Folded Supersymmetry and the LEP Paradox

TL;DR

This work addresses the LEP paradox by proposing folded supersymmetry, a framework in which Higgs mass quadratic divergences are canceled at one loop by spin partners whose gauge quantum numbers differ from conventional superpartners. It builds a bridge from SUSY to non-supersymmetric orbifold daughters via a large-N correspondence, enabling radiative stability without SM-color top-partners, and demonstrates explicit UV completions using higher-dimensional Scherk-Schwarz breaking. A concrete realistic model stabilizes the weak scale up to about 20 TeV with top-loop cancellations by colorless scalars, and predicts distinctive collider signatures such as hard leptons plus missing energy and non-colored partner states. Together, these results offer a new pathway to naturalness that yields testable TeV-scale phenomenology while remaining consistent with precision electroweak constraints.

Abstract

We present a new class of models that stabilize the weak scale against radiative corrections up to scales of order 5 TeV without large corrections to precision electroweak observables. In these `folded supersymmetric' theories the one loop quadratic divergences of the Standard Model Higgs field are cancelled by opposite spin partners, but the gauge quantum numbers of these new particles are in general different from those of the conventional superpartners. This class of models is built around the correspondence that exists in the large N limit between the correlation functions of supersymmetric theories and those of their non-supersymmetric orbifold daughters. By identifying the mechanism which underlies the cancellation of one loop quadratic divergences in these theories, we are able to construct simple extensions of the Standard Model which are radiatively stable at one loop. Ultraviolet completions of these theories can be obtained by imposing suitable boundary conditions on an appropriate supersymmetric higher dimensional theory compactified down to four dimensions. We construct a specific model based on these ideas which stabilizes the weak scale up to about 20 TeV and where the states which cancel the top loop are scalars not charged under Standard Model color. Its collider signatures are distinct from conventional supersymmetric theories and include characteristic events with hard leptons and missing energy.

Figures (5)

• Figure 1: The diagram on top shows the contribution to the Higgs mass squared parameter in the SM from the top loop, while the lower two diagrams show how this contribution is cancelled in supersymmetric theories and in little Higgs theories. In twin Higgs models the cancellation takes place through a diagram of the same form as in the little Higgs case but the particles running in the loop need not be charged under color. In analogy with this, we seek a theory where the cancellation takes the same form as in the supersymmetric diagram but the states in the loop are not charged under color.
• Figure 2: The top loop diagram for the Higgs mass in double line notation. In order to give the Higgs bifold protection SU(3) color, represented by the index $\alpha$, may be extended to SU(6) or to SU(3$)\times$ SU(3$)\times Z_2$.
• Figure 3: The Kaluza-Klein tower in theories with Scherk-Schwarz SUSY breaking admits non-degenerate fermions and bosons. However in folded-supersymmetric theory each such tower is complemented by another tower yielding a degenerate spectrum. This allows for a complete cancellation of radiative corrections to the Higgs mass at one loop.
• Figure 4: The gauge loop contribution to the Higgs mass in double line notation. In order to give the Higgs bifold protection SU(2) may be extended to SU(4).
• Figure 5: The Feynman diagrams involved in the cancellation of the radiative corrections to the Higgs mass from the top sector. For every choice of two Kaluza-Klein levels $n$ and $m$ this combination of diagrams is present, adding up to zero. The cancellation has a supersymmetric form, but the scalar tops are not charged under SM color.