Supersymmetric Models with Higher Dimensional Operators

TL;DR

This paper demonstrates that 4D N=1 supersymmetric theories with higher derivative operators can be reformulated as second order theories with additional superfields, revealing new mechanisms for supersymmetry breaking and Higgs mass enhancement.

Contribution

It provides a superfield framework to convert higher derivative supersymmetric theories into second order ones with extra superfields, enabling novel insights into supersymmetry breaking and phenomenology.

Findings

Higher derivative operators lead to equivalent second order theories with additional superfields.

Spontaneous supersymmetry breaking can emerge from higher derivative terms.

Higgs mass can be increased above experimental limits at TeV scale due to these effects.

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.