Convergence of the perturbation series for a nonlocal nonpolynomial theory $m^2/\Lambda$

In [2,3] the perturbation series in the translationally invariant case is shown to converge on the basis of correspondence with statistical theory. In the present paper, a direct estimate is made for the logarithm of the generating functional of the Euclidean $s$ matrix and an upper bound for the radius of convergence with respect to the coupling constant is obtained; this is proportional to $m^2/\Lambda$, where $m$ is the mass of the particle and $\Lambda$ is the small coupling constant.