Effective operators in SUSY, superfield constraints and searches for a UV completion

Understand

We discuss the role of a class of higher dimensional operators in 4D N=1 supersymmetric effective theories.

• The Lagrangian in such theories is an expansion in momenta below the scale of "new physics" ($\Lambda$) and contains the effective operators generated by integrating out the "heavy states" above $\Lambda$ present in the UV complete theory.
• We go beyond the "traditional" leading order in this momentum expansion (in $\partial/\Lambda$).
• Keeping manifest supersymmetry and using superfield {\it constraints} we show that the corresponding higher dimensional (derivative) operators in the sectors of chiral, linear and vector superfields of a Lagrangian can be "unfolded" into second-order operators.