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In this work the elastic scattering of two nucleons is calculated in chiraleffective field theory at next-to-leading order taking into account the coupledN$\Delta$-, $\Delta$N- and $\Delta\Delta$-channels. To solve the coupledchannel scattering equation one needs as input the potentials for allcombinations of these initial and final states. Up to next-to leading orderthese (transition) potentials arise from one-pion exchange, two-pion exchangeand contact interactions. For the two-pion exchange we give analyticexpressions for the spectral functions derived from all contributing one-loopdiagrams. The forms of the contact potentials at leading and next-to-leadingorder are determined. We perform a fit of the low energy constants, that belongto the $NN \rightarrow NN$ contact potential and contribute up tonext-to-leading order to $S$- and $P$-waves of NN scattering only. Theinfluence of the $\Delta$-isobar dynamics entering through the coupled channelsis studied in detail.

Nucleon-Nucleon Scattering with Coupled Nucleon-Delta Channels in Chiral Effective Field Theory