Neutron resonance in high-T_c superconductors is not the π particle

We discuss the interplay of particle-particle and particle-hole spin-triplet channels in high-T_c superconductors using a quasiparticle dispersion motivated by angle-resolved photoemission. Within a generalized random-phase approximation, we find a well-defined antibound state of two holes, the π resonance of Demler and Zhang, as well as a bound state of a particle and a hole, the spin exciton. We show that the energy of the π resonance always exceeds 2Δ, twice the maximum d-wave gap, therefore the neutron resonance observed in the cuprates around energy Δ is most likely a spin exciton. At the same time, we speculate that the π particle can exist at higher energies and might be observed in neutron scattering around 100 meV.