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.