A Natural SUSY Higgs Near 125 GeV

TL;DR

The paper analyzes naturalness for a Higgs mass around $125\,\mathrm{GeV}$ across MSSM, NMSSM, and $\lambda$-SUSY. It shows that the MSSM requires significant stop masses or mixing, leading to substantial fine-tuning, whereas the NMSSM can improve naturalness with a moderate $\lambda$ up to the perturbative limit, albeit with a bound from perturbativity. In contrast, $\lambda$-SUSY with large $\lambda$ (≈2) yields the light Higgs through Higgs-singlet mixing while allowing heavy colored superpartners and predicting enhanced diphoton and $WW$ rates due to non-decoupling effects. The results point to distinct experimental signatures, especially in Higgs couplings and branching ratios, offering concrete avenues to test non-minimal SUSY scenarios at the LHC.

Abstract

The naturalness of a Higgs boson with a mass near 125 GeV is explored in a variety of weak-scale supersymmetric models. A Higgs mass of this size strongly points towards a non-minimal implementation of supersymmetry. The Minimal Supersymmetric Standard Model now requires large A-terms to avoid multi-TeV stops. The fine-tuning is at least 1% for low messenger scales, and an order of magnitude worse for high messenger scales. Naturalness is significantly improved in theories with a singlet superfield S coupled to the Higgs superfields via λ S H_u H_d. If λ is perturbative up to unified scales, a fine-tuning of about 10% is possible with a low mediation scale. Larger values of λ, implying new strong interactions below unified scales, allow for a highly natural 125 GeV Higgs boson over a wide range of parameters. Even for λ as large as 2, where a heavier Higgs might be expected, a light Higgs boson naturally results from singlet-doublet scalar mixing. Although the Higgs is light, naturalness allows for stops as heavy as 1.5 TeV and a gluino as heavy as 3 TeV. Non-decoupling effects among the Higgs doublets can significantly suppress the coupling of the light Higgs to b quarks in theories with a large λ, enhancing the γγ and WW signal rates at the LHC by an order one factor relative to the Standard Model Higgs.

Figures (14)

• Figure 1: The Higgs mass in the MSSM as a function of the lightest top squark mass, $m_{\tilde{t}_1}$, with red/blue solid lines computed using Suspect/FeynHiggs. The two upper lines are for maximal top squark mixing assuming degenerate stop soft masses and yield a 124 (126) GeV Higgs mass for $m_{\tilde{t}_1}$ in the range of 350--600 (500--800) GeV, while the two lower lines are for zero top squark mixing and do not yield a 124 GeV Higgs mass for $m_{\tilde{t}_1}$ below 3 TeV. Here we have taken $\tan\beta = 20$. The shaded regions highlight the difference between the Suspect and FeynHiggs results, and may be taken as an estimate of the uncertainties in the two-loop calculation.
• Figure 2: The Higgs mass in the NMSSM as a function of $\tan \beta$. The solid lines show the tree-level result of equation \ref{['eq:hmassNMSSM']} while the shaded bands bounded by dashed lines result from adding the $\lambda^2 v^2 \sin^2 2 \beta$ contribution of equation \ref{['eq:hmassNMSSM']} to the two-loop Suspect/FeynHiggs MSSM result, with degenerate stop soft masses and no stop mixing. The top contribution $\delta_t$ is sufficient to raise the Higgs mass to 125 GeV for $\lambda = 0.7$ for a top squark mass of 500 GeV; but as $\lambda$ is decreased to 0.6 a larger value of the top squark mass is needed.
• Figure 3: The Higgs mass in $\lambda$-SUSY, as a function of the singlet soft mass $m_S$. Here, $\lambda = 2$, $\tan \beta =2$, and the other parameters are as described in Table \ref{['tab:bench']}, which gives the light Higgs a mass of $m_h = 280$ GeV in the limit of heavy singlet mass. However, we see that lowering the singlet mass $m_S$ results in a lighter Higgs due to mixing of the singlet with the Higgs.
• Figure 4: Contours of $m_h$ in the MSSM as a function of a common stop mass $m_{Q_3} = m_{u_3} = m_{\tilde{t}}$ and the stop mixing parameter $X_t$, for $\tan \beta = 20$. The red/blue bands show the result from Suspect/FeynHiggs for $m_h$ in the range 124--126 GeV. The left panel shows contours of the fine-tuning of the Higgs mass, $\Delta_{m_h}$, and we see that $\Delta_{m_h} > 75 (100)$ in order to achieve a Higgs mass of 124 (126) GeV. The right panel shows contours of the lightest stop mass, which is always heavier than 300 (500) GeV when the Higgs mass is 124 (126) GeV.
• Figure 5: A blowup of the maximal mixing regime, $X_t \sim 2 m_{\tilde{t}}$, in the MSSM, with $\tan\beta = 20$ and $m_A = 1$ TeV. The purple contours show $R_{\gamma \gamma}$, the ratio of $\sigma(g g \rightarrow h) \times \mathrm{Br}(h \rightarrow \gamma \gamma)$ in the MSSM to the Standard Model, computed with FeynHiggs. The one-loop contribution from stops depletes the rate to be $\sim80 - 95\%$ of the SM rate. Had we chosen non-degenerate squark soft masses, this effect could be larger, at the cost of increased fine-tuning. The other contours are the same as the right side of Figure \ref{['fig:MSSM']}.