Persistent Fine-Tuning in Supersymmetry and the NMSSM

TL;DR

This paper explores how modified Higgs sectors in supersymmetry, especially the NMSSM, can reduce fine-tuning issues but still face significant naturalness challenges due to model-dependent and independent tunings.

Contribution

It analyzes the naturalness constraints and tuning requirements in the NMSSM with modified Higgs sectors, highlighting the persistent fine-tuning problems.

Findings

Electroweak symmetry breaking requires 1-10% tuning in the PQ limit.

Large A-terms introduce about 10% tuning for heavy charginos.

Hiding Higgs states below 112 GeV necessitates additional tunings.

Abstract

We examine the use of modified Higgs sectors to address the little hierarchy problem of supersymmetry. Such models reduce weak-scale fine-tuning by allowing lighter stops, but they retain some fine-tuning independent of the Higgs. The modified Higgs sector can also introduce model-dependent tunings. We consider the model-independent constraints on naturalness from squark, gluino, chargino and neutralino searches, as well as the model-dependent tuning in the PQ- and R-symmetric limits of the NMSSM, where cascade decays or additional quartic interactions can hide a Higgs without relying on heavy stops. Obtaining viable electroweak symmetry breaking requires a tuning of $\sim 1-10%$ in the PQ limit. A large A-term is also necessary to make charginos sufficiently heavy, and this introduces an additional weak-scale tuning of $\sim 10%$. The R-symmetric limit requires large marginal couplings, a large singlet soft mass, and a tuning of $\sim 5-10%$ to break electroweak symmetry. Hiding MSSM-like Higgs states below $\approx 112$ GeV requires additional tunings of A-terms at the $\sim 1-10%$ level. Thus, although the NMSSM has rich discovery potential, it suffers from a unique fine-tuning problem of its own.