Mass spectrum of the two-dimensional O(3) sigma model with a theta term

Form factor perturbation theory is applied to study the spectrum of the O3 nonlinear sigma model with the topological term in the vicinity of theta=pi . 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, we show that the spectrum consists of a stable triplet of massive particles for all values of and a singlet state of higher mass. The singlet is a stable particle only in an interval of values of close to , whereas it becomes a resonance below a critical value theta_c.