1. Polarization in Hyperon Photo- and Electro- Production Reinhard Schumacher 6. Sept. 2007

2. Sep-6-2007R. A. Schumacher, Carnegie Mellon University2 Overview: What are the polarization observables? Explain what C x and C z and P represent Brief survey of recent data and models:  P: J. McNabb et al., Phys. Rev. C 69, 042201 (2004).  C x, C z : R. Bradford et al., Phys. Rev. C 75, 035205 (2007).  GRAAL (P), LEPS (  ), CLAS electroproduction.  CLAS finds: for K +   The  is produced fully polarized off a circularly polarized beam. Why!? A quantum mechanical interpretation R.S., to be published Eur. Phys. Jour. A, arXiv:nucl-ex/0611035 A semi-classical interpretation

3. Sep-6-2007R. A. Schumacher, Carnegie Mellon University3 Helicity Amplitudes N No overall helicity flip = |  –  p  | } S 1 Single helicity flip } S 2 Single helicity flip } D Double helicity flip }

4. Sep-6-2007R. A. Schumacher, Carnegie Mellon University4 Polarization Observables Photoproduction described by 4 complex amplitudes Bilinear combinations define 16 observables 8 measurements needed to separate amplitudes at any given W differential cross section: d  /d  3 single polarization observables: P, T,  4 double polarization observables… CLAS FROST program aims to create a “complete” set

5. Sep-6-2007R. A. Schumacher, Carnegie Mellon University5 16 Pseudoscalar Meson Photoproduction Observables I. S. Barker, A. Donnachie, J. K. Storrow, Nucl. Phys. B95 347 (1975). Single Polarization Beam & Target Beam & Recoil Target & Recoil { { { {

6. Sep-6-2007R. A. Schumacher, Carnegie Mellon University6 Defining C x and C z and P proton K+K+ Measure polarization transfer from  to Y in the production plane, along “z” or “x” Circular real photon polarization

7. Sep-6-2007R. A. Schumacher, Carnegie Mellon University7  density matrix;  : Pauli spin matrix  transferred polarization along x  induced polarization along y  transferred polarization along z Notation: I.S. Barker, A. Donnachie, J.K. Storrow, Nucl. Phys. B95 347 (1975). Defining C x and C z and P

8. Sep-6-2007R. A. Schumacher, Carnegie Mellon University8 Measuring C x and C z and P Unpolarized beam: Sensitive to P only: e.m. parity conservation Use  weak decay asymmetry w.r.t. y axis Circularly polarized beam: Sensitive to C x and C z via helicity asymmetry proton K+K+

9. Sep-6-2007R. A. Schumacher, Carnegie Mellon University9 The CLAS System in Hall B Electromagnetic calorimeters Lead/scintillator, 1296 photomultipliers Gas Cherenkov counters e/  separation, 256 PMTs Time-of-flight counters plastic scintillators, 516 photomultipliers Drift chambers argon/CO 2 gas, 35,000 cells CEBAF Large Acceptance Spectrometer Torus magnet 6 superconducting coils Liquid H 2 target +  start counter; e minitorus “g1c”

10. Sep-6-2007R. A. Schumacher, Carnegie Mellon University10 Analysis Ingredients 1.Require K + and p detection 2.Hyperon yields from ( ,K + )Y m.m. by 2 methods:  Gaussian + polynomial fits  sideband subtractions 3.Beam polarization  Moeller scattering for electron beam: 65±3%; 1 Hz flip rate  Pol. Transfer to photon in Bremsstrahlung: Olsen & Maximon 4.No Wigner rotation of spins  Polarization is the same in Y rest frame and c.m. frame    

11. Sep-6-2007R. A. Schumacher, Carnegie Mellon University11 cos(θ p z ) - Experimental Method N ± = helicity-dependent yields  =  weak decay asymmetry = 0.642 = photon beam polarization (via Moller polarimeter) Construct beam helicity asymmetries from extracted yields. Slope of asymmetry distribution is prop- ortional to C x and C z observables: Beam Helicity Asymmetry

12. Sep-6-2007R. A. Schumacher, Carnegie Mellon University12 P vs. W: Results for  J. McNabb et al. (CLAS) Phys. Rev. C 69, 042201 (2004). Guidal, Laget, Vanderhaeghen GENT Kaon-MAID Negative at forward K angles Positive at backward K angles

13. Sep-6-2007R. A. Schumacher, Carnegie Mellon University13 Recoil (Induced) Polarization, P Excellent agreement between CLAS and new GRAAL results up to 1500 MeV. Confirms that  is negatively polarized at forward kaon angles, and positively polarized at backward kaon angles. A. Lleres et al. (GRAAL) Eur. Phys. J. A 31, 79 (2007). J. McNabb et al. (CLAS) Phys. Rev. C 69, 042201 (2004).

14. Sep-6-2007R. A. Schumacher, Carnegie Mellon University14 C z vs. W: Results for  R. Bradford et al., Phys. Rev. C 75, 035205 (2007). Very large transfer along z Very poor performance by existing models Saclay, Argonne, Pittsburgh Bonn, Giessen, Gatchina Kaon-MAID Regge+Resonance GENT Shklyar Lenske Mosel

15. Sep-6-2007R. A. Schumacher, Carnegie Mellon University15 C x vs. W: Results for  C x ≈ C z - 1 GENT Saclay, Argonne, Pittsburgh Bonn, Giessen, Gatchina Kaon-MAID Regge+Resonance Shklyar Lenske Mosel R. Bradford et al., Phys. Rev. C 75, 035205 (2007).

16. Sep-6-2007R. A. Schumacher, Carnegie Mellon University16 Model Comparisons Effective Lagrangian Models Kaon-MAID; Mart, Bennhold, Haberzettl, Tiator S 11 (1650), P 11 (1710), P 13 (1720), D 13 (1895), K*(892), K 1 (1270) GENT: Janssen, Ryckebusch et al.; Phys Rev C 65, 015201 (2001) S 11 (1650), P 11 (1710), P 13 (1720), D 13 (1895), K*(892),  *(1800),  *(1810) RPR (Regge plus Resonance) Corthals, Rychebusch, Van Cauteren, Phys Rev C 73, 045207 (2006). Coupled Channels or Multi-channel fits SAP (Saclay, Argonne, Pittsburgh) Julia-Diaz, Saghai, Lee, Tabakin; Phys Rev C 73, 055204 (2006). rescattering of KN and  N S 11 (1650), P 13 (1900), D 13 (1520), D 13 (1954), S 11 (1806), P 13 (1893) BGG (Bonn, Giessen, Gachina): Sarantsev, Nikonov, Anisovich, Klempt, Thoma; Eur. Phys. J. A 25, 441 (2005) multichannel (pion, eta, Kaon) PWA P 11 (1840), D 13 (1875), D 13 (2170) SLM: Shklyar, Lenske, Mosel; Phys Rev C 72 015210 (2005) coupled channels S 11 (1650), P 13 (1720), P 13 (1895), but NOT P 11 (1710), D 13 (1895) Regge Exchange Model M. Guidal, J.M. Laget, and M. Vanderhaeghen; Phys Rev C 61, 025204 (2000) K and K*(892) trajectories exchanged + P 13 (1860)

17. Sep-6-2007R. A. Schumacher, Carnegie Mellon University17 Comparison to pQCD limits A. Afanasev, C. Carlson, & C.Wahlquist predicted [Phys Lett B 398, 393 (1997)]: For large t, s, u P = C x ’ = 0 C z ’ = (s 2 -u 2 )/(s 2 +u 2 )  1 at large t and small u Based on s-channel quark helicity conservation CLAS data shows clear helicity NON-conservation Spin of  points mostly along z for all production angles CLAS largest t / smallest u results are in “fair to good” agreement with prediction …but so what? data from cos  K c.m. = -0.75

18. Sep-6-2007R. A. Schumacher, Carnegie Mellon University18 Electroproduction: similar phenomonology D. S. Carman et al. (CLAS) Phys. Rev. Lett. 90, 131804 (2003). PxPxPxPx PzPzPzPz The same large polarization transfer along photon direction (not the z’ helicity axis) is seen in CLAS electro-production. 0.3<Q 2 <1.5 (GeV/c) 2 1.6<W<2.2 GeV Integrated over all K angles zy X (hadron plane)

19. Sep-6-2007R. A. Schumacher, Carnegie Mellon University19 Beam Asymmetry,  R. G. T. Zegers et al. (LEPS) Phys. Rev. Lett. 91, 092001 (2003). LEPS 1.5 < E  < 2.4 GeV GRAAL threshold range, E  < 1.5 GeV The trends are consistent:  is smooth and featureless at all energies and angles. GRAAL LEPS A. Lleres et al. (GRAAL) Eur. Phys. J. A 31, 79 (2007).

20. Sep-6-2007R. A. Schumacher, Carnegie Mellon University20 Unexpected Result / Puzzle  What is the magnitude of the  hyperon’s polarization vector given circular beam polarization?  Expect:  is not required to be close to 1, BUT angle & energy average turns out to be:  How does  come to be 100% spin polarized?  Not a “feature” in hadrodynamic models

21. Sep-6-2007R. A. Schumacher, Carnegie Mellon University21 The  appears 100% polarized when created with a fully polarized beam. R Values for the 

22. Sep-6-2007R. A. Schumacher, Carnegie Mellon University22 Average R Values for the  Energy average vs angle Angle average vs energy Energy and angle averages are consistent with unity.  2 = 1.18 (good) No model predicted this CLAS result.

23. Sep-6-2007R. A. Schumacher, Carnegie Mellon University23 Average R Values for   Energy average vs angle Angle average vs energy Poorer statistics for  0, but R is not unity everywhere.

24. Sep-6-2007R. A. Schumacher, Carnegie Mellon University24 Ansatz for the Explanation s-quark is produced polarized in a VDM picture. The hadronization process pushes its direction around, but it retains its full polarization magnitude. Quark-level dynamics manifest at the baryonic level. unpolarized proton K+K+ 3 S 1  meson S = 0 diquark

25. Sep-6-2007R. A. Schumacher, Carnegie Mellon University25 Quantum Mechanical Model Fact: a spin-orbit or spin-spin type of Hamiltonian leaves the magnitude of an angular momentum vector invariant. I.e. the spin polarization direction,, is not a constant of the motion, but its magnitude is. Scattering matrix: } Key ingredients

26. Sep-6-2007R. A. Schumacher, Carnegie Mellon University26 C x, C z, and P in terms of g (  ) (non-flip) and h (  ) (spin-flip) Can solve for g (  ) and h (  ) magnitudes and phase difference using the measured values of C x, C z, P and d  /d . Measured components of  hyperon polarization “Observables”

27. Sep-6-2007R. A. Schumacher, Carnegie Mellon University27 Computing g and h in z-spin basis Convert cross section to dimensionless matrix element, A; divide out phase space Compute magnitudes of spin non-flip ( g ) and spin flip ( h ) amplitudes Compute relative phase between amplitudes, 

28. Sep-6-2007R. A. Schumacher, Carnegie Mellon University28 | g | 2 and | h | 2 in z-spin basis | g | 2 Spin non-flip | h | 2 Spin flip Results show strong non-flip dominance

29. Sep-6-2007R. A. Schumacher, Carnegie Mellon University29  =  g -  h in z-spin basis Phase near ±  … …Phase nearer 

30. Sep-6-2007R. A. Schumacher, Carnegie Mellon University30 C x, C z, and P in helicity amplitudes Compute the effect the relation among observables has on the amplitudes: Measured components of  hyperon polarization “” “Observables”

31. Sep-6-2007R. A. Schumacher, Carnegie Mellon University31 Constraint on Amplitudes: Given that for the observables: we find that for the amplitudes: This constraint can be satisfied in many ways… Does it predict other observables? More work needed. For example, it does NOT follow that:

32. Sep-6-2007R. A. Schumacher, Carnegie Mellon University32 Fit: Bonn-Gatchina multiple channel fit BARYONS 2007, E. Klempt Bonn-Gachina Model Fits A. Anisovich, V. Kleber, E. Klempt, V.A.Nikonov, A.V.Sarantsev, U. Thoma, EPJ… “one additional resonance needed : P 13 (1860)“ Fitting with multiple resonances is “sufficient”, but is it “necessary”? If R =1 is strictly true across all W and angle, a “deeper” reason is needed for explanation

33. Sep-6-2007R. A. Schumacher, Carnegie Mellon University33 Quantum Mechanical Results The polarization observables C x, C z, and P are “explained” in terms of two complex amplitudes g (  ) –spin non-flip transition amplitude for a spin ½ quark described in a z-axis basis. h (  ) - spin flip transition amplitude for... (etc). g (  ) and h (  ) arise from a “deeper” theory of the hadronization process that we do not have. By construction, any g and h leaves |P Y | unchanged. BUT, we can do more, using a physical picture based on a semi-classical model (see next).

34. Sep-6-2007R. A. Schumacher, Carnegie Mellon University34 Classical Model Fact: the expectation value of a quantum mechanical spin operator evolves in time the same way as the classical angular momentum “spin” vector does. (cf. Cohen-Tannoudji p450, or Merzbacher p281). For any interaction of the form one gets For this discussion, where B is the external field of proton and/or magnetic moment of another quark. Use a spin-spin and spin-orbit type of interaction to model polarization evolution during hadronization. use classical electromagnetic field structures/algebra scale up strength to model strong color-magnetic interaction

35. Sep-6-2007R. A. Schumacher, Carnegie Mellon University35 Classical Model The virtual pair in a spin “triplet” state is subject to a spin-spin dipole interaction The approaching charged proton serves to precess both spins via spin-orbit interaction: Spins interact with moving proton and each other during hadronization length/time: R rms ~1fm  carries spin polarization of s at freeze-out time unpolarized proton K+K+ 3 S 1  meson S = 0 diquark Treat the picture literally

36. Sep-6-2007R. A. Schumacher, Carnegie Mellon University36 Contents of the Model: Quark triplet spaced according to photon ± /4 in { ,p} c.m. frame, Field of quarks: classical dipole form: Proton charge distribution: , and Proton motional B field in c.m. frame: Impact parameter, b, maps onto scattering angle , via the Rutherford-like form

37. Sep-6-2007R. A. Schumacher, Carnegie Mellon University37 Demonstration animation… (Hope this works…) Proton knocks spins off axis initially… …then spin-spin interaction rotates spins out of reaction plane. Impact parameter maps to scattering angle Spin direction is frozen after one hadronization time/length elapses

38. Sep-6-2007R. A. Schumacher, Carnegie Mellon University38 Initial Configuration Constant external field in y After external field in y turned off Precessed due to arriving proton

39. Sep-6-2007R. A. Schumacher, Carnegie Mellon University39 Preliminary Result, W=2 GeV Observed phenomeno- logy is reproduced: C z is large and positive C x is small and negative P is negative at forward angles, positive at backward angles The electromagnetic interaction not strong enough to account for observed magnitude: scale up strength by x30 Suggests that color- magnetic effects are what we are actually modeling P CzCzCzCz CxCxCxCx

40. Sep-6-2007R. A. Schumacher, Carnegie Mellon University40 Conclusions The 100% polarization of the  in K +  photoproduction is a remarkable new fact. Ansatz: Photon couples to an ss spin triplet, followed by spin precession in hadronizing system. Spin flip/non-flip amplitudes can model this phenomenon quantum mechanically. Dipole-dipole & spin-orbit (color-) magnetic interactions offer a physical picture of spin precession during hadronization. Speculation: polarization observables have something to say about quark-dynamics, maybe only a little about N* resonances.

41. Sep-6-2007R. A. Schumacher, Carnegie Mellon University41 Supplemental Slides

42. Sep-6-2007R. A. Schumacher, Carnegie Mellon University42 Isobar model fit for  data

43. Sep-6-2007R. A. Schumacher, Carnegie Mellon University43 Quantum Mechanical Model Fact: a spin-orbit or spin-spin type of Hamiltonian leaves the magnitude of an angular momentum vector invariant. I.e. the spin polarization direction,, is not a constant of the motion, but its magnitude is. The scattering matrix, S, has the form: where  f,0 are spin 1/2 states w.r.t. the z-axis basis, i.e.

44. Sep-6-2007R. A. Schumacher, Carnegie Mellon University44 Scattering matrix: Use a density matrix formalism and trace algebra to find: For the CLAS experiment, so we have expressions for three orthogonal components of the final state polarization. } Key ingredients