UV Divergences, RG Equations and High Energy Behaviour of the Amplitudes in the Wess-Zumino Model with Quartic Interaction

TL;DR

This paper investigates the ultraviolet divergences and high energy behavior of scattering amplitudes in the Wess-Zumino supersymmetric model with quartic interactions, deriving recurrence relations and RG equations to analyze the amplitude's properties.

Contribution

It introduces a novel algebraic method using recurrence relations and RG equations to analyze UV divergences and high energy behavior in the Wess-Zumino model.

Findings

Identifies a pole in the s-channel at high energies indicating a ghost state.

Derives recurrence relations connecting divergences at different loop orders.

Shows the amplitude exhibits a Landau pole-like behavior similar to scalar theories.

Abstract

We analyse the UV divergences for the scattering amplitude in the Wess-Zumino SUSY model with the quartic superpotential. Within the superfield formalism, we calculate the corresponding Feynman diagrams and evaluate their leading divergences up to 4 loop order of PT. Then we construct recurrence relations that connect the leading UV divergences in subsequent orders of perturbation theory. These recurrence relations allow us to calculate the leading divergences in a pure algebraic way starting from the one loop contribution. We check that the obtained relations correctly reproduce the lower order diagrams evaluated explicitly. At last, we convert the recurrence relations into the RG equations that have integro-differential form. Solving these equations for a particular sequence of diagrams, we find out the high energy behaviour of the amplitude. We then argue that the full amplitude has a similar behaviour with the key feature of the existence of a pole in the s-channel corresponding to a state with a mass ~1/g, where g is the original dimensionfull coupling of the theory. We find out the this state is actually a ghost one similar to the Landau pole in scalar theory.