Double Polarization Virtual Compton Scattering at MAMI
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Transcript of 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
Luca Doria, KPH Mainz Bosen Workshop 2007
Resonance Structure of the NucleonExample: N->Delta Transition
Form Factors Analogy
Luca Doria, KPH Mainz Bosen Workshop 2007
Elastic eN Scattering
Q2=0 : Charge/magnetic moment of the nucleon
FT: Charge/magnetic dipole spatial distribution
Form Factors Analogy
Luca Doria, KPH Mainz Bosen Workshop 2007
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
Luca Doria, KPH Mainz Bosen Workshop 2007
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
Luca Doria, KPH Mainz Bosen Workshop 2007
Observables (LEX approach)
Luca Doria, KPH Mainz Bosen Workshop 2007
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)
Luca Doria, KPH Mainz Bosen Workshop 2007
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
α
β
Observables (Dispersion Relations)
Luca Doria, KPH Mainz Bosen Workshop 2007
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
Luca Doria, KPH Mainz Bosen Workshop 2007
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
Luca Doria, KPH Mainz Bosen Workshop 2007
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
Luca Doria, KPH Mainz Bosen Workshop 2007
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
Luca Doria, KPH Mainz Bosen Workshop 2007
Focal Plane Proton Polarimeter
Luca Doria, KPH Mainz Bosen Workshop 2007
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
Luca Doria, KPH Mainz Bosen Workshop 2007
Particle ID: Time Coincidence Scintillators (A) Cerenkov Detector (B)
Reaction ID Missing Mass2
Background Random Coincidences Other Particles
Data Analysis: Cross Section
Luca Doria, KPH Mainz Bosen Workshop 2007
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
Luca Doria, KPH Mainz Bosen Workshop 2007
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
Luca Doria, KPH Mainz Bosen Workshop 2007
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
Largest effect given by PLT
Less information from Py
Pz not measured with sufficent
accuracy
Data Analysis: Extraction of PLT
Luca Doria, KPH Mainz Bosen Workshop 2007
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