Measuring Spin-Polarizabilities of the Proton in

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1 Measuring Spin-Polarizabilities of the Proton in Polarized Compton Scattering at MAMI-Mainz M Rory Miskimen University of Massachusetts, Amherst for the Mainz A2 Collaboration Chiral Dynamics 2012 Compton scattering and nucleon spin-polarizabilities First measurements of double-polarized Compton scattering asymmetries on the proton

2 Measuring nucleon spin-polarizabilities p in polarized Compton scattering At O(ω 3 ) four nucleon structure terms involving nucleon spin-flip operators enter the Real Compton Scattering expansion. H (3),spin eff 1 r r &r r r &r = 4π γe1e1σ E E + γm1m1σ B B 2γM1E2EijσjHj + 2γE1M2HijσjEj 2 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 h st ffn ss of th sp n can thought of as ar s ng from the nucleon s spin interacting with the pion cloud.

3 Experiments The GDH experiments at Mainz and ELSA used the Gell-Mann, Goldberger, and Thirring sum rule to evaluate the forward S.-P. γ 0 γ 0 = γ γ γ E1E1 E1M2 M1M1 γm1e2 γ 0 = 1 4π 2 m π σ 1 2 σ ω dω 4 γ 0 = ( 1.01 ± 0.08 ± 0.10) 10 fm 4 Backward spin polarizability from dispersive analysis of backward angle Compton scattering γ π = γ E1E1 γ E1M2 + γ M1M1 + γ M1E2 γ π = 4 4 ( 8.0 ± 1.8) 10 fm The pion-pole contribution has been subtracted from γ π

4 Proton spin-polarizability measurements and predictions in units of 10-4 fm 4 O(p 3 ) O(p 4 ) O(p 4 ) LC3 LC4 SSE BGLMN HDPV KS DPV ΔΤheory Experiment γ E1E No data γ M1M No data γ E1M No data γ M1E No data γ ±0.08 ±0.10 γ π ± 8.0± Calculations l labeled l O(p n ) are ChPT LC3 and LC4 are O(p 3 )ando(p 4 ) Lorentz invariant ChPT calculations SSE is small scale expansion Other calculations are dispersion theory

5 Polarization observables in real Compton scattering Circular polarization Circular polarization Linear polarization

6 Polarization observables in real Compton scattering Circular polarization Σ 2x = σ σ σ + σ Circular polarization Linear polarization

7 Polarization observables in real Compton scattering Circular polarization Σ 2x = σ σ σ + σ Circular polarization Σ 2z = σ σ σ + σ Linear polarization

8 Polarization observables in Compton scattering Circular polarization Σ 2x = σ σ σ + σ Circular polarization Σ 2z = σ σ σ + σ Σ 3 = σ σ σ + σ Linear polarization

9 Dispersion Model for RCS and VCS γ γ γ π γ Im = N N N N 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 s M N + 2m π 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.

10 Sensitivity Study for Σ 2x Vary α, β, γ 0 and γ π within experimental error bars, and vary γ E1E1 holding γ M1M1 fixed, or vary γ M1M1 holding γ E1E1 fixed E γ = 280 MeV Δγ E1E1 = ±1 Δγ M1M1 = ±1 Σ 2x Σ 2x

11 Polarization observables in real Compton scattering Circular polarization σ σ Sensitive to γ = E1E1 2 σ + σ Σ x Circular polarization σ σ = Sensitive to γ M1M1 2 σ + σ Σ z Linear polarization σ σ Σ3 = Sensitive to γ E1E1 σ + σ and γ M1M1

12 Measurements of Σ 2x at MAMI-Mainz Circular polarization σ σ Sensitive to γ = E1E1 2 σ + σ Σ x Phil Martel s Ph.D. thesis, UMass Amherst

13 E γ 280 MeV (large sensitivity spin-polarizabilities)

14 Frozen spin target 2 cm butanol P ~ 90% target polarized at 25 mk > 1000 hours relaxation time 0.6 T holding field

15 Crystal Ball and TAPS 4π photon detection, 4 < θ < 160 CB: 672 NaI crystals, ΔE~3%, Δθ~2.5 TAPS: 366 BaF 2 and 72 PbW0 4 crystals ΔE~5%, Δθ~0.7

16 Crystal Ball TAPS scintillators cylindrical WC

17 Crystal Ball TAPS

18 Crystal Ball TAPS

19 Proton detection efficiency ency measured in the γp π 0 p reaction Peak efficiency ~60% Low energy cutoff ~ 75 MeV

20 Signal and Background Reactions Proton Compton Coherent Compton i. Require only two tracks in the detector, one neutral and one charged, and ii. require correct opening angle between Compton scattered photon and charged track, and co-planarity Proton π 0 Coherent π 0 Incoherent Compton Incoherent π 0

21 Crystal Ball TAPS

22 Yield on butanol Background Compton peak

23 Yield on butanol Background Compton peak Yield on carbon

24 Carbon subtracted Background Compton peak

25 Carbon subtracted Background Compton peak π 0 photon goes down beampipe

26 Carbon subtracted Background Compton peak π 0 photon goes up beampipe

27 Carbon subtracted Background Compton peak π 0 photon goes between CB and TAPS

28 Missing Mass MeV, deg π 0 subtracted Compton peak Background Missing Mass (MeV)

29 Missing Mass MeV, deg Integrate Missing Mass (MeV)

30 Asymmetry with transverse polarized target and circularly ypolarized photons E γ ~ 285 MeV PRELIMINARY Σ 2x Changing γ E1E1

31 Summary First measurement of a double-polarized Compton scattering asymmetry on the nucleon, Σ 2x Data have sensitivity to the γ E1E1 spin-polarizability i Outlook Data taking on Σ 3 later this year at MAMI ( for γ E1E1 and γ M1M1 ) Data taking on Σ 2z in 2013 ( for γ M1M1 ) A global analysis of all polarized Compton scattering data on the proton using dispersion analysis treatment is in progress Development of an active polarized target has been approved for MAMI. Polarizable scintillators t have been developed d at UMass.