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Polarization Observables T and F in Single 0 and -Photoproduction off Quasi-Free Nucleons Thomas Strub, Basel Group, A2 Collaboration University of Basel 30th May 2014 A 2 Outline Short Motivation Experimental Setup Polarization

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SLIDE 1

Polarization Observables T and F in Single π0 and η-Photoproduction

  • ff Quasi-Free Nucleons

Thomas Strub, Basel Group, A2 Collaboration

University of Basel

30th May 2014

2 A

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SLIDE 2

Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

Outline

1 Short Motivation 2 Experimental Setup 3 Polarization Observables 4 Analysis Methods 5 Selected Results 6 Conclusion

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

Motivation

Problem

◮ Nucleons’ excitation spectrum is a complicated overlap of many short

lived, broad resonances

◮ Cannot be understood from differential cross sections alone

Polarization observables from meson photoproduction

◮ Probing spin degrees of freedom ◮ Need 8 carefully chosen observables for complete experiment ◮ Need high precision measurements

Proton and neutron channel

◮ Probe isospin degree of freedom ◮ Isospin decomposition into AV 3, AIV , AIS for π photoproduction

A(γp → π+n) = −

  • 1

3 AV 3 +

  • 2

3

  • AIV − AIS

A(γp → π0p) = +

  • 2

3 AV 3 +

  • 1

3

  • AIV − AIS

A(γn → π0n) = +

  • 1

3 AV 3 −

  • 2

3

  • AIV + AIS

A(γn → π−p) = +

  • 2

3 AV 3 +

  • 1

3

  • AIV + AIS

◮ At least one measurement off the neutron needed.

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

Motivation

Special case η

◮ Isospin I = Iz = 0. ◮ No isospin changing current (AV 3 = 0)

A(γp → ηp) = AIS + AIV A(γn → ηn) = AIS − AIV = ⇒ only N∗ resonances contribute

◮ Recent results show a narrow structure

arround 1670 MeV Photoproduction off the neutron

◮ Neutron bound in nucleus

= ⇒ quasi free neutron

◮ Correct treatment of Fermi motion ◮ Comparision of free and quasi free

proton data

P11(939) P11(1440) D13(1520) S11(1535) S11(1650) D15(1675) F15(1680) D13(1700) P33(1232) P33(1600) S31(1620) D33(1700)

1000 1200 1400 1600

Mass [MeV/c2]

N(I=1/2) (I=3/2)

  • Notation:

L2I2J ; L=0(S),1(P),2(D),...

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

Experimental Setup Experimental Setup

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

MAinzer MIcrotron

High quality electron beam

◮ Energy up to 1.5 GeV ◮ Intensity up to 100 µA ◮ Polarization ≈ 80%

Bremsstrahlungs photons

◮ 1/Eγ distribution ◮ Photon polarization: Olsen

maximum function

Photon Energy 200 400 600 800 1000 1200 1400 Polarization degree 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

Crystal Ball/TAPS @ MAMI

CB

◮ PID ◮ MPWC ◮ NaI crystals

TAPS

◮ BaF2/PWO crystals ◮ Veto wall

= ⇒ Almost 4π acceptance

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

Polarization Observables Polarization Observables

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

Definition of T and F (experimental approach)

T and F are defined by T cos(φ′) = 1 PTPγ dσ↑(φ′) − dσ↓(φ′) dσ↑(φ′) + dσ↓(φ′), where (↑, ↓) denotes the target polarization state, F cos(φ) = 1 PTPγ dσ−(φ) − dσ+(φ) dσ−(φ) + dσ+(φ), where (+, −) denotes the photon helicity state. Here, F = F(E, θ), T = T(E, θ), PT = PT(t) and Pγ = Pγ(E γ, PB(t))

◮ Symmetric contributions cancel in the

numerator

◮ Denominator equals unpolarized dσ ◮ φ = Angle between target

polarization vector and production plane

◮ φ′ = Angle between target

polarization vector and normal to production plane

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

Methods to extract T and F

◮ Target: D-butanol (C4D9OD), only deuterons are polarized. ◮ Carbon/oxygen contribution vanish in numerator ◮ Two methods can be used:

◮ 1. Normalize with deuterium target

A cos(φ) = 1 PT Pγ dσ−

DB(φ) − dσ+ DB(φ)

dσ−

D (φ) + dσ+ D(φ)

= ⇒ Needs flux and efficiency correction of count rates.

◮ 2. Normalize with D-butanol target

A cos(φ) = 1 PT Pγ dN−

DB(φ) − dN+ DB(φ)

dN−

DB(φ) + dN+ DB(φ)

· d = ⇒ No need for flux and efficiency correction, but dilution factor d, i.e., d = 1 + dσ0

C

dσ0

DB

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

Analysis Methods Analysis Methods

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

Event selection

◮ Event selection

◮ Full exclusive on proton (neutron as spectator)

γ + d − → π0 + p(n) − → 2γ + p(n) 2 neutral, 1 charged γ + d − → η + p(n) − → 2γ + p(n) 2 neutral, 1 charged γ + d − → η + p(n) − → 3π0 + p(n) − → 6γ + p(n) 6 neutral, 1 charged

◮ Full exclusive on neutron (proton as spectator)

γ + d − → π0 + n(p) − → 2γ + n(p) 3 neutral, 0 charged γ + d − → η + n(p) − → 2γ + n(p) 3 neutral, 0 charged γ + d − → η + n(p) − → 3π0 + p(n) − → 6γ + n(p) 7 neutral, 0 charged

◮ Determination of the neutron candidate by χ2-test. ◮ Invariant mass cut on all 3 π0 from η → 6γ decay.

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

Applied Cuts

All cuts are determined from LD2 target for all θ and energy bins.

◮ Coplanarity cut

∆φ = 180◦ − |φmeson − φrecoil|

◮ Invariant mass cut

∆mmeson = |Pµ

meson| − mtheo. meson ◮ Missing mass cut

∆MM = |Pµ

γ + Pµ nucleon − Pµ meson| − mtheo nucleon

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

Reconstruction of Kinematics

Transfer kinematics into CM frame

◮ Fermi momentmum from deuterium (carbon/oxygen) targed

= ⇒ Initial state not determined

◮ Reconstruction of nucleons fermi momentum from final state, i.e., solve

Pµ

γ + Pµ nucleon = Pµ meson + Pµ recoil

for Pµ

nucleon. ◮ Have enough information to reconstruct Fermi momentum of nucleon.

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

Dilution Factor

◮ Determination of the dilution factor from missing mass spectra

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

TOMultiPad_Dummy_0

Entries Mean RMS 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

TOMultiPad_Dummy_1

Entries Mean RMS 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

TOMultiPad_Dummy_2

Entries Mean RMS 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

TOMultiPad_Dummy_3

Entries Mean RMS 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

TOMultiPad_Dummy_4

Entries Mean RMS 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

TOMultiPad_Dummy_5

Entries Mean RMS 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

TOMultiPad_Dummy_6

Entries Mean RMS 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

TOMultiPad_Dummy_7

Entries Mean RMS

  • 200
  • 200
  • 200
  • 200

200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

  • p [MeV]

η MM counts [a.u.]

◮ Carbon + x Deuterium = Sum ≈ D-butanol ◮ Dilution factor d = 1 +

  • MMcut ∆MMcarbon/
  • MMcut ∆MMdeuterium

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

Selected Results Selected Results (preliminary)

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

T and F for Single π0 Photoproduction

Invariant mass W [MeV] 1200 1300 1400 1500 1600 1700 1800 1900 Asymmetry F

  • 1
  • 0.5

0.5 1 0.067 ± ) = 0.000 θ cos(

free proton (V. Kashevarov) q.f. proton SAID MAID

Invariant mass W [MeV] 1200 1300 1400 1500 1600 1700 1800 1900 Asymmetry F

  • 1
  • 0.5

0.5 1 0.067 ± ) = 0.000 θ cos(

q.f. neutron q.f. proton SAID neutron MAID neutron SAID proton MAID proton

Invariant mass W [MeV] 1200 1300 1400 1500 1600 1700 1800 1900 Asymmetry T

  • 1
  • 0.5

0.5 1 0.067 ± ) = 0.000 θ cos(

free proton (V. Kashevarov) q.f. proton SAID MAID

Invariant mass W [MeV] 1200 1300 1400 1500 1600 1700 1800 1900 Asymmetry T

  • 1
  • 0.5

0.5 1 0.067 ± ) = 0.000 θ cos(

q.f. neutron q.f. proton SAID neutron MAID neutron SAID proton MAID proton

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

T and F for η Photoproduction

Invariant mass W [MeV] 1450 1525 1600 1675 1750 1825 1900 Asymmetry F

  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.167 ± ) = -0.167 θ cos(

free proton (V. Kashevarov) q.f. proton MAID proton BnGa proton

Invariant mass W [MeV] 1450 1525 1600 1675 1750 1825 1900 Asymmetry F

  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.167 ± ) = -0.167 θ cos(

q.f. neutron q.f. proton MAID neutron MAID proton BnGa neutron BnGa proton

Invariant mass W [MeV] 1450 1525 1600 1675 1750 1825 1900 Asymmetry T

  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.167 ± ) = -0.167 θ cos(

free proton (V. Kashevarov) q.f. proton MAID proton BnGa proton

Invariant mass W [MeV] 1450 1525 1600 1675 1750 1825 1900 Asymmetry T

  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.167 ± ) = -0.167 θ cos(

q.f. neutron q.f. proton MAID neutron MAID proton BnGa neutron BnGa proton

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

Conclusion

Conclusion

◮ First preliminary results for T and F for single π0- and η photoproduction

  • ff quasi free nucleons

◮ Very good agreement with free proton ◮ Models fail for higher energies, for the neutron and η channel

Outlook

◮ Main goal (η): double energy and theta bins w/o increasing errors ◮ Kinematic fit (energy and angular resolution) ◮ Expected impact on models ◮ Observables from double meson photoproduction.

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

Thanks Thank you for your attention.

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

Definition of T and F

◮ General decomposition of dσ into 16 polarization observables reads

dσ(Pγ, PT, PR) = 1 2dσ0{1 + . . . + T [PT

y − Pγ L PR y′ cos()]

+ F [PT

c PT x − Pγ L PT z PR y′ sin(2φγ)]

+ . . . }.

◮ For PR = 0 (unpolarized recoil), Pγ = Pγ c (circular photon polarization)

and PT = Py, Pz = 0 (transversal target polarization) it reduceses to dσ(Pγ, PT) = dσ0

  • 1 + TPT

y + FPγ c PT x

  • = dσ0
  • 1 + T|PT| cos(φ′) + F|Pγ||PT| cos(φ)
  • .

◮ Observables T and F manifest themself by a cosine-modulated

unpolarized cross-section

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

F: ηp

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = -0.833 θ cos(

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = -0.500 θ cos(

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = -0.167 θ cos(

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = 0.167 θ cos(

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = 0.500 θ cos(

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = 0.833 θ cos( 1450 1525 1600 1675 1750 1825 1450 1525 1600 1675 1750 1825 1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

  • 0.4

0.2

W [MeV] Asymmetry F

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

F: ηn

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = -0.833 θ cos(

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = -0.500 θ cos(

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = -0.167 θ cos(

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = 0.167 θ cos(

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = 0.500 θ cos(

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = 0.833 θ cos( 1450 1525 1600 1675 1750 1825 1450 1525 1600 1675 1750 1825 1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

  • 0.4

0.2

W [MeV] Asymmetry F

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

T: ηp

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = -0.833 θ cos(

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = -0.500 θ cos(

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = -0.167 θ cos(

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = 0.167 θ cos(

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = 0.500 θ cos(

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = 0.833 θ cos( 1450 1525 1600 1675 1750 1825 1450 1525 1600 1675 1750 1825 1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

  • 0.4

0.2

W [MeV] Asymmetry T

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

T: ηn

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = -0.833 θ cos(

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = -0.500 θ cos(

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = -0.167 θ cos(

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = 0.167 θ cos(

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = 0.500 θ cos(

1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

0.167 ± ) = 0.833 θ cos( 1450 1525 1600 1675 1750 1825 1450 1525 1600 1675 1750 1825 1450 1525 1600 1675 1750 1825 1900

  • 0.4

0.2 0.8

  • 0.4

0.2

W [MeV] Asymmetry T

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

F: π0p

1200 1550 1900

  • 1

1 0.067 ± ) = -0.933 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.800 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.667 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.533 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.400 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.267 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.133 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.000 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.133 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.267 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.400 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.533 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.667 θ cos(

1200 1550 1200 1550 1200 1550

  • 1

1

  • 1
  • 1

W [MeV] F

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

F: π0n

1200 1550 1900

  • 1

1 0.067 ± ) = -0.933 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.800 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.667 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.533 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.400 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.267 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.133 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.000 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.133 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.267 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.400 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.533 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.667 θ cos(

1200 1550 1200 1550 1200 1550

  • 1

1

  • 1
  • 1

W [MeV] F

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

T: π0p

1200 1550 1900

  • 1

1 0.067 ± ) = -0.933 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.800 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.667 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.533 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.400 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.267 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.133 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.000 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.133 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.267 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.400 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.533 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.667 θ cos(

1200 1550 1200 1550 1200 1550

  • 1

1

  • 1
  • 1

W [MeV] T

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration

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Outline Short Motivation Experimental Setup Polarization Observables Analysis Methods Selected Results Conclusion

T: π0n

1200 1550 1900

  • 1

1 0.067 ± ) = -0.933 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.800 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.667 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.533 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.400 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.267 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = -0.133 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.000 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.133 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.267 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.400 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.533 θ cos( 1200 1550 1900

  • 1

1 0.067 ± ) = 0.667 θ cos(

1200 1550 1200 1550 1200 1550

  • 1

1

  • 1
  • 1

W [MeV] T

Polarization Observables T and F Thomas Strub, Basel Group, A2 Collaboration