Near-thresholdNN→dπreaction in chiral perturbation theory

Abstract

The near-threshold $\mathit{np}\ensuremath{\rightarrow}d{\ensuremath{\pi}}^{0}$ cross section is calculated in chiral perturbation theory to next-to-leading order in the expansion parameter $\sqrt{M{m}_{\ensuremath{\pi}}}/{\ensuremath{\Lambda}}_{\ensuremath{\chi}}$. At this order irreducible pion loops contribute to the relevant pion-production operator. Although their contribution to this operator is finite, considering initial- and final-state distortions produces a linear divergence in its matrix elements. We renormalize this divergence by introducing a counterterm, whose value we choose to reproduce the threshold $\mathit{np}\ensuremath{\rightarrow}d{\ensuremath{\pi}}^{0}$ cross section measured at TRIUMF. The energy dependence of this cross section is then predicted in chiral perturbation theory, being determined by the production of p-wave pions, and also by energy dependence in the amplitude for the production of s-wave pions. With an appropriate choice of the counterterm, the chiral prediction for this energy dependence converges well.