Construction of the Reggeon calculus in4−εdimensions

We study the Reggeon field theory in $4-\epsilon$ dimensions. When the Pomeranchuk singularity has intercept 1, the theory cannot be renormalized order by order in the perturbation series. Nevertheless we are able to develop systematic techniques for constructing the Pomeranchuk Green's functions. An integral representation is obtained for the Pomeranchuk propagator which allows us to explicitly display its infrared ($l\approx 1$, $t\approx 0$) behavior and to show that the perturbation series is an asymptotic expansion for small values of the coupling constant and for large values of the angular momentum or momentum transfer. We also obtain an integral representation for the intercept renormalization counterterm. We find that for the renormalized Pomeranchuk singularity to have intercept 1, the bare Pomeranchuk pole must have intercept greater than 1.