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

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.

arXiv comment28 pages, 6 figures v2: minor changes, typos corrected

References in corpus (12)

• Review of AdS/CFT Integrability: An Overview
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Loop amplitudes in gauge theories: modern analytic approaches
• On-shell superamplitudes in N<4 SYM
• Renormalization group equations for effective field theories
• Leading Infrared Logarithms from Unitarity, Analyticity and Crossing
• Summation of all-loop UV Divergences in Maximally Supersymmetric Gauge Theories
• RG Equations and High Energy Behaviour in Non-Renormalizable Theories
• Leading and Subleading UV Divergences in Scattering Amplitudes for D=8 N=1 SYM Theory in All Loops
• The Structure of UV Divergences in Maximally Supersymmetric Gauge Theories
• Kinematically Dependent Renormalization
• Quasi-Renormalizable Quantum Field Theories

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