Double Polarization Virtual Compton Scattering at MAMI

Double PolarizationVirtual Compton Scattering

at MAMI

Luca Doriafor the A1 Collaboration

Institut fuer Kernphysik, Mainz (Germany)

24th Students' Workshop on Electromagnetic InteractionsBosen (Saar), 9-14 Sept. 2007

Talk Outline

Physical Motivations

Theoretical Aspects

Experimental Setup

Data Analysis and Results

Conclusions and Outlook

Luca Doria, KPH Mainz Bosen Workshop 2007

Polarizabilities: Classical Picture

Electric Polarizability α

Magnetic Polarizability β

Diamagnetism

β<0

Paramagnetism

β>0

Displacement of electric chargesInduced dipole moment p=αE

For atomic systems α/V~1

Nucleons: α~10-4 fm3, V~1fm3

ChPT: Pions are relevant degrees of freedom„Pion Cloud“ : Induced currents of spinless charged particles


Resonance Structure of the NucleonExample: N->Delta Transition

Form Factors Analogy


Elastic eN Scattering

Q2=0 : Charge/magnetic moment of the nucleon

FT: Charge/magnetic dipole spatial distribution

Form Factors Analogy


Elastic eN Scattering

(Virtual) Compton Scattering

Q2=0 : Charge/magnetic moment of the nucleon

FT: Charge/magnetic dipole spatial distribution

Q2=0 : Electric/magnetic polarizabilities of the nucleon

FT: Spatial distribution of the polarizabilities inside the nucleon

α(Q2), β(Q2) +4 new observables:Generalized Polarizabilities

?

RCS

Virtual Compton Scattering


Bethe-Heitler ContributionNon separable from VCSLorentz Boost: g in the direction of eCross Section proportional to 1/kKnowledge of the Form Factos needed

Born ContributionFirst Order TermSuppressed by 1/m

VCS ContributionAccess to the Generalized Polarizabilities

Full electron photoproduction amplitude

Virtual Compton Scattering


Observables (LEX approach)


P i=d 5 e , i −d 5 e ,−i

d 5 e , i d 5 e ,−i = d5

2d5= d 5 B HB q ' M n Bo rn h , i O q ' 2

2d5

d 5 E x p

dk ' L a b d ' La b d ' p

−d 5 B HB

dk ' L a B d ' L ab d ' p

=q ' [v L L P L L q −1

PT T q v L T P LT q]O q ' 2

M n B o r n h , z = 4h [ v 1z P T T v 2

z P L Tz v 3

z P ' L Tz ]

M n B o r n h , x = 4h [ v 1x P LT

⊥ v 2x P T T

⊥ v 3x P ' T T

⊥ v 4x P ' LT

⊥ ]

M n B o r n h , y = 4h [ v 1y P LT

⊥ v 2y P T T

⊥ v 3y P ' T T

⊥ v 4y P ' LT

⊥ ]

P L L= aP C 1C 1

P T T= c1 P M 1 M 1 S c 2 P M 2 E 1 S

P L T=bP M 1 M 1 c 3 [ PC 0 M 1 S d 1 P C 2 M 1 S ]

P L Tz = c 4 P M 1 M 1 S c3 [P

C 0 M 1 S d 1 P C 2 M 1 S ]

P ' L Tz = c 5 P M 1 M 1 S c 3 [ P

C 0 M 1 S d 1 P C 2 M 1 S ]

P ' L T⊥ = d 2 P C 0 M 1 S d 3 P C 2 M 1 S

Cross Section

Double Polarization Observable

Generalized Polarizabilities

P.A.M. Guichon, at al., Nucl Phys A 591 (1995) 606-638

Observables (LEX approach)


P i=d 5 e , i −d 5 e ,−i

d 5 e , i d 5 e ,−i = d5


2d5

d 5 E x p

dk ' L a b d ' La b d ' p

−d 5 B HB

dk ' L a B d ' L ab d ' p

=q ' [v L L P L L q −1

PT T q v L T P LT q]O q ' 2

M n B o r n h , z = 4h [ v 1z P T T v 2

z P L Tz v 3

z P ' L Tz ]

M n B o r n h , x = 4h [ v 1x P LT

⊥ v 2x P T T

⊥ v 3x P ' T T

⊥ v 4x P ' LT

⊥ ]

M n B o r n h , y = 4h [ v 1y P LT

⊥ v 2y P T T

⊥ v 3y P ' T T

⊥ v 4y P ' LT

⊥ ]

P L L= aP C 1C 1

P T T= c1 P M 1 M 1 S c 2 P M 2 E 1 S

P L T=bP M 1 M 1 c 3 [ PC 0 M 1 S d 1 P C 2 M 1 S ]

P L Tz = c 4 P M 1 M 1 S c3 [P

C 0 M 1 S d 1 P C 2 M 1 S ]

P ' L Tz = c 5 P M 1 M 1 S c 3 [ P

C 0 M 1 S d 1 P C 2 M 1 S ]

P ' L T⊥ = d 2 P C 0 M 1 S d 3 P C 2 M 1 S

Cross Section

Double Polarization Observable

Generalized Polarizabilities

P.A.M. Guichon, at al., Nucl Phys A 591 (1995) 606-638

α

β

Observables (Dispersion Relations)


B.Pasquini et al, Eur. Phys J. 11 (2001) 185-208

Q2−N=− N

1Q 2 / 2 2

Q2− N=− N

1Q 2 / 22

Q 2=−q2

t=q−q ' 2

=s−u4M

=E LAB

14Mt−Q

2

ℜ F inB Q2 , , t = 2

∫ th

∞d

' ℑ F i Q2 , , t

' 2− 2

VCS defined by

Amplitudes analytical in ν, Unitarity, Crossing Symmetry Analytical continuation

Parameterization of α and β Fit to the experimental data Prediction for the 4 Spin GPs Dipole Form

πN part given by MAID2000 π-photoproduction amplituds

P C 1E1 0Q 2=− 23

4e2 Q

2

P M 1M 10 Q2=− 83

4e2 Q

2

Im ν

Re ννth-ν

th

Theoretical Models


NRQM: P.A.M. Guichon, at al., Nucl Phys A 591 (1995) 606-638

HBChPT O(3): T.R.Hemmert et al. Phys. Rev. D 62 (2000) 014013

HBChPT O(4/5): Kao et al, Phys.Rev.D 70 (2004) 114004

LSM: A.Metz, D.Drechsel, Z. der Physik A356 (1996) 351

ELM: M.Vanderhaeghen, Phys.Lett. B368 (1996) 13

DR: B.Pasquini et al, Eur. Phys J. 11 (2001) 185-208

Experimental Status


MAMI: J. Roche et al, Phys. Rev. Lett. 85 (2000) 708-711 JLAB: Phys.Rev.Lett., 93 (2004) 122001MIT-Bates: P.Bourgeois et al., Phys.Rev.Lett 97 (2006) 212001

Unpolarized Cross Section 2 Combinations of GPs Measurements from three laboratoriesBates point: LEX not applicable

α and β extracted with the DR model

Not all the data can be described Dipole parameterization

Two distinct regions of βLEX and DR consistent for Jlab points DR analysis for MAMI data coming soonPolarizability rms radius consistent with thepion cloud interpretation

Experimental Setup (1)

(Photo: M.Weiss)

(A.Jankowiak)

MAMI Accelerator: 3 Cascaded Racetrack Microtrons:

E = 855 MeV/c2

Max. Current = 20Duty Cycle: 100%

Energy Spread 30 keV (FWHM)

Detector Packagefor each Spectrometer:

Cerenkov Detector (e/p id.)Vertical Drift Chambers (4 planes)

2 Scintillator Planes


Experimental Setup (2)

Out-of-Plane Capability for Spectrometer B

Moller Polarimeter

Spectrometer A:>20

p<735 MeV/c=28msrp/p=20%

Spectrometer B:>8

p<870 MeV/c=5.6msrp/p=15%

Spectrometer C:>55

p<655 MeV/c=28msrp/p=25%

- 70%-80% Beam Polarization

- 5 Min. pro Measurement

- 1% Systematic Uncertainty


Focal Plane Proton Polarimeter


Polarization Reconstruction Three polarization components accesible in principle Maximum Likelihood Fit Full spin precession taken into account

Systematic Error Px ~ 1%

Pz , Py ~ 2%

Data Analysis: Cross Section


Particle ID: Time Coincidence Scintillators (A) Cerenkov Detector (B)

Reaction ID Missing Mass2

Background Random Coincidences Other Particles

Data Analysis: Cross Section


25.6± 2.9± 2.8

−5.0±1.1± 2.1

25.3±2.9± 2.8

−7.5±1.1±2.1

Mergell et al. Friedrich-Walcher HBChPT

P L L−1 / PT T

P LT

26.3 /26.0

−5.5 /−5.4

[2] J. Friedrich and Th. Walcher, Eur. Phys. J. A 17 (2003) 607-623

[1] P.Mergell et al. , Nucl.Phys. A596 (1996) 367-391

Data Analysis: Double Polarization Observable


θγγ

Px

Theoretical Curves based on the mean exp. Kinematics Projection to nominal kinematics needed

False asymmetries and background asymmetriesnegligible

Py

θγ

γPx higher than BH+B

Py consistent with 0

Pz constrained to BH+B

Very low correlation with Px

Data Analysis: Extraction of PLT


P i=d 5 e , i −d 5 e ,−i

d 5 e , i d 5 e ,−i = d5


2d5

Largest effect given by PLT

Less information from Py

Pz not measured with sufficent

accuracy

Data Analysis: Extraction of PLT


Mergell et al. Friedrich-Walcher HBChPT

25.6± 2.9± 2.8

−5.0±1.1± 2.1

25.3±2.9± 2.8

−7.5±1.1±2.1

P L L−1 / PT T

P LT

26.3 /26.0

−5.5 /−5.4

P LT⊥ −13.7± 2.8± 2.2 −13.7± 4.0±2.2 −10.7 /−10.6

Summary and Outlook

Herzlichen Dank an:H. Fonvieille (UBP Clermont-Ferrand, France)P. Janssens (Ghent University, Belgium)N. d'Hose and the Saclay Group (Paris)

Collaboration Accelerator Staff

Virtual Compton Scattering Intuitive physical interpretation of the GPs Fundamental as the form factors New test for the thoretical models

Experimental activity Accessed through photon electroproduction First unpolarized experiment at MAMI (Q2=0.33 GeV2/c2) Experiments by MIT-Bates (Q2=0.05 GeV2/c2) and JLab (Q2 = 0.92 , 1,76 GeV2/c2) Single Spin Asymmetry measured at MAMI I. Bensafa et al., Eur. Phys. J. A 32, (2007) 69-75

NOW: Double Polarization Observable

The Future Enhance the statistics/accuracy for the double polarization experiment Measure new kinematical points for improving the knowledge of α and β

Double Polarization Virtual Compton Scattering at MAMI

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