Helicity dependence and contribution to the Gerasimov-Drell-Hearn sum rule of theγ→d→→πNNreaction channels

Abstract

The helicity dependence of the γ d → π − pp, γ d → π + nn, and γ d → π 0 np reaction channels is studied for incident photon energies from threshold up to the (1232) resonance with inclusion of leading πNN effects. The doubly polarized total and differential cross sections for parallel and antiparallel helicity states are predicted. Then the contribution of various channels to the deuteron spin asymmetry and the double polarization E asymmetry is calculated. In addition, the contribution to the Gerasimov-Drell-Hearn (GDH) integral from separate channels is evaluated by explicit integration up to a photon lab energy of 350 MeV. Sizeable effects from final-state interactions, specially for π 0 production, are found. The sensitivity of the results to the elementary pion photoproduction operator is also investigated. Considerable dependence of the results on the elementary amplitude is found. We expect that these results may be useful to interpret the recent measurements from LEGS@BNL, A2, and GDH@MAMI Collaborations.

Photoproduction of π0-Mesons from the Nucleon and Deuteron

“…In addition, we have plotted the corresponding elementary cross section for the γN→π 0 N reaction (dashed curve) for comparison. For this purpose, the MAID-2007 model [9] as parametrized in terms of invariant amplitudes defined in Ref. [13] is taken.…”

“…The γd → π 0 np amplitude is evaluated by taking the isobar MAID-2007 model [9] for the elementary operator, allowing one to extend the calculation up to photon energies of 1.5 GeV. Moreover, FSI effects are perturbatively taken into account up to the first order in the corresponding np-and π 0 N-scattering amplitudes.…”

“…As in the case of incoherent reaction, the γd→π 0 d amplitude is evaluated by taking the MAID-2007 model [9] for the elementary operator. For the various hadronic and electromagnetic two-body reactions included in the treatment of the rescattering diagrams, only the S 11 (1535) resonance was taken into account.…”

“…Within our model for the γd → π 0 np reaction, the scattering amplitude is treated in such a way that besides the pure impulse approximation (IA incoh ), the complete rescattering by FSI within each of the np and π 0 N twobody subsystems is included. Therefore, the total transition matrix element reads in this approximation The γd → π 0 np amplitude is evaluated by taking the isobar MAID-2007 model [9] for the elementary operator, allowing one to extend the calculation up to photon energies of 1.5 GeV. Moreover, FSI effects are perturbatively taken into account up to the first order in the corresponding np-and π 0 N-scattering amplitudes.…”

“…The ultimate goal of this work is to report on a theoretical prediction for the semi-exclusive reaction γd→π 0 X (X=np+d) for incident photon energy up to 1.5 GeV by using the isobar MAID-2007 model [9] for the elementary γN→π 0 N process. The influence of rescattering effects on the unpolarized and helicity-dependent total cross sections as well as on the Gerasimov-Drell-Hearn (GDH) sum rule [10] will be investigated. We will also compare the predicted results with the available experimental data.…”