Twice-iterated boson-exchange scattering amplitudes

We calculate at two-loop order the complex-valued scattering amplitude related to the twice-iterated scalar-isovector boson exchange between nucleons. Compared to the once-iterated boson-exchange amplitude, it shows less dependence on the scattering angle. We calculate also the iteration of the (static) irreducible one-loop potential with the one-boson exchange and find similar features. Together with the irreducible three-boson exchange potentials and the two-boson exchange potentials with vertex corrections, which are also evaluated analytically, our results comprise all nonrelativistic contributions from scalar-isovector boson exchange at one- and two-loop orders. The applied methods can be straightforwardly adopted to the pseudoscalar pion with its spin- and momentum-dependent couplings to the nucleon.