Polarization in Hyperon Photo and Electro Production

1
Polarization in Hyperon Photo- and Electro-
Production
6. Sept. 2007
Reinhard Schumacher
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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 KL
• 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,
  arXivnucl-ex/0611035
• A semi-classical interpretation

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Helicity Amplitudes

N No overall helicity flip
g (p -L)

S1 Single helicity flip

S2 Single helicity flip

D Double helicity flip
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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
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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).
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Defining Cx and Cz and P
Circular real photon polarization
Measure polarization transfer from g to Y in the
production plane, along z or x
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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).
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Measuring Cx and Cz and P

• 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
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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
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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 653 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
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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(?p z)
N helicity-dependent yields ? L
weak decay asymmetry 0.642 photon
beam polarization (via Moller polarimeter)
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P vs. W Results for L
Kaon-MAID
GENT
Guidal, Laget, Vanderhaeghen
J. McNabb et al. (CLAS) Phys. Rev. C 69, 042201
(2004).
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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).
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Cz vs. W Results for L
R. Bradford et al., Phys. Rev. C 75, 035205
(2007).
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Cx vs. W Results for L
R. Bradford et al., Phys. Rev. C 75, 035205
(2007).
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Model Comparisons

• 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

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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)/(s2u2) ? 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 cos qKc.m. -0.75
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Electroproduction similar phenomonology
Pz
The same large polarization transfer along photon
direction (not the z helicity axis) is seen in
CLAS electro-production.
Px
0.3ltQ2lt1.5 (GeV/c)2 1.6ltWlt2.2 GeV Integrated over
all K angles
D. S. Carman et al. (CLAS) Phys. Rev. Lett. 90,
131804 (2003).
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Beam Asymmetry, S
GRAAL threshold range, Eg lt 1.5 GeV
LEPS 1.5 lt Eg lt 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).
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Unexpected Result / Puzzle

• What is the magnitude of the L hyperons
  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

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R Values for the L
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Average R Values for the L
Energy average vs angle
c2n 1.18 (good)
Angle average vs energy
No model predicted this CLAS result.
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Average R Values for S0
Energy average vs angle
Angle average vs energy
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Ansatz for the Explanation
Quark-level dynamics manifest at the baryonic
level.
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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
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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.
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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
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g2 and h2 in z-spin basis
g2 Spin non-flip
h2 Spin flip
Results show strong non-flip dominance
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Df fg- fh in z-spin basis
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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
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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
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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 R1 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
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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, any g and h leaves PY
  unchanged.
• BUT, we can do more, using a physical picture
  based on a semi-classical model (see next).

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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

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Classical Model
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

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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

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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

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Initial Configuration
Constant external field in y
After external field in y turned off
Precessed due to arriving proton
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Preliminary Result, W2 GeV

• 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

Cz
P
Cx
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Conclusions

• The 100 polarization of the L in KL
  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.

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Supplemental Slides
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Isobar model fit for L data
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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
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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 .