Shadowing in multiparton proton - deuteron collisions

We study the screening effect for the multiparton interactions (MPI) for proton--deuteron collisions in the kinematics where one parton belonging to the deuteron has small $x_1$ so the leading twist shadowing is present while the second parton ($x_2$) is involved in the interaction %%ms in the kinematics where shadowing effects are small. We find that the ratio of the shadowing and the impulse approximation terms is approximately factor of two larger for MPI than for the single parton distributions. We also calculate the double parton antishadowing (DPA) contribution to the cross section due to the independent interactions of the partons ofthe projectile proton with two nucleons of the deuteron and find that shadowing leads to a strong reduction ofthe DPA effect.For example, for the resolution scale $Q_1^2 \sim 4$~$\mbox{GeV}^2$ of the interaction with parton $x_1$ we find that shadowing reduces the DPA effect by $\sim$ 30%. It is argued that in the discussed kinematics the contribution of interference diagrams, which correspond to the interchange ofpartonsbetween the proton and neutron, constitutes only a small correction to the shadowing contributions.