  By using the perturbation expansion up to the fifth order, we study the
two-triplet-dimer excitation spectra in the Shastry-Sutherland model, where the
localized nature of a triplet-dimer, the propagation of a triplet-dimer pair by
the correlated hopping and the long-range interactions between triplet-dimers
play an essential role. It is found that the dispersion relations for
first-neighbor triplet-dimer pair excitations with S=1 and p-type symmetry
qualitatively explain the second-lowest branch observed in the neutron
inelastic scattering experiment. It is also predicted that the second-lowest
branch consists of two components, p_x- and p_y-states, with slightly different
excitation energies. The origin of the singlet mode at 3.7meV observed in the
Raman scattering experiment is also discussed.
