Dynamical symmetry and asymptotic scale invariance in ladder models

Class of ladder equations for the absorptive part of the scalar off-shell forward scattering amplitude $A(s,p^2,p'^2)$ is considered. The models possess hidden symmetry $O(4,1)$ and differ from each other by the values of real positive parameter $\nu$. The case $\nu =1$ corresponds to the standard ladder model in scalar theory of $\lambda\varphi^3$ type with the exchange by massless particle. The amplitude depends on the only variable $sm^2/(p^2-m^2)\times(p'^2-m^2)$ (up to the kinematical factor $s^{\nu-2}$, which guarantees its asymptotic scale invariance (in particular, the Bjorken scaling). At the integer positive $\nu$, the solution is expressed in terms of the hypergeometric functions of one variable.