The fine-tuning of the generalised NMSSM

TL;DR

The paper investigates the fine-tuning of a generalized NMSSM (GNMSSM) derived from discrete $R$-symmetries ($Z_4^R$ or $Z_8^R$) and gravity mediation. By comparing to the MSSM and NMSSM, it shows that the GNMSSM significantly reduces electroweak-scale tuning and broadens the acceptable Higgs-mass region, with the smallest tuning occurring near $m_{h_1} \approx 130$ GeV due to both an enhanced $M_{11}^2$ contribution from $\lambda$ and a stabilizing singlet-induced operator for large $\mu_s$. The analysis uses one-loop RGEs and CMSSM-like boundary conditions to relate high-scale parameters to the electroweak scale, finding that, though the singlet sector can be heavy under universal conditions, tuning remains noticeably smaller than in the MSSM. The work suggests discrete $R$-symmetries provide a natural, less-tuned extension to the MSSM/NMSSM with potential distinctive collider phenomenology, and plans for more exhaustive numerical studies are outlined.

Abstract

We determine the degree of fine-tuning needed in a generalised version of the NMSSM that follows from an underlying Z4 or Z8 R-symmetry. We find that it is significantly less than is found in the MSSM or NMSSM and extends the range of Higgs mass that have acceptable fine-tuning. Remarkably the minimal fine-tuning is achieved for Higgs masses of around 130 GeV.

Figures (2)

• Figure 1: Comparison of fine-tuning in the MSSM (orange) and GNMSSM (blue) for a minimal unified gaugino mass $m_{1/2} > 300 \,(500) \:\text{Ge V}$. For the GNMSSM the lowest fine-tuning is at low $\tan\beta=\mathcal{O}(2)$ while in the MSSM it is at higher $\tan\beta=\mathcal{O}(10)$. Remarkably the lowest fine-tuning is achieved for rather large Higgs masses, $m_{h_1} \sim 130 \:\text{Ge V}$.
• Figure 2: The lightest Higgs mass versus the high-scale singlet mass parameter $\mu_s^0$ for points with fine-tuning $\Delta <100$.