Triangle diagram in heavy-baryon chiral perturbation theory

Understand

The pion-baryon triangle diagram is inspected for a special kinematic region where the squared momentum transfer $t$ is close to $4m_\pi^2$: $|t - 4m_\pi^2| \lesssim m_\pi^4/m_N^2$.

• 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 $\sim m_\pi$ 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.