Supersymmetric Models with Higher Dimensional Operators

TL;DR

The work develops a systematic method to map 4D N=1 supersymmetric theories with higher derivative operators into equivalent second-order models with additional ghost superfields, yielding renormalised couplings and tree-level threshold corrections that depend on the operator scale $M_*$. This unfolding preserves SUSY and allows a standard two-derivative framework to analyze higher-dimensional effects, including in the presence of SUSY breaking and soft terms. The approach is applied to the MSSM, showing that higher derivative operators can raise the lightest Higgs mass by sizable amounts for $M_*\, ext{in the TeV range}$, offering a phenomenologically relevant mechanism. While providing a powerful EFT tool, the paper also discusses stability, unitarity near the ghost scale, and the conditions under which the two formulations remain equivalent, including implications for renormalisability in Euclidean space.

Abstract

In 4D renormalisable theories, integrating out massive states generates in the low energy effective action higher dimensional operators (derivative or otherwise). Using a superfield language it is shown that a 4D N=1 supersymmetric theory with higher derivative operators in either the Kahler or the superpotential part of the Lagrangian and with an otherwise arbitrary superpotential, is equivalent to a 4D N=1 theory of second order (i.e. without higher derivatives) with additional superfields and renormalised interactions. We provide examples where a free theory with trivial supersymmetry breaking provided by a linear superpotential becomes, in the presence of higher derivatives terms and in the second order version, a non-trivial interactive one with spontaneous supersymmetry breaking. The couplings of the equivalent theory acquire a threshold correction through their dependence on the scale of the higher dimensional operator(s). The scalar potential in the second order theory is not necessarily positive definite, and one can in principle have a vanishing potential with broken supersymmetry. We provide an application to MSSM and argue that at tree-level and for a mass scale associated to a higher derivative term in the TeV range, the Higgs mass can be lifted above the current experimental limits.