Triangle diagram in heavy-baryon chiral perturbation theory

Abstract

The pion-baryon triangle diagram is inspected for a special kinematic region where the squared momentum transfer $t$ is close to $4m_π^2$: $|t - 4m_π^2| \lesssim m_π^4/m_N^2$. Instead of arguing on the ground of anomalous threshold, we investigate possible impacts on power counting. The pion can have very small energies, as opposed to $\sim m_π$ in the physical region, which allows all three propagators to be extremely near their mass shell and contributes significantly to the loop integral. We find that in this narrow kinematic window the static-limit approximation for the baryon propagator is invalid and the resummation of the kinetic energy is necessary. Interestingly, in contrast to low-energy two-baryon processes, this resummation of baryon recoils does not lead to overall enhancement of power counting of the diagram.