Forward Pion-Pion Scattering in theλφ4Theory

An exact expression is obtained for the sum of the bubble diagrams for forward pion-pion scattering in the $\lambda {\phi }^4$ theory, with zero mass internal pions. The exact solution of the problem for massless internal pions follows naturally from the solution of the Bethe-Salpeter equation, with the bubble-exchange kernel, which is the asymptotic limit of the equation for pions with finite mass.