1. Higher order forward spin polarizabilities Barbara Pasquini Pavia U. and INFN Pavia Paolo Pedroni Dieter Drechsel Paolo Pedroni Dieter Drechsel INFN Pavia Mainz U. INFN Pavia Mainz U.

2. Outline  Real Compton scattering off the proton and polarizabilities Status of theoretical and experimental analysis  Forward spin-dependent amplitude  Real Compton scattering off the neutron GDH sum rule and dispersion integrals for leading and higher order forward spin polarizabilities dispersion analysis from helicity-dependent photon absorption cross section: experimental data and phenomenological studies B.P., P. Pedroni, D. Drechsel, arXiv:1001.4230 [hep-ph], to appear in PLB

3. Static polarizabilities in Real Compton Scattering Powell cross section: photon scattering off a pointlike nucleon with anomalous magnetic moment Static polarizabilities: response of the internal nucleon degrees of freedom to a static electric and magnetic field spin-independent dipole spin-dependent dipole spin-dependent dipole-quadrupole

4. Spin independent dipole polarizabilities Baldin Sum Rule (1960) Olmos de Leon et al., EPJ A10 (2001) Compton scattering

5. Spin polarizabilities forward spin polarizability GDH Coll. (MAMI & ELSA) Ahrens et al., PRL87 (2001) Dutz et al. PRL91 (2003) backward spin polarizability (unpolarized Compton scattering) TAPS, LARA, SENECA Schumacher, Prog. Part. Nucl. Phys. 55(2005)

6. HB 3 : Heavy Baryon ChPT at O(p 3 ) [Hemmert et al, 1998] HB 4 : Heavy Baryon ChPT at O(p 4 ) [Kumar et al, 2000] SSE: Heavy Baryon with  at O(p 3 ) [Hemmert et al, 1998] LC: Lorentz covariant ChPT [Djukanovic, PhD Thesis, Mainz, 2008] DRs: Dispersion Relations [Drechsel et al., 2003] HB 3 HB 4 SSE LC 3 LC 4 DRs Exp.  E1E1 -5.7-1.4-5.4-3.2-2.8-4.3 no data  M1M1 -1.1 3.3 1.4-1.4-3.1 2.9 no data  E1M2 1.1 0.2 1.0 0.7 0.8 0.0 no data  M1E2 1.1 1.8 1.0 0.7 0.3 2.1 no data  0 4.6-3.92.03.1 4.8-0.7 -1.00  0.08  0.10   4.6 6.36.81.8-0.8 9.3 -38.7  1.8 Spin Polarizabilities

7. Double and single polarization experiments at MAMI (proposal A2/11-2009-contact person D. Hornidge)  leading spin polarizabilities are treated as free parameters  higher order polarizabilities are fixed by subtracted dispersion relations based on pion-photoproduction multipoles How well is the model dependence under control? 0 40 80 120 160 1.2 0.8 0.4 0.  M1M1 0 40 80 120 160 0.8 0.4 0. -0.4 -0.8  E1E1 0 40 80 120 160 0.1 0.06 0.02 -0.02 -0.06 -0.1  M1M1 circularly pol. photons longitudinally pol. target circularly pol. photons transversely pol. target beam asymmetry E  =240 MeV

8. Forward Real Compton Scattering Forward scattering: k=k’, p=p’ Photon crossing: Optical theorem: Dispersion relations:

9. Make a Low Energy Expansion of both left and right hand sides of DRs Sum Rules for Forward Scattering Amplitude Forward Spin Polarizability Higher order Forward Spin Polarizab. Low Energy Theorem Low, Gell-Mann, Goldberger (1954) GDH Sum Rule (1966) Sum Rule for FSP Sum Rule for Higher Order FSP

10. helicity-dependent data for the total inclusive cross section ¾ 1/2 - ¾ 3/2 in the energy range (0.204 0.009) – (2.82 0.09) GeV GDH Coll. and A2 Coll. (MAMI and ELSA) Experimental Data Base helicity-dependent differential cross section data for the n ¼ + channel in the angular range µ *  = 45 o – 109 o at E  = (0.18 0.005) and E  = (0.19 0.005) SAID MAID HDT Hanstein, Drechsel, Tiator, NPA(1998) Drechsel, Hanstein, Kamalov, Tiator, NPA(1999) Arndt, Briscoe, Strakovsky, Workman (2002) Ahrens, et al, GDH Coll., EPJA 21(2004) 323 use HDT to extrapolate the data in the whole angular range and obtain the total cross section with error bar estimated by comparison with other models very good agreement with HDT

11. E , min = 0.158 GeV E , min = 0.175 GeV Running Integral for Higher Order FSP extrapolation of differential cross sections

12. S-wave contribution to ¢¾  large contribution from the S-wave multipole E 0+ in the threshold region unmeasured region 0.15 0.175 GeV  low energy theorems for pion photo-production constrain the value of E 0+ at threshold  good agreement between predictions of HBChPT and other multipole analysis, except for MAID  contribution below 0.175 evaluated with HDT  systematic error estimated by comparison with other models, excluded MAID

14. Forward Spin Polarizabilities  Recent calculation at NNLO order in Lorentz covariant ChPT with the ¢  0 = -0.90 0.15 (Pascalutsa & Lensky, in preparation)

15. Dispersion Relations and Multipole analysis o simple model to estimate of the multipion contribution by assuming the same helicity structure of the one-pion channel o contribution to the GDH from exp. data at 325 < E < 800 MeV: 39 1 3 ¹ b

16. HDT SAID MAID DMT sd syst. Running Integrals GDH

17. S waveP wavesTOT Multipole decomposition

18. Dynamic Forward Spin Polarizability MAID DMT sd syst. HDT SAID LEX

19. Neutron Polarizabilities Baldin Sum Rule (1960) [Levchuk, L’vov, 2001] Quasi-free Compton scattering and electromagnetic neutron scattering: [MAMI,Lund,SAL] M. Schumacher, Prog. Part. Nucl. Phys. 55 (2005) [MAMI] no experimental information on the other spin polarizabilities Dispersion relation analysis requires more precise information for the input from multipoles of neutron pion-photoproduction ! test like dispersion analysis of spin- dependent forward scattering amplitude from polarized inclusive cross section planned measurements at Hi  s: o Unpolarized Compton scattering from the deuteron at photon energies between 30 and 80 MeV ! and o Double polarized Compton scattering from the He 3 target at photon energies between 5 and 114 MeV ! neutron spin polarizabilities planned measurements at Lund: unpol. RCS on deuterium target at E < 115 MeV

20. -4.0 -6.0 -8.0  E1E1 5.86 3.86 1.86  M1M1 Circularly pol. Photon - Neutron pol. along z or along x fixed values for other polarizabilities neutron pol. along zneutron pol. along x

21. Summary  spin polarizabilities require: double polarization experiments above pion threshold ! upcoming data from MAMI theoretical framework which goes beyond the low energy expansion, such as subtracted dispersion relations with input from pion photoproduction data  electric and magnetic dipole polarizabilities of the proton known quite precisely from low-energy Compton scattering  Necessary independent test of the model dependence of dispersion analysis  GDH sum rule: dispersion analysis of the forward spin-dependent amplitude from helicity dependent photoabsorption cross section data (MAMI and ELSA) o good agreement up to photon energy of 300 MeV for the one-pion channel o deviations at higher energies up to 10-20% due to multi-pion production  Higher order forward spin polarizability: o higher energy contribution suppressed ! very good agreement with experimental analysis  Analysis of RCS with SUBtracted dispersion relations is well under control

22. Spin Polarizabilities HB 3 : Heavy Baryon ChPT at O(p 3 ) [Hemmert et al, 1998] HB 4 : Heavy Baryon ChPT at O(p 4 ) [Kumar et al, 2000] SSE: Heavy Baryon with  at O(p 3 ) [Hemmert et al, 1998] LC: Lorentz covariant ChPT [Djukanovic, PhD Thesis, Mainz, 2008] DRs: Dispersion Relations [Drechsel et al., 2003] LC 3 +  -resonance: expansion in  » m  /  M »  M/M; no free-parameters [Lensky, Pascalutsa, 2008] HB 3 HB 4 SSE LC 3 LC 4 DRsLC 3 + ¢ Exp.  E1E1 -5.7-1.4-5.4-3.2-2.8-4.3 no data  M1M1 -1.1 3.3 1.4-1.4-3.1 2.9 no data  E1M2 1.1 0.2 1.0 0.7 0.8 0.0 no data  M1E2 1.1 1.8 1.0 0.7 0.3 2.1 no data  0 4.6-3.92.03.1 4.8-0.7 -1.00  0.08  0.10   4.6 6.36.81.8-0.8 9.3 -38.7  1.8

23. -4.0 -6.0 -8.0  E1E1 5.86 3.86 1.86  M1M1 Circularly pol. Photon - Neutron pol. along z fixed values for other polarizabilities Similar effects in the beam asymmetry and asymmetry with circularly polarized photon and transversely polarized neutron