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Important contributions to meson-nucleus scattering are produced by terms inthe multiple-scattering series, which is defined as the sum of all diagramswhere the meson scatters back and forth between a pair of static nucleonsbefore leaving the nucleus. In particular, the sum of this series is needed foran accurate description of kaon-deuteron scattering, and appears as part of thenucleon-nucleon potential. In this article we present someeffective-field-theory (EFT)-based insights into this series in the case oftwo-nucleon systems. In particular, we discuss the fact that, if meson-nucleonscattering is approximated by the scattering-length term, individual terms ofthe series are divergent, and enhanced with respect to the straightforwardexpectation from chiral perturbation theory ($\chi$PT). This apparentlyindicates the presence of similarly enhanced counterterms. However, we showthat when the series is resummed the divergences cancel, such that noadditional information on short-range interactions is needed to obtainpredictions for observables after resummation. We discuss the conditions underwhich this resummation is justified. We show that the same issues arise in the$NN$ potential, where the resummed series produces poles whose appearanceindicates the breakdown scale of the $\chi$PT expansion for that quantity. Thisdemonstrates unequivocally that $\chi$PT cannot be applied to compute $V(r)$for distances smaller than $r \sim 1$ fm at least in the theory withoutexplicit Delta(1232) degrees of freedom. We briefly discuss whether this boundcan be lowered if the Delta resonance is included in the EFT as an explicitdegree of freedom.

The multiple-scattering series in pion-deuteron scattering and the nucleon-nucleon potential: perspectives from effective field theory