The $p p \to p pπ^0$ Reaction near Threshold: A Chiral Power Counting Approach

Abstract

We use power-counting arguments as an organizing principle to apply chiral perturbation theory, including an explicit $Δ$, to the $p p \rightarrow p p π^0$ reaction near threshold. There are two lowest-order leading mechanisms expected to contribute to the amplitude with similar magnitudes: an impulse term, and a $Δ$-excitation mechanism. We examine formally sub-leading but potentially large mechanisms, including pion-rescattering and short-ranged contributions. We show that the pion-rescattering contribution is enhanced by off-shell effects and has a sign opposite to that of a recent estimate based on a PCAC pion interpolating field. Our result is that the impulse term interferes destructively with the pion rescattering and $Δ$-excitation terms. In addition, we have modeled the short-ranged interaction using $σ$ and $ω$ exchange mechanisms. A recoil correction to the impulse approximation is small. The total amplitude obtained including all of these processes is found to yield cross sections substantially smaller than the measured ones.