Square root singularity in boundary reflection matrix

Two-particle scattering amplitudes for integrable relativistic quantum field theory in 1+1 dimensions can normally have at most singularities of poles and zeros along the imaginary axis in the complex rapidity plane. It has been supposed that single-particle amplitudes of the exact boundary reflection matrix exhibit the same structure. In this paper, single-particle amplitudes of the exact boundary reflection matrix corresponding to the Neumann boundary condition for affine Toda field theory associated with twisted affine algebras a2n(2) are conjectured, based on one-loop result, as having a new kind of square root singularity.