Low-Energy D-Wave Effects in Neutral Pion Photoproduction

The contribution of D waves to physical observables for neutral pion photoproduction in the near threshold region is studied. Heavy Baryon Chiral Perturbation Theory to one loop, and up to $\mathcal{O}(q^4)$, is used to account for the S and P waves, while D waves are added in an almost model-independent way using standard Born terms and vector mesons. It is found that the inclusion of D waves is necessary to extract the $E_{0+}$ multipole reliably from present and forthcoming data and to assess the low-energy constants of Chiral Perturbation Theory. Arguments are presented demonstrating that F-wave contributions are negligible in the near-threshold region.