Measuring Proton Spin-Polarizabilities with the Crystal Ball

• Compton scattering and nucleon polarizabilities • Measuring proton spin-polarizabilities with the Crystal Ball• How well can we measure the proton spin-polarizabilities?• A polarized scintillating target for Compton scattering

studies below pion threshold.

Rory MiskimenUniversity of Massachusetts

Amherst

22

22Bcos1

2cos1

2M4e),(

dd),(

dd

Compton scattering from the proton

g*

g

N N

g*

g

N N

=Im

Dispersion Model for RCS and VCS†

Connects pion electroproduction amplitudes from MAID with VCS• Unconstrained asymptotic contributions to two of the 12

VCS amplitudes are fit to the data. Valid up to

πN 2mMs Enhanced sensitivity to the polarizabilities

†B. Pasquini, et al., Eur. Phys. J. A11 (2001) 185, and D. Drechsel et al., Phys. Rep. 378 (2003) 99.

gggg jjij2M1Ejjij2E1M1M1M1E1E

spin),3(eff EH2HE2BBEE42

1H

• At O(3) four new nucleon structure terms that involve nucleon spin-flip operators enter the RCS expansion.

Measuring nucleon spin-polarizabilities in polarized real Compton scattering

Spin polarizabilities tell us about the response of the nucleon spin to the photon polarization. The “stiffness” of the spin can be thought of as arising from the nucleon’s spin interacting with the pion cloud.

+

Spin polarizability: “Pionic” Faraday effect

Proton spin polarizability

E

Rotating electric field induces pion current. Lorentz force moves pion outward

+

Spin polarizability: “Pionic” Faraday effect

Proton spin polarizability

E

Rotating electric field induces pion current. Lorentz force moves pion inward

g

d41

m3

232120

Experiments

2E1M1M1M2M1E1E1E0 ggggg

2E1M1M1M2M1E1E1E ggggg

The GDH experiments at Mainz and ELSA used the Gell-Mann, Goldberger, and Thirring sum rule to evaluate the forward S.-P. g0

440 fm10)10.008.001.1( g

Backward spin polarizability from dispersive analysis of backward angle Compton scattering

44fm10)8.17.38( g

  O(p3) O(p4) O(p4) LC3 LC4 SSE BGLMN HDPV KS DPV ExperimentgE1E1 -5.7 -1.4 -1.8 -3.2 -2.8 -5.7 -3.4 -4.3 -5.0 -4.3 No data

gM1M1 -1.1 3.3 2.9 -1.4 -3.1 3.1 2.7 2.9 3.4 2.9 No data

gE1M2 1.1 0.2 .7 .7 .8 .98 0.3 -0.01 -1.8 0 No data

gM1E2 1.1 1.8 1.8 .7 .3 .98 1.9 2.1 1.1 2.1 No data

g0 4.6 -3.9 -3.6 3.1 4.8 .64 -1.5 -.7 2.3 -.7 -1.01 ±0.08 ±0.10 g 4.6 6.3 5.8 1.8 -.8 8.8 7.7 9.3 11.3 9.3 8.0± 1.8†

† The pion-pole contribution has been subtracted from the experimental value for g

Calculations labeled O(pn) are ChPTLC3 and LC4 are O(p3) and O(p4) Lorentz invariant ChPT calculationsSSE is small scale expansionOther calculations are dispersion theoryLattice QCD calculation by Detmold is in progress

Proton spin-polarizability measurements and predictions in units of 10-4 fm4

and nature is always full of surprises!

Proton electric and magnetic polarizabilities from real Compton scattering†

34 fm10x)6.00.12(

34fm10x)6.09.1(

Prior to the 1991 publication of Federspiel et al., it was surmised that

≈ 10 ×10-4 fm3

† M. Schumacher, Prog. Part. and Nucl. Phys. 55, 567 (2005).

34 fm10)33(

Courtesy of Helene Fonvieille

E

Virtual Compton Scattering

N* ?

• Measuring proton spin-polarizabilities at MAMI Crystal ball detector, ≈ 4 photon detection detectionEg≈ 280 MeV (large sensitivity to g’s)Possible problems:i. Photon backgrounds from 0 productionii. Coherent and incoherent scattering on 12C in the butanol

target. Solution detect recoil protons from Compton events.

Signal and Background Reactions

Coherent Compton

Incoherent Compton

Proton π0

Coherent π0

Incoherent π0

Proton Compton

i. Require recoil proton

ii. Require only two energy clusters

iii. Require correct opening angle between proton and photon, and co-planarity

Polarization observables in real Compton scattering

Circular polarization

Circular polarization

Linear polarization

Polarization observables in real Compton scattering

Circular polarization

Circular polarization

Linear polarization

x2

Polarization observables in real Compton scattering

Circular polarization

Circular polarization

Linear polarization

z2

x2

Polarization observables in real Compton scattering

Circular polarization

Circular polarization

Linear polarization

z2

x2

||

||

3

Sensitivity Study I: • Hold g0 and g fixed at experimental values• Vary gE1E1 or gM1M1

• Do this at photon energies of 240 and 280 MeV.

is mostly sensitive to x2 1E1Eg

11E1E g 11M1M g

Eg=240 MeV

Eg=280 MeV

x2

is mostly sensitive to

z2 1M1Mg

Eg=240 MeV

Eg=280 MeV

z2

11E1E g 11M1M g

is mostly sensitive to and

3 1M1Mg 2E1Mg

Eg=240 MeV

Eg=280 MeV

3

11E1E g 11M1M g

Sensitivity Study II: • Hold g’s fixed at values given by Pasquini et al.• Vary g’s individually• Do this at photon energies of 240 and 280 MeV.

11E1E g 11M1M g12M1E g 12E1M g

is mostly sensitive to x2 1E1Eg

x2

Eg=240 MeV

Eg=280 MeV

is mostly sensitive to

z2 1M1Mg

z2

Eg=240 MeV

Eg=280 MeV11E1E g 11M1M g12M1E g 12E1M g

is mostly sensitive to and

3 1M1Mg 2E1Mg

3

Eg=240 MeV

Eg=280 MeV11E1E g 11M1M g12M1E g 12E1M g

Sensitivity Study III: • Study what happens when you vary two

polarizabilities simultaneously? • Vary a primary S.P. by ± 1, and• vary a secondary S.P. by 0, or +1. • Do this at photon energies of 240 and 280 MeV.

is mostly sensitive to x2 1E1Eg

x2Eg=240 MeV

Eg=280 MeV11E1E g 11M1M g12M1E g 12E1M g

is mostly sensitive to

z2 1M1Mg

z2Eg=240 MeV

Eg=280 MeV11E1E g 11M1M g12M1E g 12E1M g

is mostly sensitive to and

3 1M1Mg 2E1Mg

Eg=240 MeV

Eg=280 MeV11E1E g 11M1M g12M1E g 12E1M g

3

Sensitivity Study IV: • Produce pseudo-data for the asymmetries 2x, 2z, 3 with the expected statistical errors

• Fit the pseudo-data with gE1E1, gE1M2, gM1E2, gM1M1, and .

• Option 1: constrain the fit with the experimental values of g0 and g

• Option 2: no constraint on g0 or g

Eg (Mev) gE1E1 gE1M2 gM1E2 gM1M1

240 .27 .60 .34 .51280 .24 .51 .34 .39

Option 1: Constrain the fit with the experimental values of g0 and g

Projected Errors

Eg (Mev) gE1E1 gE1M2 gM1E2 gM1M1

240 .95 2.1 1.3 .81280 .28 .72 .44 .49

Option 2: No constraint on g0 or g

Least well constrained of the 4 S.P.’s.

3y: Linearly polarized photons, target polarization perpendicular to scattering plane

is mostly sensitive to and

y3 1E1Eg 2M1Eg

Pasquini, et al., Phys. Rev. C, 76, 015203

After doing everything you can do with butanol: an active target for the A2 frozen spin target?We would like to extend Compton measurements below pion threshold, ≈100 MeV, not to measure the S.P.’s, but rather to test theoretical models for Compton scattering: HBChPT, dispersion theory, effective field theories.

• An active polarized target will be required to do this.

• A polarized scintillator target for Compton scattering at HIGS/TUNL is under construction

• Probably not possible to reach polarizations or relaxation times equal to those routinely attained for butanol. However, what is achievable might be good enough for Compton studies @ 100 MeV, where asymmetries are large.

Existing A2 target with active insert

Fused silica shellScintillator foils suspended on graphite rods

BCF-92 WLS fibers on outside of transparent shell

Photodetector

Polarization studies of polystyrene scintillators

DNP measurements at UVa EPR measurements at UMass

• Data are consistent with a loss of oxo-tempo in the fabrication process at the level of 0.8×1019 molecules/cc.

• More polarization studies are planned at UVa and at JLab using the FROST target.

T≈2° K

Photo-detector: Radiation Monitoring Devices SS-PMT

QE ≈ 30% Gain = 103 to 104

3 mm

3 mm

Summary

• We can measure all four proton spin-polarizabilities with the crystal ball and the frozen-spin target with a sensitivity at the level of ≈0.5 x 10-4 fm4.

• One of the spin observables, 3, requires only linearly polarized photons and a liquid hydrogen target.

• We have responded to all of the critical comments of the PAC, and have submitted a detailed report to the A2 Steering Committee.

• Polarized Compton scattering below pion threshold will require an active target. The HIGS scintillating insert can probably be adapted to the A2 target.

• We look forward to data taking in 2010 !