Cumulative proton production in $pd$ collisions

The model of backward proton production in the exclusive reaction $pd \to ppn$ at proton beam momenta up to several GeV/c is constructed on the basis of Feynman diagrams for one- and two-step amplitudes. The latter include nucleon and $Δ(1232)$ resonance intermediate scattering states with propagators reduced to eikonal form using the generalized eikonal approximation. The model calculations are compared with available experimental data on the energy spectra of protons at backward polar angles in the deuteron rest frame. It is shown that inclusion of two-step amplitudes significantly increases the production of backward protons with energies above $\sim$ 50 MeV, thereby significantly improving the agreement with experiment. The remaining theoretical problem related to the description of the off-shell behavior of the elementary amplitudes of the $NN \to NN$ and $NN \leftrightarrow NΔ$ transitions is discussed. Partial discrepancies between different sets of experimental data do not allow us to conclude that exotic effects, such as proton interactions with density fluctuations and/or $6q$ clusters in the deuteron, are present.