Single-pion contribution to the Gerasimov--Drell--Hearn sum rule and related integrals

Abstract

Phenomenological amplitudes obtained in partial-wave analyses (PWA) of single-pion photoproduction are used to evaluate the contribution of this process to the Gerasimov-Drell-Hearn (GDH), Baldin and Gell-Mann-Goldberger-Thirring (GGT) sum rules, by integrating up to 2 GeV in photon energy. Our study confirms that the single-pion contribution to all these sum rules converges even before the highest considered photon energy, but the levels of saturation are very different in the three cases. Single-pion production almost saturates the GDH sum rule for the proton, while a large fraction is missing in the neutron case. The Baldin integrals for the proton and the neutron are both saturated to about four fifths of the predicted total strength. For the GGT sum rule, the wide variability in predictions precludes any definitive statement.

12 pages, 7 figure, 3 tables; discussion refined, references added, Minor fixes to the authorship list found during production; acknowledgement added; final version accepted by Phys Rev C

References in corpus (11)

• Unitary Isobar Model - MAID2007
• Direct high-precision measurement of the magnetic moment of the proton
• Compton scattering from the proton in an effective field theory with explicit Delta degrees of freedom
• Experimental study of isovector spin sum rules
• New Measurement of Compton Scattering from the Deuteron and an Improved Extraction of the Neutron Electromagnetic Polarizabilities
• Measurement of the Bjorken Sum at very low $Q^2$
• Measurement of the proton spin structure at long distances
• First measurement of the polarization observable $E$ and helicity-dependent cross sections in single ${\pi }^0$ photoproduction from quasi-free nucleons
• Proton scalar dipole polarizabilities from real Compton scattering data, using fixed-t subtracted dispersion relations and the bootstrap method
• Measurement of the generalized spin polarizabilities of the neutron in the low $Q^2$ region
• Measurement of the high-energy contribution to the Gerasimov-Drell-Hearn sum rule

Cited by in corpus (3)

• First concurrent extraction of the leading-order scalar and spin proton polarizabilities
• Measurement of the nucleon spin structure functions for 0.01<$Q^2$<1 GeV${}^2$ using CLAS
• Coupled-channel contributions to the GDH sum rule from the Jülich-Bonn approach