measurement of the proton spin...
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Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Measurement Of The Proton Spin PolarisabilitiesBaryons2013
D. G. Middleton
Institut für Kernphysik, Universität MainzMt. Allison University/
24/06/2013
university Collaboration
2a
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Outline
IntroductionCompton ScatteringScalar PolarisabilitiesSpin Polarisabilities
Experimental Set-UpMAMIDetectorsPolarised Target
Analysis and ResultsPossible Reactionsπ0 Photo-ProductionData AnalysisPreliminary Results
Conclusions & Outlook
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Compton Scattering• Nucleon polarisabilities are fundamental structure observablesrelated to the nucleon's internal dynamics and describe its responseto an applied electric or magnetic �eld.
• They can be measured with the Compton scattering reaction.
Photon
Proton
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Compton Scattering• Nucleon polarisabilities are fundamental structure observablesrelated to the nucleon's internal dynamics and describe its responseto an applied electric or magnetic �eld.
• They can be measured with the Compton scattering reaction.
ScatteredPhoton
Recoil Proton
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Compton Scattering Formulae 1
Zeroth Order - Mass and Electric Charge
H(0)eff =
~π2
2m+ eφ (where ~π =~p− e~A)
First Order - Anomalous Magnetic Moment
H(1)eff =−e(1+ κ)
2m~σ ·~H− e(1+2κ)
8m2~σ ·[~E ×~π−~π×~E
]Second Order - Electric and Magnetic polarisabilities
H(2)eff =−4π
[1
2αE1
~E 2 +1
2βM1
~H2
]
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Compton Scattering Formulae 1
Zeroth Order - Mass and Electric Charge
H(0)eff =
~π2
2m+ eφ (where ~π =~p− e~A)
First Order - Anomalous Magnetic Moment
H(1)eff =−e(1+ κ)
2m~σ ·~H− e(1+2κ)
8m2~σ ·[~E ×~π−~π×~E
]Second Order - Electric and Magnetic polarisabilities
H(2)eff =−4π
[1
2αE1
~E 2 +1
2βM1
~H2
]
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Compton Scattering Formulae 1
Zeroth Order - Mass and Electric Charge
H(0)eff =
~π2
2m+ eφ (where ~π =~p− e~A)
First Order - Anomalous Magnetic Moment
H(1)eff =−e(1+ κ)
2m~σ ·~H− e(1+2κ)
8m2~σ ·[~E ×~π−~π×~E
]Second Order - Electric and Magnetic polarisabilities
H(2)eff =−4π
[1
2αE1
~E 2 +1
2βM1
~H2
]
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Electric Polarisabilty: αE1
Describes the response of a proton to an applied electric �eld.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Electric Polarisabilty: αE1
Describes the response of a proton to an applied electric �eld.
Induces a current in the pion cloud which vertically`stretches' the proton.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Magnetic Polarisabilty: βM1
Describes the response of a proton to an applied magnetic �eld.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Magnetic Polarisabilty: βM1
Describes the response of a proton to an applied magnetic �eld.
Induces a diamagnetic moment in the pion cloud that opposes theparamagnetic moment of the quarks.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Scalar PolarisabilitiesBoth αE1 and βM1 have been determined for the proton using unpolarised Compton Scattering.
αE1 = [12.1±0.3(stat)∓0.4(syst)±0.3(mod)]×10−4 fm3
βM1 = [1.6±0.4(stat)±0.4(syst)±0.4(mod)]×10−4 fm3
V. Olmos de Leon et al., Eur. Phys. J. A10, 207 (2001)
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Scalar PolarisabilitiesBoth αE1 and βM1 have been determined for the proton using unpolarised Compton Scattering.
αE1 = [10.8±0.7]×10−4 fm3
βM1 = [4.0±0.7]×10−4 fm3
V. Lensky, V. Pascalutsa, Eur. Phys. J. C65, 195 (2010)
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Compton Formulae 2
Third Order - Spin Polarisabilities
H(3)eff =−4π
[1
2γE1E1~σ · (~E ×~̇E ) +
1
2γM1M1~σ · (~H× ~̇H)
− γM1E2EijσiHj + γE1M2HijσiEj
]
• These parameters describe the response of the proton spin to anapplied electric or magnetic �eld.
• To date, these have not been individually determined. However, twolinear combinations of them have been.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Compton Formulae 2
Third Order - Spin Polarisabilities
H(3)eff =−4π
[1
2γE1E1~σ · (~E ×~̇E ) +
1
2γM1M1~σ · (~H× ~̇H)
− γM1E2EijσiHj + γE1M2HijσiEj
]
Forward and Backward Spin Polarisabilities
γ0 =−γE1E1− γE1M2− γM1E2− γM1M1
γπ =−γE1E1− γE1M2 + γM1E2 + γM1M1
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Forward and Back Spin Polarisabilities
Forward Spin Polarisability: γ0
Determined from data taken for a measurement of the GDH sum rule
γ0 = (−1.0±0.08)×10−4 fm4
J. Ahrens et al., Phys. Rev. Lett. 87, 022003 (2001)H. Dutz et al., Phys. Rev. Lett. 91, 192001 (2003)
Backward Spin Polarisability: γπ
Determined using a �tting to backward angle Compton scattering datasuch as that taken at MAMI.
γπ = (8.0±1.8)×10−4 fm4
M. Camen, et al., Phys. Rev. C 65 032202 (2002)
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Forward and Back Spin Polarisabilities
Forward Spin Polarisability: γ0
Determined from data taken for a measurement of the GDH sum rule
γ0 = (−1.0±0.08)×10−4 fm4
J. Ahrens et al., Phys. Rev. Lett. 87, 022003 (2001)H. Dutz et al., Phys. Rev. Lett. 91, 192001 (2003)
Backward Spin Polarisability: γπ
Determined using a �tting to backward angle Compton scattering datasuch as that taken at MAMI.
γπ = (8.0±1.8)×10−4 fm4
M. Camen, et al., Phys. Rev. C 65 032202 (2002)
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Spin Polarisabilities: Predicted Values
Extracting the proton spin polarisabilities would provide a useful test ofnucleon structure.
O(p3) O(p4) O(p4) LC3 LC4 SSE BGLMN HDPV KS
γE1 -5.7 -1.4 -1.8 -3.2 -2.8 -5.7 -3.4 -4.3 -5.0
γM2 1.1 0.2 0.7 0.7 0.8 .98 0.3 -0.01 -1.8
γE2 1.1 1.8 1.8 0.7 0.3 .98 1.9 2.1 1.1
γM1 -1.1 3.3 2.9 -1.4 -3.1 3.1 2.7 2.9 3.4
γ0 4.6 -3.9 -3.6 3.1 4.8 .64 -1.5 -0.7 2.3
γπ 4.6 6.3 5.8 1.8 -0.8 8.8 7.7 9.3 11.3
Table: Values for the spin polarisabilities. O(pn) are Chiral Perturbation Theory (ChPT)
calculations. LC3 and LC4 are O(p3) and O(p4) Lorentz invariant ChPT calculations,
respectively. SSE is a Small Scale Expansion calculation. The remaining three are all
dispersion relation calculations.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Spin Polarisabilities: Measurements
• Circularly polarised photons, transversely polarised protons.
Σ2x =NR+x−NL
+x
NR+x
+NL+x
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Spin Polarisabilities: Measurements
• Circularly polarised photons, transversely polarised protons.
Σ2x =NR+x−NL
+x
NR+x
+NL+x
• Circularly polarised photons, longitudinally polarised protons.
Σ2z =NR+z−NL
+z
NR+z
+NL+z
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Spin Polarisabilities: Measurements
• Circularly polarised photons, transversely polarised protons.
Σ2x =NR+x−NL
+x
NR+x
+NL+x
• Circularly polarised photons, longitudinally polarised protons.
Σ2z =NR+z−NL
+z
NR+z
+NL+z
• Linearly polarised photons, unpolarised protons.
Σ3 =N‖−N⊥N‖+N⊥
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Mainzer Mikrotron: MAMI
• Injector →3.5 MeV
• RTM1 → 14.9 MeV
• RTM2 → 180 MeV
• RTM3 → 882 MeV
• HDSM → 1.6 GeV
For these experimentsonly the RTMs arerequired.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Polarised Photon Beam
• A high energy electron can produce Bremsstrahlung photons whenslowed down by a material.
• If the electron beam is longitudinally polarised it produces acircularly polarised photon beam through a helicity transfer.
• Circular beam helicity can be �ipped by alternating the e− beampolarisation (about 1 Hz).
• Pe measured with a Mott
Polarimeter before the
RTMs.
• Pe ∼ 80% at MAMI.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Photon Tagger
• e− beam with energy E0,strikes radiator producingBremsstrahlung photon beamwith energy distribution from 0to E0.
• Residual e− paths are bent in aspectrometer magnet.
• With proper magnetic �eld,array of 353 detectorsdetermines the e− energy, and`tags' the photon energy byenergy conservation.
• Can `tag' 5 - 90 % of E0.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Crystal Ball & TAPS
TAPS
CB
Veto
BaF2
NaI
PIDMWPC
target
Crystal Ball (CB)
• 672 NaI Crystals
• 24 Particle Identi�cation Detector (PID)Paddles
• 2 Multiwire Proportional Chambers (MWPCs)
• 21◦ < θ < 159◦
• ∆E ≈ 3%; ∆θ ≈ 2.5◦
Two Arms Photon Spectrometer (TAPS)
• 366 BaF2 and 72 PbWO4 Crystals
• 384 Veto Paddles
• Fills in downstream hole
• ∆E ≈ 3%; ∆θ ≈ 0.7◦
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Crystal Ball & TAPS
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Polarised Target
Transversely/longitudinally polarised frozen spin Butanol target utilisingDynamic Nuclear Polarisation (DNP).
3He/4He dilution refrigerator.
Schematic of target insert wherehashed region is 2 cm of Butanol(C4H9OH).
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Possible Reactions
Butanol Target (C4H9OH)
• Compton o� of H
• Coherent scatter o� of C (or O)
• Incoherent scatter o� of C (or O)
• Pion photo-production o� of H
• Coherent pion o� of C (or O)
• Incoherent pion o� of C (or O)
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Possible Reactions
Butanol Target (C4H9OH)
• Compton o� of H
• Coherent scatter o� of C (or O)
• Incoherent scatter o� of C (or O)
• Pion photo-production o� of H
• Coherent pion o� of C (or O)
• Incoherent pion o� of C (or O)
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Possible Reactions
Butanol Target (C4H9OH)
• Compton o� of H
• Coherent scatter o� of C (or O)
• Incoherent scatter o� of C (or O)
• Pion photo-production o� of H
• Coherent pion o� of C (or O)
• Incoherent pion o� of C (or O)
Subtract data taken on a Car-bon target, with density cho-sen to match the number ofnon-hydrogen nuclei in theButanol target.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Possible Reactions
Butanol Target (C4H9OH)
• Compton o� of H
• Coherent scatter o� of C (or O)
• Incoherent scatter o� of C (or O)
• Pion photo-production o� of H
• Coherent pion o� of C (or O)
• Incoherent pion o� of C (or O)
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
π0 Photo-Production
ScatteredPhoton
Recoil Proton
Compton Scattering
Photon
Proton
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
π0 Photo-Production
ScatteredPhoton
Recoil Proton
Compton Scattering
Neutral Pion
Recoil Proton
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
π0 Photo-Production
ScatteredPhoton
Recoil Proton
Compton Scattering
DecayPhotons
Recoil Proton
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
π0 Photo-Production
ScatteredPhoton
Recoil Proton
Compton Scattering
DecayPhotons
Recoil Proton
If one of the decay photons is lost,this can look like Compton
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Event Selection
Require detection of ONLY one photon and ONLY one charged particlewithin a de�ned 'opening angle cut' in time with a tagger hit.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Coincidence Time
Time di�erence
Cut on accidentals
Cut on prompts
Close up of peak
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Missing Mass
Apart from timing cuts to determine events of interest the missing massof the reaction is determined:
mmiss =√
(Eγi+mp−Eγf
)2− (~pγi−~pγf
)2 =Compton
mp
• Eγi/fis the energy of the incident/scattered photon.
• −−→pγi/fis the momentum of the incident/scattered photon.
• mp is the mass of the proton.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Missing Mass: Eγ=273-303 MeV, θγ ′=100-120◦
Missing Mass (MeV)800 850 900 950 1000 1050 1100 1150 1200
Co
un
ts
0
1000
2000
3000
4000
5000
Initial missing mass distribution from the Butanol target.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Missing Mass: Eγ=273-303 MeV, θγ ′=100-120◦
Missing Mass (MeV)800 850 900 950 1000 1050 1100 1150 1200
Co
un
ts
0
1000
2000
3000
4000
5000
Background from accidental (random) events in tagger.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Missing Mass: Eγ=273-303 MeV, θγ ′=100-120◦
Missing Mass (MeV)800 850 900 950 1000 1050 1100 1150 1200
Co
un
ts
0
500
1000
1500
2000
2500
3000
Distribution after removing accidentals.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Missing Mass: Eγ=273-303 MeV, θγ ′=100-120◦
Missing Mass (MeV)800 850 900 950 1000 1050 1100 1150 1200
Co
un
ts
0
500
1000
1500
2000
2500
3000
Background from the Carbon target.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Missing Mass: Eγ=273-303 MeV, θγ ′=100-120◦
Missing Mass (MeV)800 850 900 950 1000 1050 1100 1150 1200
Co
un
ts
0
500
1000
1500
2000
2500
Distribution after removing Carbon background.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Missing Mass: Eγ=273-303 MeV, θγ ′=100-120◦
Missing Mass (MeV)800 850 900 950 1000 1050 1100 1150 1200
Co
un
ts
0
500
1000
1500
2000
2500
Background from π0 photon in downstream (TAPS) hole.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Missing Mass: Eγ=273-303 MeV, θγ ′=100-120◦
Missing Mass (MeV)800 850 900 950 1000 1050 1100 1150 1200
Co
un
ts
0
500
1000
1500
2000
2500
Background from π0 photon in upstream (CB) hole.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Missing Mass: Eγ=273-303 MeV, θγ ′=100-120◦
Missing Mass (MeV)800 850 900 950 1000 1050 1100 1150 1200
Co
un
ts
0
500
1000
1500
2000
2500
Background from π0 photon between CB/TAPS.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Missing Mass: Eγ=273-303 MeV, θγ ′=100-120◦
Missing Mass (MeV)800 850 900 950 1000 1050 1100 1150 1200
Co
un
ts
0
500
1000
1500
2000
Final distribution after subtracting backgrounds.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Missing Mass: Eγ=273-303 MeV, θγ ′=100-120◦
Missing Mass (MeV)800 850 900 950 1000 1050 1100 1150 1200
Co
un
ts
0
500
1000
1500
2000
Total events determined by integrating up to proton mass.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Transverse Asymmetries: Eγ=273-303 MeV
Compton Theta0 20 40 60 80 100 120 140 160 180
2xΣ
-0.6
-0.4
-0.2
0
0.2
0.4
0.6 = -2.3
E1E1γ
= -3.3E1E1
γ = -4.3
E1E1γ
= -5.3E1E1
γ = -6.3
E1E1γ
Preliminary
Vary γE1E1, holding γM1M1 �xed at 2.9.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Transverse Asymmetries: Eγ=273-303 MeV
Compton Theta0 20 40 60 80 100 120 140 160 180
2xΣ
-0.6
-0.4
-0.2
0
0.2
0.4
0.6 = 4.9
M1M1γ
= 3.9M1M1
γ = 2.9
M1M1γ
= 1.9M1M1
γ = 0.9
M1M1γ
Preliminary
Vary γM1M1, holding γE1E1 �xed at -4.3.
Introduction Experimental Set-Up Analysis and Results Conclusions & Outlook
Conclusions and Outlook
• These are the �rst double polarised asymmetries, at these energies,observed in real Compton scattering o� of the proton.
• Even with conservative integration limit, these asymmetries agreewith a value for γE1E1 =−4.3±1.5×10−4 fm4.
• A global χ2 �t using all available data is in progress, as well asfurther simulation to improve integration.
• In December 2012 data for the Σ3 asymmetry were taken.Calibration of the data and �rst analysis is uynderway.
• The installation of the frozen spin target with the longitudinal coil isunderway. A measurement of Σ2z will hopefully take place in 2014.
• With all three experiments, the extraction of the protonspin-polarisabilities will provide an important test ofnucleon structure.