Quasirenormalizable quantum field theories

Leading logarithms in massless nonrenormalizable effective field theories can be computed using nonlinear recurrence relations. These recurrence relations follow from the fundamental requirements of unitarity, analyticity, and crossing symmetry of scattering amplitudes and generalize the renormalization group technique to the case of nonrenormalizable effective field theories. We review the existing exact solutions of nonlinear recurrence relations relevant for field theory applications. We introduce a new class of quantum field theories (quasirenormalizable field theories) in which resumming leading logarithms for $2\to2$ scattering amplitudes yields a possibly infinite number of Landau poles.