Transcript Folie 1 - uni

24th Students' Workshop on
Electromagnetic Interactions
Bosen (Saar), 9-14 Sept. 2007
Double Polarization
Virtual Compton Scattering
at MAMI
Luca Doria
for the A1 Collaboration
Institut fuer Kernphysik, Mainz (Germany)
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
Displacement of electric charges
Induced dipole moment p=αE
For atomic systems α/V~1
Nucleons: α~10-4 fm3, V~1fm3
Magnetic Polarizability β
Diamagnetism
β<0
ChPT: Pions are relevant degrees of freedom
„Pion Cloud“ :
Induced currents of
spinless charged particles
Paramagnetism
β>0
Resonance Structure of the Nucleon
Example: N->Delta Transition
Luca Doria, KPH Mainz
Bosen Workshop 2007
Form Factors Analogy
Elastic eN Scattering
Q2=0 : Charge/magnetic
moment of the nucleon
FT: Charge/magnetic dipole
spatial distribution
Luca Doria, KPH Mainz
Bosen Workshop 2007
Form Factors Analogy
Elastic eN Scattering
Q2=0 : Charge/magnetic
moment of the nucleon
FT: Charge/magnetic dipole
spatial distribution
(Virtual) Compton Scattering
RCS
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
Luca Doria, KPH Mainz
Bosen Workshop 2007
Virtual Compton Scattering
Full electron photoproduction amplitude
Bethe-Heitler Contribution
Non separable from VCS
Lorentz Boost: g in the direction of e
Cross Section proportional to 1/k
Knowledge of the Form Factos needed
Born Contribution
First Order Term
Suppressed by 1/m
VCS Contribution
Access to the Generalized Polarizabilities
Luca Doria, KPH Mainz
Bosen Workshop 2007
Virtual Compton Scattering
Luca Doria, KPH Mainz
Bosen Workshop 2007
Observables (LEX approach)
Cross Section
d5 E x p
dk ' L a b d ' La b d
'p
−
d5
dk ' L a B d
BH B
' L ab d
'p
= q'
[v L L P L L q −
Double Polarization Observable
1
v L T P LT q ] O q ' 2
PT T q
Pi=
d5
e ,i
− d5
e ,−
i
d5
e ,i
d5
e ,−
i
=
d5
d5
=
2d 5
BH B
q'
M n Bo rn h , i
2d 5
O q' 2
M n B or n h , z = 4h [v 1z P T T v 2z P zLT v 3z P ' zLT ]
Generalized Polarizabilities
M n B or n h , x = 4h [v 1x P LT⊥
v 2x P T⊥T
v 3x P ' T ⊥T
M n B or n h , y = 4h [v 1y P LT⊥
v y2 P T⊥T
v 3y P ' T⊥T
P L L= aP C 1
v 4x P ' LT⊥ ]
v 4y P ' LT⊥ ]
C1
P T T = c1 P M 1
P LT = bP M 1
M1 S
M1
P zLT = c 4 P M 1
c3[ P C 0
M1 S
P ' zLT = c 5 P M 1
P ' LT⊥ = d 2 P C 0
c2 P M 2
M1 S
M1 S
E1 S
M1 S
c3 [P C 0
d 1 PC2
M1 S
c3 [ P C 0
M1 S
d 3 PC2
M1 S
M1 S
d 1 PC 2
d1 PC 2
]
M1 S
M1 S
]
]
P.A.M. Guichon, at al., Nucl Phys A 591 (1995) 606-638
Luca Doria, KPH Mainz
Bosen Workshop 2007
Observables (LEX approach)
Cross Section
d5 E x p
dk ' L a b d ' La b d
'p
−
d5
dk ' L a B d
BH B
' L ab d
'p
= q'
[v L L P L L q −
Double Polarization Observable
1
v L T P LT q ] O q ' 2
PT T q
Pi=
d5
e ,i
− d5
e ,−
i
d5
e ,i
d5
e ,−
i
=
d5
d5
=
2d 5
BH B
q'
M n Bo rn h , i
2d 5
O q' 2
M n B or n h , z = 4h [v 1z P T T v 2z P zLT v 3z P ' zLT ]
Generalized Polarizabilities
M n B or n h , x = 4h [v 1x P LT⊥
v 2x P T⊥T
v 3x P ' T ⊥T
M n B or n h , y = 4h [v 1y P LT⊥
v y2 P T⊥T
v 3y P ' T⊥T
P L L= aP C 1
P LT = bP M 1
M1 S
M1
P zLT = c 4 P M 1
P ' LT⊥ = d 2 P C 0
c2 P M 2
c3[ P C 0
M1 S
P ' zLT = c 5 P M 1
v 4y P ' LT⊥ ]
α
C1
P T T = c1 P M 1
v 4x P ' LT⊥ ]
M1 S
M1 S
E1 S
M1 S
c3 [P C 0
d 1 PC2
M1 S
c3 [ P C 0
M1 S
d 3 PC2
M1 S
M1 S
d 1 PC 2
d1 PC 2
]
M1 S
M1 S
β
]
]
P.A.M. Guichon, at al., Nucl Phys A 591 (1995) 606-638
Luca Doria, KPH Mainz
Bosen Workshop 2007
Observables (Dispersion Relations)
VCS defined by
Q 2= − q2
t= q− q'
=
2
s− u
1
LAB
2
=E
t− Q
4M
4M
Im ν
Amplitudes analytical in ν, Unitarity, Crossing Symmetry
Analytical continuation
ℜ F nB
i
2
Q , ,t =
2
∫
∞
d
th
' ℑ F i Q2 , , t
' 2− 2
Re ν
-νth νth
πN part given by MAID2000 π-photoproduction amplituds
Parameterization of α and β
Fit to the experimental data
Prediction for the 4 Spin GPs
Dipole Form
Q −
N
Q2 −
N
2
−
=
1 Q 2/
N
−
1 Q 2/
N
=
2 2
P C1
2 2
P
M1
E1 0
M1 0
Q2 = −
Q2 = −
24
3 e2
Q2
84
3 e2
Q2
B.Pasquini et al, Eur. Phys J. 11 (2001) 185-208
Luca Doria, KPH Mainz
Bosen Workshop 2007
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
Luca Doria, KPH Mainz
Bosen Workshop 2007
Experimental Status
Unpolarized Cross Section
2 Combinations of GPs
Measurements from three laboratories
Bates 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 β
LEX and DR consistent for Jlab points
DR analysis for MAMI data coming
soon
Polarizability rms radius consistent with the
pion cloud interpretation
MAMI: J. Roche et al, Phys. Rev. Lett. 85 (2000) 708-711
JLAB: Phys.Rev.Lett., 93 (2004) 122001
MIT-Bates: P.Bourgeois et al., Phys.Rev.Lett 97 (2006)
212001
Luca Doria, KPH Mainz
Bosen Workshop 2007
Experimental Setup (1)
(A.Jankowiak)
MAMI Accelerator:
3 Cascaded Racetrack Microtrons:
E = 855 MeV/c2
Max. Current = 20
Duty Cycle: 100%
Energy Spread 30 keV (FWHM)
Detector Package
for each Spectrometer:
(Photo: M.Weiss)
Luca Doria, KPH Mainz
Cerenkov Detector (e/p id.)
Vertical Drift Chambers (4 planes)
2 Scintillator Planes
Bosen Workshop 2007
Experimental Setup (2)
Spectrometer A:
>20
p<735 MeV/c
=28msr
p/p=20%
Spectrometer
B:
>8
p<870 MeV/c
=5.6msr
p/p=15%
Spectrometer C:
>55
p<655 MeV/c
=28msr
p/p=25%
Out-of-Plane Capability
for Spectrometer B
Moller Polarimeter
- 70%-80% Beam Polarization
- 5 Min. pro Measurement
- 1% Systematic Uncertainty
Luca Doria, KPH Mainz
Bosen Workshop 2007
Focal Plane Proton Polarimeter
Polarization Reconstruction
Three polarization components accesible in principle
Maximum Likelihood Fit
Full spin precession taken into account
Luca Doria, KPH Mainz
Systematic Error
Px
~ 1%
Pz , Py ~ 2%
Bosen Workshop 2007
Data Analysis: Cross Section
Particle ID:
Time Coincidence
Scintillators (A)
Cerenkov Detector (B)
Reaction ID
Missing Mass2
Background
Random Coincidences
Other Particles
Luca Doria, KPH Mainz
Bosen Workshop 2007
Data Analysis: Cross Section
Mergell et al.
P L L− 1/
P LT
PT T
Friedrich-Walcher
HBChPT
25.6± 2.9± 2.8
25.3± 2.9± 2.8
26.3 /26.0
− 5.0± 1.1± 2.1
− 7.5± 1.1± 2.1
− 5.5/− 5.4
[1] P.Mergell et al. , Nucl.Phys. A596 (1996) 367-391
[2] J. Friedrich and Th. Walcher, Eur. Phys. J. A 17 (2003) 607-623
Luca Doria, KPH Mainz
Bosen Workshop 2007
Data Analysis: Double Polarization Observable
Px
Py
θγγ
Theoretical Curves based on the mean exp. Kinematics
Projection to nominal kinematics needed
False asymmetries and background asymmetries
negligible
Luca Doria, KPH Mainz
θγ
γ
Px higher than BH+B
Py consistent with 0
Pz constrained to BH+B
Very low correlation with Px
Bosen Workshop 2007
Data Analysis: Extraction of PLT
Pi=
d5
e ,i
− d5
d5
e ,i
d5
d5
=
=
2d 5
e ,− i
e ,−
i
d5
BH B
q'
M n Bo rn h , i
2d 5
Largest effect given by PLT
Less information from Py
Pz not measured with sufficent accuracy
Luca Doria, KPH Mainz
Bosen Workshop 2007
O q' 2
Data Analysis: Extraction of PLT
Mergell et al.
Friedrich-Walcher
HBChPT
25.6± 2.9± 2.8
25.3± 2.9± 2.8
26.3 /26.0
P LT
− 5.0± 1.1± 2.1
− 7.5± 1.1± 2.1
− 5.5/− 5.4
P LT⊥
− 13.7± 2.8± 2.2
− 13.7± 4.0± 2.2
− 10.7 /− 10.6
P L L− 1/
Luca Doria, KPH Mainz
PT T
Bosen Workshop 2007
Summary and Outlook
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
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