Probing High-Scale and Split Supersymmetry with Higgs Mass Measurements

TL;DR

The paper analyzes Higgs-mass predictions in High-Scale and Split Supersymmetry by tying the low-energy SM Higgs quartic to its SUSY boundary value at a high scale $\tilde{m}$ via $\lambda(\tilde{m})$. It provides a comprehensive two-loop RGE analysis for Split SUSY, including one-loop threshold effects, revealing that these corrections shift the predicted $m_h$ by a few GeV. With the LHC hint of $m_h \approx 124$–$126$ GeV, the authors find a robust upper bound $\tilde{m} \lesssim 10^8$ GeV for Split SUSY, while High-Scale SUSY remains less constrained due to larger theoretical and experimental uncertainties. The work highlights how precise measurements of $m_h$ and SM inputs, plus higher-order thresholds, can probe SUSY scales far beyond direct collider reach.

Abstract

We study the range of Higgs masses predicted by High-Scale Supersymmetry and by Split Supersymmetry, using the matching condition for the Higgs quartic coupling determined by the minimal field content. In the case of Split Supersymmetry, we compute for the first time the complete next-to-leading order corrections, including two-loop renormalization group equations and one loop threshold effects. These corrections reduce the predicted Higgs mass by a few GeV. We investigate the impact of the recent LHC Higgs searches on the scale of supersymmetry breaking. In particular, we show that an upper bound of 127 GeV on the Higgs mass implies an upper bound on the scale of Split Supersymmetry of about 10^8 GeV, while no firm conclusion can yet be drawn for High-Scale Supersymmetry.

Figures (5)

• Figure 1: Contour plot of the Higgs quartic coupling renormalized at the supersymmetry breaking scale ${\tilde{m}}$. The regions marked as "metastable" (yellow) and "unstable" (red) correspond to $\lambda<0$; the green band shows the range of the Higgs mass allowed by the supersymmetric matching condition for the Higgs quartic coupling, in the case of High-Scale Supersymmetry (left panel; the dashed and dotted curves correspond to the cases of maximal and minimal stop threshold corrections) and Split Supersymmetry (right panel, dashed curves; double contour-lines and partially overlapped regions are due to the variation with $\tan\beta$ of the gaugino couplings). The values of $\alpha_3$ and $m_t$ are fixed to their central values, see eq. (\ref{['mtalpha3']}), and the horizontal band $124\,{\rm GeV}<m_h<126\,{\rm GeV}$ shows the experimentally favored range.
• Figure 2: Prediction for the Higgs mass $m_h$ at two loops in High-Scale Supersymmetry (left panel) and Split Supersymmetry (right panel) as a function of the supersymmetry breaking scale $\tilde{m}$ and $\tan\beta$ for the central values of $\alpha_3$ and $m_t$. In the case of Split Supersymmetry we have chosen the light sparticle spectrum of eq. (\ref{['eq:Mi']}); in the case of High Scale Supersymmetry we assumed maximal stop mixing. Excluded values $m_h<115\,{\rm GeV}$ and $m_h>128\,{\rm GeV}$ are shaded in gray; the favorite range $124\,{\rm GeV}<m_h < 126\,{\rm GeV}$ is shaded in green.
• Figure 3: Next-to-leading order prediction for the Higgs mass $m_h$ in High-Scale Supersymmetry (blue, lower) and Split Supersymmetry (red, upper) for $\tan\beta=\{1,2,4,50\}$. The thickness of the lower boundary at $\tan\beta=1$ and of the upper boundary at $\tan\beta=50$ shows the uncertainty due to the present $1\sigma$ error on $\alpha_3$ (black band) and on the top mass (larger colored band).
• Figure 4: The impact of neutrino Yukawa couplings on the predicted range for the Higgs mass in High-Scale Supersymmetry assuming best-fit values for $m_t$ and $\alpha_3$ and varying $\tan\beta$. Each band corresponds to a different value of the right-handed neutrino mass, as indicated in the figure. The arrows show the points where ${\tilde{m}} =M$, below which the effect disappears.
• Figure 5: Assuming the existence of supersymmetry we compute, as function of $\tan\beta$, the preferred value of the SUSY scale ${\tilde{m}}$ implied by the Higgs mass $m_h=124\,{\rm GeV}$ (upper) and $126\,{\rm GeV}$ (lower) at $68,90,99\%$ C.L. in the cases of High-Scale Supersymmetry (left, assuming a degenerate sparticle spectrum at the SUSY breaking scale with arbitrary stop mixing) and Split Supersymmetry (right, assuming the spectrum of light fermions in eq. (\ref{['eq:Mi']}) and a degenerate sparticle spectrum at the SUSY breaking scale).