1. Spin Polarization in d  → n p Chang Ho Hyun Daegu University Work with S. Ando (Daegu) Y.-H. Song (South Carolina) K. Kubodera (South Carolina) HNP2011, Pohang, Korea February 21-24

2. Outline Motivation Formalism Spin polarization P’ y Results Conclusion

3. Motivation NN force well understood at E lab ≤ 300 MeV Nevertheless many discrepancies in the polarization observables Puzzles with spin - Spin crisis: origin of the nucleon spin - P’ y in deuteron photo-disintegration - Ay puzzle in neutron-deuteron scattering Spin is still an open problem in few-body systems

4. Spin polarization P’ y - Experiments: 1961-1983 (John61, Jewell65, Nath72, Holt83) - Jewell65 Jewell et al., PR 139, B71 (1965)

5. - SNPA (standard nuclear physics approach) R. Schiavilla, PRC 72, 034001 (2005) “New and more accurate measurements of the induced polarization in the 2 H(γ,n) 1 H reaction are needed to establish unequivocally whether there is a discrepancy between theory and experiment.”

6. Need to investigate the problem with modern theories - Effective field theories (EFTs) provide proper tools Our choice: Pionless EFT with dibaryon fields

7. Formalism NN force with chiral perturbation theory Meson-exchange currents with systematic expansion rules - Integrate out heavy degrees of freedom Pionless theory - Integrate out the pion - NN contact interactions - Low energy constants determined by low-energy data Dibaryon fields - Nucleon bubbles summed infinitely, the deuteron pole reproduced successfully - Ensure fast convergence with only a few leading terms

8. Lagrangians -s i, t i : dibaryon fields in 1 S 0 and 3 S 1 states, respectively -B i : external photon fields

9. Low energy constants -y s, y t : dNN coupling constants. Fitted to effective range parameters -L 1, L 2 : ddV coupling constants. Fitted to np capture cross section at threshold and deuteron magnetic moment -Total np capture cross section

10. Definition Spin polarization P’ y p n  z’ y’  +,- (  ) : differential cross section with parallel and anti-parallel neutron spin Py’ becomes non-zero due to the interference of even and odd transition amplitudes

11. Amplitudes and cross sections -Feynman diagrams -Amplitudes

13. -Cross section for unpolarized neutron -Projection operator for the neutron spin

14. -Cross section for polarized neutron -Result for P’ y

15. Results Differential cross section of unpolarized neutron E  = 19.8MeV De Pascale et al. PRC 32, 1830 (1985) Our workSNPA

16. P’ y at E  = 2.75 MeV Our work SNPA

17. P’ y at  = 45 

18. P’ y at  = 90 

19. P’ y at  = 135 

20. Conclusion What is the correct answer? Experiment side - Large errors - Data do not converge (  = 90  ) - Revival of the measurement at modern facilities and instruments is absolutely necessary Theory side - Results for unpolarized cross section show good agreement - SNPA results are discrepant from pionless EFT - Systematic investigation at higher orders are inevitable works in the future

21. Possible scenarios - New measurements or other theories consistent with SNPA - New measurements or other theories consistent with pionless EFT - New measurements still inconsistent with any theory Spin is still an open and active subject in the nuclear physics P’ z ∝ cos  : Parity-violating effect. In progress with Ando and Shin