The NMSSM Close to the R-symmetry Limit and Naturalness in $h \to aa$ Decays for $m_a<2\mb$

TL;DR

This paper demonstrates that in the NMSSM, a SM-like Higgs with $m_{h_1}\sim 100$ GeV can evade LEP bounds if it decays mostly to a pair of light CP-odd Higgses through $h_1\to a_1 a_1$, provided $m_{a_1}<2 m_b$ and ${\rm Br}(h_1\to a_1 a_1)\gtrsim 0.7$. It analyzes the NMSSM near the $R$-symmetry limit, showing that $a_1$ mass is controlled by soft trilinears $A_λ$ and $A_κ$ and that $a_1$ becomes dominantly singlet, reducing couplings to SM states. A quantitative tuning measure $F_{\max}$ indicates that achieving these conditions typically requires only ~5–10% tuning in $A_λ(m_Z)$ and $A_κ(m_Z)$, with potential further reductions in specialized SUSY-breaking scenarios; RG running from the GUT scale naturally yields the required trilinear sizes. The work also explores how varying parameters like $\mu$, $\tanβ$, and the SUSY scale shapes the viable region and Higgs spectrum, and it discusses collider implications, highlighting nonstandard Higgs decays as a key discovery channel at the LHC and possibly the ILC.

Abstract

Dominant decay of a SM-like Higgs boson into particles beyond those contained in the minimal supersymmetric standard model has been identified as a natural scenario to avoid fine tuning in electroweak symmetry breaking while satisfying all LEP limits. In the simplest such extension, the next-to-minimal supersymmetric model, the lightest CP-even Higgs boson can decay into two pseudoscalars. In the scenario with least fine tuning the lightest CP-even Higgs boson has mass of order 100 GeV. In order to escape LEP limits it must decay to a pair of the lightest CP-odd Higgs bosons with Br(h -> aa)>.7 and m_a<2m_b (so that a -> τ^+ τ^- or light quarks and gluons). The mass of the lightest CP-odd Higgs boson is controlled by the soft-trilinear couplings, A_λ(m_Z) and A_κ(m_Z). We identify the region of parameter space where this situation occurs and discuss how natural this scenario is. It turns out that in order to achieve m_a < 2 m_b with A_λ(m_Z), A_κ(m_Z) of order the typical radiative corrections, the required tuning of trilinear couplings need not be larger than 5-10 %. Further, the necessity for this tuning can be eliminated in specific SUSY breaking scenarios. Quite interestingly, Br(h -> aa) is typically above 70 % in this region of parameter space and thus an appropriately large value requires no additional tuning.

Figures (25)

• Figure 1: Allowed parameter space in the $A_\kappa - A_\lambda$ and $\kappa - \lambda$ planes. Light grey (cyan) large crosses are points that satisfy all experimental limits. The dark (blue) diamonds are those points that do not have large enough ${\rm Br}(h_1\to a_1a_1)$ so as to suppress ${\rm Br}(h_1\to b\bar{b})$ sufficiently to escape LEP limits.
• Figure 2: Allowed parameter space in the $A_\kappa - \kappa$ and $A_\lambda - \kappa$ planes. Point conventions as in Fig. \ref{['fig:AkAl_and_kl']}.
• Figure 3: A selected region of the allowed parameter space in the $A_\kappa - A_\lambda$ plane for fixed values of $\lambda=0.38$ and $\kappa=0.4$. Point conventions as in Fig. \ref{['fig:AkAl_and_kl']}.
• Figure 4: Br($h_1\to a_1a_1$) vs. $A_\kappa$ and $A_\lambda$ for $\mu=150~{\rm GeV}$ and $\tan\beta=10$. Point conventions as in Fig. \ref{['fig:AkAl_and_kl']}.
• Figure 5: Tuning in $m_{a_1}^2$ vs. $A_\kappa$ and $A_\lambda$. Point conventions as in Fig. \ref{['fig:AkAl_and_kl']}.