Persistent Fine-Tuning in Supersymmetry and the NMSSM

TL;DR

The paper analyzes naturalness in supersymmetry with a focus on NMSSM-like Higgs-sector modifications. It distinguishes model-independent naturalness constraints from NMSSM-specific tunings in the PQ and R limits, showing that electroweak symmetry breaking and Higgs phenomenology impose typical tunings of 1–10%, with additional tuning required to hide a light Higgs via cascade decays. While the NMSSM offers mechanisms to alleviate some constraints, it introduces its own fine-tuning challenges, suggesting that it shifts rather than eliminates the little hierarchy problem. The work highlights how cascade decays, large λ, and singlet dynamics shape naturalness and points to further avenues for model-building that balance Higgs-sector tunings with electroweak requirements.

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.

Figures (6)

• Figure 1: White region: Allowed soft mass ranges for electroweak symmetry breaking with $M_Z=91$ GeV for some $m_{H_d}^2$, in the PQ limit of the NMSSM, with parameters $\lambda=0.68$, $\kappa= 0.03$, $A_\lambda= 350$, and $A_\kappa=50$. Below the black line, an electroweak symmetry-breaking global minimume exists, but cosmologically viable electroweak symmetry breaking is not guaranteed.
• Figure 2: Phenomenology constraints on the NMSSM as $\lambda$ and $\kappa$ are varied. Fixed parameters are listed in Table \ref{['tab:phenonumbers']}. The red region at the top and black region just below it are phenomenologically allowed, with the second-heaviest (MSSM-like) Higgs heavier and lighter than 114.4 GeV, respectively. The center-right blue region is excluded by Higgs decays to nonsupersymmetric particles. The yellow region on the lower left is excluded by light neutralino searches, while the lower-right green region is excluded by both neutralino searches and Higgs decay searches.
• Figure 3: Phenomenology of regions of $m_{H_u}^2$-$m_S^2$ parameter space where EWSB consistent with $M_Z$ is possible. Fixed parameters are listed in Table \ref{['tab:phenonumbers']}. The black region on the right is phenomenologically allowed, and has the second-heaviest (MSSM-like) Higgs hidden below 114.4 GeV. The small red region directly below it is also allowed, but with the MSSM-like Higgs mass $\ge$ 114.4 GeV. The lower blue region is excluded by Higgs decays to nonsupersymmetric particles. The yellow regions on the upper left and middle are excluded by light neutralino searches, while the $\Gamma$-shaped green region is excluded by both neutralino searches and Higgs decay searches. Only points above the white line are cosmologically viable if symmetry is restored at high temperatures. Points below the line roll first along the singlet axis, and typically do not roll off into an electroweak symmetry-breaking vacuum
• Figure 4: White region: Allowed soft mass ranges for electroweak symmetry breaking with $M_Z=91$ GeV for some $m_{H_d}^2$, in the R-symmetric limit of the NMSSM, with $\lambda=\kappa=0.63$, $A_\lambda=0.5$, $A_\kappa=0$.
• Figure 5: Phenomenology constraints on the NMSSM as $\lambda$ and $\kappa$ are varied in the R-symmetric limit. Fixed parameters are listed in Table \ref{['tab:R-params']}. The red region at the top and black region just below it are phenomenologically allowed, with the lightest Higgs heavier and lighter than 112 GeV, respectively. The blue region at the bottom is excluded by Higgs decays.