SUSY Faces its Higgs Couplings

TL;DR

The paper examines how the Higgs mass near $125\,\mathrm{GeV}$ in supersymmetric models constrains the Higgs couplings through the quartic structure of the Higgs potential. It develops a general mass/couplings connection in two-Higgs-doublet frameworks and applies it to the MSSM under various assumptions (heavy stops, stop mixing) and to extensions with extra D- and F-terms, including NMSSM/BMSSM scenarios. The analysis shows that to raise $m_h$ one typically induces measurable deviations in the light Higgs couplings to fermions, especially to bottom quarks and tops, while vector couplings remain close to SM values in most cases. Using the latest LHC data, the authors derive bounds on heavy Higgs masses and $m_A$ that are competitive with direct searches, and they discuss how future precision measurements could further constrain natural SUSY realizations or point to NMSSM-like dynamics.

Abstract

In supersymmetric models, a correlation exists between the structure of the Higgs sector quartic potential and the coupling of the lightest CP-even Higgs to fermions and gauge bosons. We exploit this connection to relate the observed value of the Higgs mass ~ 125 GeV to the magnitude of its couplings. We analyze different scenarios ranging from the MSSM with heavy stops to more natural models with additional non-decoupling D-term/F-term contributions. A comparison with the most recent LHC data, allows to extract bounds on the heavy Higgs boson masses, competitive with bounds from direct searches.

Figures (9)

• Figure 1: The mixing between $h$ and $H$, induced by the quartic interaction $\delta h^3 H$, modifies the couplings of $h$ to the fermions w.r.t to its SM value.
• Figure 2: Theoretical expectation for Higgs couplings deviations for the MSSM with heavy stops and no mixing, taking $m_h=125\,\mathrm{GeV}$, showing contours of constant $m_A$ (solid blue) and $\tan \beta$ (dashed), obtained from the exact expressions of Eqs. (\ref{['hmass']},\ref{['alpha']}) of Appendix II. Also shown are the 68% (green), 95%(yellow) and 99%(grey) C.L. regions obtained by a global fit of the most recent LHC Higgs data, as explained in Appendix I, neglecting loop contributions to the $hgg$ and $h\gamma\gamma$ couplings. The dashed red lines show the approximate results of Eq. (\ref{['stopapprox']}) for $m_H=300,500\,\mathrm{GeV}$.
• Figure 3: Exclusion plot in the $m_A,\tan\beta$ plane for the MSSM with heavy stops (red), for models with additional non-decoupling D-terms (blue) and F-terms (green); regions to the left of the lines are excluded. The shaded region corresponds to bounds from direct searches CMSHtautau. Left: present data; right: longterm projection based on Peskin:2012we assuming no deviations from the SM, shaded region from Ref. Linssen:2012hp (the dashed part of the line corresponds to a region where $\lambda_S$ is bigger than 2 and non reaches the non-perturbative regime below approximately 10 TeV Lodone:2010ktHall:2011aa).
• Figure 4: Same as FIG.\ref{['stop']}, but for near maximal mixing and, again, we adjust $\sqrt{m_{\tilde{t}_1}m_{\tilde{t}_2}}\in [550, 2000]$ GeV in order to obtain the observed Higgs mass. We take $x_t = \sqrt{6}\pm0.1$ for the blue/red curve in order to show the influence, for large $\tan\beta$, of small deviations from maximal mixing; $\mu=400 \,\mathrm{GeV}$.
• Figure 5: Higgs couplings deviations in the MSSM with additional non-decoupling D-terms to raise the Higgs mass to 125 GeV (on top of the effect of light stops $m_{\tilde{t}}=500\,\mathrm{GeV}$). The global fit (Colors as in Fig. \ref{['stop']}) includes the effect of a 500 GeV stop (to be compared with Fig. \ref{['stop']} where the effects of stops on the fit are vanishingly small).