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Higher order forward spin polarizabilities Barbara Pasquini Pavia U. and INFN Pavia

Higher order forward spin polarizabilities Barbara Pasquini Pavia U. and INFN Pavia Paolo Pedroni Dieter Drechsel INFN Pavia Mainz U. Outline. Real Compton scattering off the proton and polarizabilities.

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Higher order forward spin polarizabilities Barbara Pasquini Pavia U. and INFN Pavia

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

  2. Outline • Real Compton scattering off the proton and polarizabilities Status of theoretical and experimental analysis • Forward spin-dependent amplitude 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 • Real Compton scattering off the neutron 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 astatic electric and magnetic field spin-independent dipole spin-dependent dipole spin-dependent dipole-quadrupole

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

  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, SENECASchumacher, Prog. Part. Nucl. Phys. 55(2005)

  6. Spin Polarizabilities HB3: Heavy Baryon ChPT at O(p3) [Hemmert et al, 1998] HB4: Heavy Baryon ChPT at O(p4) [Kumar et al, 2000] SSE: Heavy Baryon with  at O(p3) [Hemmert et al, 1998] LC: Lorentz covariant ChPT [Djukanovic, PhD Thesis, Mainz, 2008] DRs: Dispersion Relations [Drechsel et al., 2003]

  7. Double and single polarization experiments at MAMI (proposal A2/11-2009-contact person D. Hornidge) circularly pol. photons longitudinally pol. target circularly pol. photons transversely pol. target beam asymmetry 1.20.8 0.4 0. gM1M1 gE1E1 0.1 0.8 Eg=240 MeV Eg=240 MeV gM1M1 Eg=240 MeV 0.06 0.4 0.02 0. -0.02 -0.4 -0.06 -0.8 0 40 80 120 160 0 40 80 120 160 -0.1 0 40 80 120 160 • 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?

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

  9. Sum Rules for Forward Scattering Amplitude Make a Low Energy Expansion of both left and right hand sides of DRs 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. Experimental Data Base helicity-dependent data for the total inclusive cross section ¾1/2-¾3/2 in the energy range (0.204 0.009) – (2.82 0.09) GeV GDH Coll. and A2 Coll. (MAMI and ELSA) helicity-dependent differential cross section data for the n ¼+ channel in the angular range µ*p =45o – 109o at Eg= (0.18 0.005) and Eg = (0.19 0.005) Ahrens, et al, GDH Coll., EPJA 21(2004) 323 SAID Arndt, Briscoe, Strakovsky, Workman (2002) MAID Drechsel, Hanstein, Kamalov, Tiator, NPA(1999) Hanstein, Drechsel, Tiator, NPA(1998) very good agreement with HDT 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 HDT

  11. Running Integral for Higher Order FSP n ¼+ extrapolation of differential cross sections Eg, min= 0.175 GeV p ¼0 Eg, min= 0.158 GeV

  12. S-wave contribution to ¢¾ • large contribution from the S-wave multipole E0+ in the threshold region • low energy theorems for pion photo-production constrain the value of E0+ at threshold • good agreement between predictions of HBChPT and other multipole analysis, except for MAID unmeasured region 0.15 0.175 GeV • contribution below 0.175 evaluated with HDT • systematic error estimated by comparison with other models, excluded MAID

  13. Forward Spin Polarizabilities • Recent calculation at NNLO order in Lorentz covariant ChPT with the ¢g0 = -0.90 0.15 (Pascalutsa & Lensky, in preparation)

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

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

  16. Multipole decomposition S wave P waves TOT

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

  18. Neutron Polarizabilities [Levchuk, L’vov, 2001] Baldin Sum Rule (1960) 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 planned measurements at Higs: • Unpolarized Compton scattering from the deuteron at photon energies between 30 and 80 MeV ! and • Double polarized Compton scattering from the He3 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 • 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

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

  20. Summary • electric and magnetic dipole polarizabilities of the proton known quite preciselyfrom low-energy Compton scattering • 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 • Necessary independent test of the model dependence of dispersion analysis dispersion analysis of the forward spin-dependent amplitude from helicity dependent photoabsorption cross section data (MAMI and ELSA) • GDH sum rule: • good agreement up to photon energy of 300 MeV for the one-pion channel • deviations at higher energies up to 10-20% due to multi-pion production • Higher order forward spin polarizability: • higher energy contribution suppressed ! very good agreement with experimental analysis • Analysis of RCS with SUBtracted dispersion relations is well under control

  21. Spin Polarizabilities HB3: Heavy Baryon ChPT at O(p3) [Hemmert et al, 1998] HB4: Heavy Baryon ChPT at O(p4) [Kumar et al, 2000] SSE: Heavy Baryon with  at O(p3) [Hemmert et al, 1998] LC: Lorentz covariant ChPT [Djukanovic, PhD Thesis, Mainz, 2008] DRs: Dispersion Relations [Drechsel et al., 2003] LC3 + -resonance: expansion in  » m/ M » M/M; no free-parameters[Lensky, Pascalutsa, 2008]

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

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