S-wave π⁰ production in pp collision from chiral perturbation theory calculations with loop contributions

The total cross section for the pp⃗ppπ⁰ reaction at energies close to threshold is calculated within the frame of chiral perturbation theory, taking into account tree and one loop diagrams up to chiral order D=2. We confirm that (i) the leading order impulse and rescattering terms have opposite signs and their overall contributions to chiral order D=1 underestimates the cross section by a factor of 3, and (ii) one loop contributions are substantially larger than lower order contributions, indicating that the heavy fermion formalism power series expansion converges very slowly, and therefore, may not be suitable to apply to pion production in NN collisions.