The NMSSM Solution to the Fine-Tuning Problem, Precision Electroweak Constraints and the Largest LEP Higgs Event Excess

TL;DR

This work demonstrates that the NMSSM can drastically reduce electroweak fine-tuning by allowing a SM-like Higgs with $m_h\sim100$ GeV to exist while decaying predominantly via $h\to a_1a_1$ with $m_{a_1}<2m_b$, thereby evading LEP Higgs limits and aligning with precision electroweak data. A light, largely singlet $a_1$ arises naturally in the NMSSM (enhanced by small $A_\lambda$, $A_\kappa$ and approximate $U(1)_R$-like symmetry), enabling large $B(h_1\to a_1a_1)$ and potentially explaining the LEP $Z+2b$ excess through a reduced $B(h_1\to b\bar b)$. The analysis shows that moderate to very low fine-tuning (e.g., $F\lesssim 20$–$10$) is achievable for $m_{h_1}\approx100$ GeV across various $\tan\beta$, with heavier Higgs states in ranges that could be probed at the LHC, especially at large $\tan\beta$, or at a future linear collider. It also explores alternative low-$F$ scenarios including $a_1\to\gamma\gamma$ and even rare $h\to aa\to 4\gamma$ channels, highlighting distinctive collider signatures and the need for refined LEP and flavor-search analyses. Overall, the NMSSM emerges as a compelling natural extension with concrete, testable predictions for Higgs phenomenology and beyond.

Abstract

We present an extended study of how the Next to Minimal Supersymmetric Model easily avoids fine-tuning in electroweak symmetry breaking for a SM-like light Higgs with mass in the vicinity of $100\gev$, as beautifully consistent with precision electroweak data, while escaping LEP constraints due to the dominance of $h\to aa$ decays with $m_a<2m_b$ so that $a\to \tauptaum$ or jets. The residual $\sim 10%$ branching ratio for $h\to b\anti b$ explains perfectly the well-known LEP excess at $\mh\sim 100\gev$. Details of model parameter correlations and requirements are discussed as a function $\tan(β)$. Comparisons of fine-tuning in the NMSSM to that in the MSSM are presented. We also discuss fine-tuning associated with scenarios in which the $a$ is essentially pure singlet, has mass $m_a>30\gev$, and decays primarily to $\gam\gam$ leading to an $h\to aa\to 4\gam$ Higgs signal.

Figures (37)

• Figure 1: Expected and observed 95% CL limits on $C_{\rm eff}^{2b}$ from Ref. oldleplimits are shown vs. $m_{h}$. Also plotted are the predictions for the NMSSM parameter cases discussed in Dermisek:2005gg having fixed $\tan\beta=10$, $M_{1,2,3}(m_Z)=100,200,300~{\rm GeV}$ that give fine-tuning measure $F<25$ and $m_{a_1}<2m_b$ and that are consistent with Higgs constraints obtained using the preliminary LHWG analysis code bechtle.
• Figure 2: Fine tuning vs. $\overline m_{\widetilde{t}}$ (top), $m_{h}$ (middle) and $A_t$ (bottom) for randomly generated MSSM parameter choices with $\tan\beta=10$ and $M_{1,2,3}(m_Z)=100,200,300~{\rm GeV}$. Blue pluses correspond to parameter choices such that $m_{h}<114~{\rm GeV}$. Red crosses are points with $m_{h}>114~{\rm GeV}$.
• Figure 3: For the NMSSM, we plot the fine-tuning measure $F$ vs. $\overline m_{\widetilde{t}}$, $m_{h_1}$ and $A_t$ for NMHDECAY-accepted scenarios with $\tan\beta=10$ and $M_{1,2,3}(m_Z)=100,200,300~{\rm GeV}$. Points marked by blue '$+$'s are consistent with LEP limits on the $Z+2b$ channel and the $Z+4b$ channel newleplimits, considered separately, but not necessarily with LEP limits on the combined $Z+2b$ and $Z+4b$ channels). Points marked by red '$\times$'s escape LEP limits due to $m_{h_1}>114~{\rm GeV}$.
• Figure 4: For the NMSSM, we plot $C_{\rm eff}^{2b}$ and $C_{\rm eff}^{4b}$ as a functions of $m_{h_1}$ for NMHDECAY-accepted scenarios with $\tan\beta=10$ and $M_{1,2,3}(m_Z)=100,200,300~{\rm GeV}$. Point notation as in Fig. \ref{['fvsmh1nmssm1']}.
• Figure 5: For the NMSSM, we plot the fine-tuning measure $F$ vs. $BR(h_1\to a_1a_1)$ and vs. $m_{a_1}$ for NMHDECAY-accepted scenarios with $\tan\beta=10$ and $M_{1,2,3}(m_Z)=100,200,300~{\rm GeV}$. Point notation as in Fig. \ref{['fvsmh1nmssm1']}.