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 O(3) 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 e(+/-isqrt8pi]phi(x)), we show that the spectrum consists of a stable triplet of massive particles for all values of theta and a singlet state of higher mass. The singlet is a stable particle only in an interval of values of theta close to pi, whereas it becomes a resonance below a critical value theta(c).