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

TL;DR

This paper develops a method to reformulate higher derivative operators in supersymmetric theories into polynomial interactions with additional superfields, enabling better understanding of their UV completions and phenomenological implications.

Contribution

It introduces a superfield constraint-based unfolding technique that transforms higher derivative operators into polynomial form, revealing the UV structure and fixing operator coefficients.

Findings

Unfolded operators are polynomial and ghost-free in examples.

The method applies to all orders in momentum expansion.

UV theory naturally determines operator coefficients and signs.

Abstract

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. The "unfolded" formulation has only polynomial interactions and additional massive superfields, some of which are ghost-like if the effective operators were {\it quadratic} in fields. Using this formulation, the UV theory emerges naturally and fixes the (otherwise unknown) coefficient and sign of the initial (higher derivative) operators. Integrating the massive fields of the "unfolded" formulation generates an effective theory with only polynomial effective interactions relevant for phenomenology. We also provide several examples of "unfolding" of theories with higher derivative {\it interactions} in the gauge or matter sectors that are actually ghost-free. We then illustrate how our method can be applied even when including {\it all orders} in the momentum expansion, by using an infinite set of superfield constraints and an iterative procedure, with similar results.