Upper Energy Limit of Heavy Baryon Chiral Perturbation Theory in Neutral Pion Photoproduction

With the availability of the new neutral pion photoproduction from the proton data from the A2 and CB-TAPS Collaborations at Mainz it is mandatory to revisit Heavy Baryon Chiral Perturbation Theory (HBChPT) and address the extraction of the partial waves as well as other issues such as the value of the low-energy constants, the energy range where the calculation provides a good agreement with the data and the impact of unitarity. We find that, within the current experimental status, HBChPT with the fitted LECs gives a good agreement with the existing neutral pion photoproduction data up to $\sim$170 MeV and that imposing unitarity does not improve this picture. Above this energy the data call for further improvement in the theory such as the explicit inclusion of the \Delta (1232). We also find that data and multipoles can be well described up to $\sim$185 MeV with Taylor expansions in the partial waves up to first order in pion energy.