ar X iv : n uc l - th / 0 61 10 51 v 1 1 4 N ov 2 00 6 Large two - pion - exchange contributions to the pp → ppπ 0 reaction

The large two-pion exchange amplitudes are calculated in HBχPT and their net contribution to the reaction cross section is large. Refs. [1, 2] evaluated this reaction at threshold in HBχPT. They found that the impulse approximation (I.A.) and one-pion-exchange (Resc) diagrams interfere destructively resulting in a very small reaction cross section. According to Lee and Riska [3] a model explanation of the measured reaction cross section near threshold requires the contributions from heavy meson (σ and ω) exchange in addition to the one-pion-exchange. The σ-meson-exchange is more properly described by correlated two-pion-exchange. This knowledge prompted a HBχPT study of two-pion-exchange (TPE) contributions to the pp → ppπ 0 reaction amplitude [4]. In Weinberg chiral counting the TPE contributions are of higher chiral order in HBχPT. However, it was shown by Ref. [4] that some TPE amplitudes are as large or larger than the lower chiral order Resc contribution. At threshold the typical momentum is p ∼ √ m π m N. This large momentum prompted Cohen et al. [2] to propose a momentum counting rule, reviewed in Ref. [5]. According to this counting, one finds that the Resc diagram is higher order in p/Λ compared to some " dominant " TPE diagrams, and this counting agrees with the numerical evaluations of the TPE diagrams of Ref. [4]. One drawback with the momentum counting is that the sum of the diagrams in each " momentum order " no longer is independent of the definition of the pion field. Hanhart and Kaiser (HK) [6] used momentum counting to evaluate the " leading " momentum behavior of the dominant TPE diagrams. HK also found that diagram II in Ref. [4] should have opposite sign (which we confirmed), and they found that the sum of the leading momentum behavior of the three dominant TPE diagrams cancel. We will present results from Ref. [4] and a recent calculations [7] which