$NN \to NN \pi$ reaction near threshold in a covariant   one-boson-exchange model
  We calculate the cross sections for the $p(p,n\pi^{+})p$ and $p(p,p\pi^{0})p$ reactions for proton beam energies near threshold in a covariant one-boson-exchange model, which incorporates the exchange of $\pi$, $\rho$, $\sigma$ and $\omega$ mesons and treats both nucleon and delta isobar as intermediate states. The final state interaction effects have also been included. The $\omega$ meson exchange is found to contribute significantly at these energies, which, along with other meson exchanges, provides an excellent agreement with the data. The cross sections at beam energies $\leq$ 300 MeV are almost free from the contributions of the $\Delta$ isobar excitation. 
R. Shyam and U. Mosel