New analysis of the single-pion contribution to photo-production sum rules published in PRC

Our group’s new analysis on nucleon sum rules has now been published in the journal Physical Review C. The Gerasimov-Drell-Hearn (GDH) sum rule, the Baldin sum rule, and the Gell-Mann–Goldberger–Thirring (GGT) sum rule are important relationships between photo-production cross sections and fundamental properties of protons and neutrons: their anomalous magnetic moments, their electromagnetic polarizabilities, and forward spin polarizability, respectively. While these sum rules cover the probabilities for all possible combinations of particles produced in photon scattering, in principle the most important contribution comes from the reaction in which one pion is produced.

The total measured photo-production cross section (gold points) on the proton is compared to the cross section for single pion production predicted by the SAID (red), MAID (blue), and Regge (cyan) models. The single pion contribution is dominant at lower photon energies.

To study the single-pion contribution, we looked at predictions of SAID, a global partial wave analysis tool developed at GW. One of the striking findings is that the convergence of the GDH sum rule is very different for protons and neutrons. Whereas the GDH sum rule is nearly entirely satisfied by single-pion production for protons, on the neutron, single pion production only satisfies about 60% of the sum rule.

The convergence of the GDH sum rule (an integral over incoming photon energy) as a function of photon energy. The single-pion contribution nearly converges the sum rule for protons (left), whereas it only gets about 60% of the sum rule for neutrons (right).

Still to tackle is the Schwinger sum rule, which involves a particular contribution to the electro-production cross section called the LT interference. We plan to address the convergence of this sum rule in a future paper.