Mass Spectrum of the Two-Dimensional O(3) Sigma Model with a θ Term

Form factor perturbation theory is applied to study the spectrum of the O(3) nonlinear sigma model with the topological term in the vicinity of θ=π. Its effective action near this value is given by the nonintegrable double sine-Gordon model. Using previous results by Affleck and the explicit expressions of the form factors of the exponential operators e^{±i√8πφ(x)}, we show that the spectrum consists of a stable triplet of massive particles for all values of θ and a singlet state of higher mass. The singlet is a stable particle only in an interval of values of θ close to π, whereas it becomes a resonance below a critical value θ_c.