributions for spin ½ hyperons are predominantly s-wave, with only the parity-violating component giving polarization information (Parity conserving part only – α Ω = 0.02 )

7. Disadvantages of Ω - Production The Ω- is produced rarely, and therefore event samples are susceptible to contamination by other, mimicking decays. These come from particles produced much more copiously, so only a small contamination has a large effect on the Ω sample. Not very favourable branching ratios make it more difficult to collect Ω samples in which all decay products are seen.

8. Decay Channels and Possible Backgrounds Ω - → ΛK - ; Λ → pK - 67.8%

9. Decay Channels and Possible Backgrounds Ω - → Ξ 0 π - ; Ξ → Λπ 0 ; Λ → pK 23.6% --

10. Decay Channels and Possible Backgrounds Ω - → (Ξ 0 )K - 23.6% Ξ - → (Λ)π - Ω - → ΛK - 67.8% → pπ - 63.9% Ξ - → Λπ - 43.3% K - → (π 0 )π - K - → (ν)μ- Σ - → (n)π -

11. Population of angular distribution Study where misidentified candidates accumulate Example for Ξ - → Λπ - misidentified as Ω - → Ξ 0 π -

12. Example I Sweeps to Larger cosθ

13. Example II Enhances negative cosθ

14. Example III

15. Cross-checks As the angular distribution can so easily be distorted, it is important to have independent checks of the purity of sample Correct lifetime Correct branching ratios Correct ionization (where available)

16. Application of Criteria I 8 GeV/c bubble chamber data Only Ω→ΛK decays used, with all particles seen Decay Ξ→Λπ also studied as possible source of contamination Lifetime for good sample  =(0.8±0.15)  10 -10 s –PDG (0.821 ±0.11)  10 -10 s Mass is 1673±0.8 MeV –PDG 1672.45 ±0.29 MeV Weak decay parameter   =0.58±0.5  –PDG   =0.0175±0.0024

17. Angular Distribution 58 Ξ/Ω ambiguous rejected

18. Application of Criteria II 10 and 16 GeV/c bubble chamber data Both Ω→ΛK and Ω→Ξπ decays used; missing neutrals can be fitted Lifetime for good sample  =(1.41±0.20)  10 -10 s  –PDG (0.821 ±0.11)  10 -10 s Mass is 1671±0.78 MeV –PDG 1672.45 ±0.29 MeV Weak decay parameter   =-0.66±0.33  –PDG   =0.0175±0.0024 Branching ratio Ω→ΛK - / Ω→Ξ 0 π - wrong . More Ω→Ξ 0 π - than Ω→ΛK -. (51/38)

19. Angular Distribution

20. Application of Criteria III BaBar analysis different category Exclusive decay in  c 0 →  -   imposes many constraints Very good quality data careful treatment of PID “Quality checks” on lifetime and α Ω not quoted. Probably OK in this case. More risky in an inclusive study.  c mass peak Gives J Ω = 3/2 provided J Ξc = 1/2

21. Conclusions Ω polarization seen through parity-conserving (dominant) contribution to angular distribution  angular distributions very sensitive to contamination from other, more copiously produced hadrons. Need careful attention to treatment of such contamination to produce reliable data. Cross checks essential, especially in inclusive data. Different kinematics affect different parts of angular distribution. Predictions for ρ 33 wanted.