The n-loop expansion of the Reggeon calculus

Abstract

We apply the technique known in solid state physics as the n-loop expansion to calculate the critical indices of the φ 3 Gribov Reggeon calculus directly in two transverse dimensions. Infrared pathologies of the massless theory require the calculation to be done in the infinite momentum limit of the massive theory. For n = 1 the results are close to those of the ε-expansion in O(ε). For n = 2 the β function has no zero, analogously to the case in solid state physics. Use of a Padé approximant for β yields σ tot ≈ (1 n s) 0.27 at infinity, close to the O(ε 2) result.