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Polarization in Hyperon Photo- and Electro- Production

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

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Polarization in Hyperon Photo- and Electro- Production

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

  2. Overview: • What are the polarization observables? • Explain what Cx and Cz and P represent • Brief survey of recent data and models: • P: J. McNabb et al., Phys. Rev. C 69, 042201 (2004). • Cx, Cz: R. Bradford et al., Phys. Rev. C 75, 035205 (2007). • GRAAL (P) , LEPS (S), CLAS electroproduction. • CLAS finds: for K+L • The L 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 R. A. Schumacher, Carnegie Mellon University

  3. Helicity Amplitudes } N No overall helicity flip = |g – (p -L)| } S1 Single helicity flip } S2 Single helicity flip } D Double helicity flip R. A. Schumacher, Carnegie Mellon University

  4. 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 R. A. Schumacher, Carnegie Mellon University

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

  6. Defining Cx and Cz and P K+ proton proton Circular real photon polarization Measure polarization transfer from g to Y in the production plane, along “z” or “x” R. A. Schumacher, Carnegie Mellon University

  7. Defining Cx and Cz and P  density matrix; s: 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). R. A. Schumacher, Carnegie Mellon University

  8. Measuring Cx and Cz and P K+ proton • Unpolarized beam: • Sensitive to P only: e.m. parity conservation • Use L weak decay asymmetry w.r.t. y axis • Circularly polarized beam: • Sensitive to Cx and Cz via helicity asymmetry proton R. A. Schumacher, Carnegie Mellon University

  9. The CLAS System in Hall B CEBAF Large Acceptance Spectrometer Torus magnet 6 superconducting coils Electromagnetic calorimeters Lead/scintillator, 1296 photomultipliers Liquid H2 target + g start counter; e minitorus Drift chambers argon/CO2 gas, 35,000 cells “g1c” Gas Cherenkov counters e/p separation, 256 PMTs Time-of-flight counters plastic scintillators, 516 photomultipliers R. A. Schumacher, Carnegie Mellon University

  10. Analysis Ingredients • Require K+ and p detection • Hyperon yields from (g,K+)Y m.m. by 2 methods: • Gaussian + polynomial fits • sideband subtractions • Beam polarization • Moeller scattering for electron beam: 65±3%; 1 Hz flip rate • Pol. Transfer to photon in Bremsstrahlung: Olsen & Maximon • No Wigner rotation of spins • Polarization is the same in Y rest frame and c.m. frame L L S0 S0 R. A. Schumacher, Carnegie Mellon University

  11. Experimental Method • Construct beam helicity asymmetries from extracted yields. • Slope of asymmetry distribution is prop-ortional to Cx and Cz observables: Beam Helicity Asymmetry - cos(θp z) N±= helicity-dependent yields  = L weak decay asymmetry = 0.642 = photon beam polarization (via Moller polarimeter) R. A. Schumacher, Carnegie Mellon University

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

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

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

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

  16. Model Comparisons + P13(1860) • Effective Lagrangian Models • Kaon-MAID; Mart, Bennhold, Haberzettl, Tiator • S11(1650), P11(1710), P13(1720), D13(1895), K*(892), K1(1270) • GENT: Janssen, Ryckebusch et al.; Phys Rev C 65, 015201 (2001) • S11(1650), P11(1710), P13(1720), D13(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 pN • S11(1650), P13(1900), D13(1520), D13(1954), S11(1806), P13(1893) • BGG (Bonn, Giessen, Gachina): Sarantsev, Nikonov, Anisovich, Klempt, Thoma; Eur. Phys. J. A 25, 441 (2005) • multichannel (pion, eta, Kaon) PWA • P11(1840), D13(1875), D13(2170) • SLM: Shklyar, Lenske, Mosel; Phys Rev C 72 015210 (2005) • coupled channels • S11(1650), P13(1720), P13(1895), but NOT P11(1710), D13(1895) • Regge Exchange Model • M. Guidal, J.M. Laget, and M. Vanderhaeghen; Phys Rev C 61, 025204 (2000) • K and K*(892) trajectories exchanged R. A. Schumacher, Carnegie Mellon University

  17. Comparison to pQCD limits • A. Afanasev, C. Carlson, & C.Wahlquist predicted [Phys Lett B 398, 393 (1997)]: • For large t, s, u P = Cx’ = 0 Cz’ = (s2-u2)/(s2+u2)  1 at large t and small u • Based on s-channel quark helicity conservation • CLAS data shows clear helicity NON-conservation • Spin of L 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 cosqKc.m. = -0.75 R. A. Schumacher, Carnegie Mellon University

  18. Electroproduction: similar phenomonology y X(hadron plane) z Pz The same large polarization transfer along photon direction (not the z’ helicity axis) is seen in CLASelectro-production. Px 0.3<Q2<1.5 (GeV/c)2 1.6<W<2.2 GeV Integrated over all K angles D. S. Carman et al. (CLAS) Phys. Rev. Lett. 90, 131804 (2003). R. A. Schumacher, Carnegie Mellon University

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

  20. Unexpected Result / Puzzle • What is the magnitude of the L 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 L come to be 100% spin polarized? • Not a “feature” in hadrodynamic models R. A. Schumacher, Carnegie Mellon University

  21. R Values for the L The L appears 100% polarized when created with a fully polarized beam. R. A. Schumacher, Carnegie Mellon University

  22. Average R Values for the L Energy and angle averages are consistent with unity. Energy average vs angle c2n= 1.18 (good) Angle average vs energy No model predicted this CLAS result. R. A. Schumacher, Carnegie Mellon University

  23. Average R Values for S0 Poorer statistics for S0, but R is not unity everywhere. Energy average vs angle Angle average vs energy R. A. Schumacher, Carnegie Mellon University

  24. Ansatz for the Explanation K+ unpolarized proton 3S1f meson S = 0 diquark s-quark is produced polarized in a VDM picture. The hadronization process pushes its direction around, but it retains its full polarization magnitude. S = 0 diquark Quark-level dynamics manifest at the baryonic level. R. A. Schumacher, Carnegie Mellon University

  25. 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 R. A. Schumacher, Carnegie Mellon University

  26. Cx, Cz, and P in terms of g(q) (non-flip) and h(q) (spin-flip) Measured components of L hyperon polarization “Observables” Can solve for g(q) and h (q) magnitudes and phase difference using the measured values of Cx, Cz, P and ds/dW. R. A. Schumacher, Carnegie Mellon University

  27. 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, Df R. A. Schumacher, Carnegie Mellon University

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

  29. Df= fg- fh in z-spin basis Phase near ±p/2… …Phase nearer p R. A. Schumacher, Carnegie Mellon University

  30. Cx, Cz, and P in helicity amplitudes Measured components of L hyperon polarization “Observables” Compute the effect the relation among observables has on the amplitudes: R. A. Schumacher, Carnegie Mellon University

  31. 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: R. A. Schumacher, Carnegie Mellon University

  32. Bonn-Gachina Model Fits • A. Anisovich, V. Kleber, E. Klempt, V.A.Nikonov, A.V.Sarantsev, U. Thoma, EPJ… • “one additional resonance needed : P13(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 BARYONS 2007, E. Klempt Fit: Bonn-Gatchina multiple channel fit R. A. Schumacher, Carnegie Mellon University

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

  34. 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 R. A. Schumacher, Carnegie Mellon University

  35. Classical Model K+ unpolarized proton 3S1f meson S = 0 diquark S = 0 diquark Treat the picture literally • 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: Rrms ~1fm • L carries spin polarization of s at freeze-out time R. A. Schumacher, Carnegie Mellon University

  36. Contents of the Model: • Quark triplet spaced according to photon ±l/4 in {g,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 q, via the Rutherford-like form R. A. Schumacher, Carnegie Mellon University

  37. 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 R. A. Schumacher, Carnegie Mellon University

  38. Initial Configuration Constant external field in y Precessed due to arriving proton After external field in y turned off R. A. Schumacher, Carnegie Mellon University

  39. Observed phenomeno-logy is reproduced: Cz is large and positive Cx 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 Preliminary Result, W=2 GeV Cz P Cx R. A. Schumacher, Carnegie Mellon University

  40. Conclusions • The 100% polarization of the L in K+L 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. R. A. Schumacher, Carnegie Mellon University

  41. Supplemental Slides R. A. Schumacher, Carnegie Mellon University

  42. Isobar model fit for L data R. A. Schumacher, Carnegie Mellon University

  43. 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. where cf,0 are spin 1/2 states w.r.t. the z-axis basis, i.e. The scattering matrix, S, has the form: R. A. Schumacher, Carnegie Mellon University

  44. Scattering matrix: }Key ingredients 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 . R. A. Schumacher, Carnegie Mellon University

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