The Higgs Mass as a Signature of Heavy SUSY

TL;DR

The paper addresses how the observed Higgs mass around 126 GeV can arise if supersymmetry is broken at a high scale M_SS. It develops a calculational framework combining Higgs mass unification at the unification scale with MSSM boundary conditions, running through RG equations and incorporating threshold corrections to predict m_H as a function of M_SS. The main finding is that for M_SS ≳ 10^10 GeV the predicted Higgs mass centers around 126 ± 3 GeV, while lower M_SS values trend toward a finely-tuned MSSM with m_H ≲ 130 GeV, suggesting the Higgs mass acts as indirect evidence for SUSY at high scales. The results are shown to be robust across reasonable soft-term variations and can be embedded in string-inspired unification scenarios, with several indirect experimental implications such as precision measurements, dark matter axions, and proton decay.

Abstract

We compute the mass of the Higgs particle in a scheme in which SUSY is broken at a large scale M_{SS} well above the electroweak scale M_{EW}. Below M_{SS} one assumes one is just left with the SM with a fine-tuned Higgs potential. Under standard unification assumptions one can compute the mass of the Higgs particle as a function of the SUSY breaking scale M_{SS}. For M_{SS} > 10^{10} GeV one obtains m_H=126 \pm 3 GeV, consistent with CMS and ATLAS results. For lower values of M_{SS} the values of the Higgs mass tend to those of a fine-tuned MSSM with m_H < 130 GeV. These results support the idea that the measured value of the Higgs mass at LHC may be considered as indirect evidence for the existence of SUSY at some (not necessarily low) mass scale.

Figures (5)

• Figure 1: Higgs mass versus SUSY breaking scale $M_{SS}$. The grey bands correspond to the Higgs mass for different values of tan$\beta$, for $X_t=0$, without impossing unification of Higgs soft parameters. The other colored bands correspond to impossing tan$\beta$ values consistent with unification of soft terms, $m_{H_u}=m_{H_d}$. Results are shown for a choice of universal soft terms $M=\sqrt{2}m$, $A=-3/2M$ and four values for the $\mu$-term. The stop mixing parameter $X_t$ is computed from the given soft parameters. The width of the bands correspond to the error from the top quark mass which is taken to be $m_t=173.1\pm 0.7$. The horizontal band corresponds to the ATLAS and CMS average Higgs mass result.
• Figure 2: The black line shows the value of the SM self-coupling $\lambda$ as a function of $M_{SS}$, using as input the LHC Higgs data. The remaining curves show values of $\lambda_{SUSY}$ consistent with $m_{H_u}(M_C)=m_{H_d}(M_C)$ for different values of $\mu$. When these $\lambda_{SUSY}$ lines cross the $\lambda$ curve the SUSY model is consistent with LHC Higgs data.
• Figure 3: Higgs mass versus SUSY breaking scale $M_{SS}$ for $\mu=-M/2$ (red band). Its width reflects the uncertainty on $m_t=173.1\pm 0.7$. The grey bands, as in fig.\ref{['plotguay']} show the Higgs mass for several values of tan$\beta=1,2,4,50$ and are displayed to guide the eye.
• Figure 4: Left: Evolution of the SM Higgs selfcoupling $\lambda(t)$ and the combination $\lambda_{SUSY}=(g_1^2(t)+g_2^2(t))/4\times cos^2(2\beta)(M_{SS})$ in the model with $\mu=-M/2$ and an intermediate scale $M_{SS}\approx 3\cdot10^{10}$GeV. They unify at $M_{SS}$ where SUSY starts to hold. Right: Values of the 3-d generation squark soft masses $m_{Q,U,D}$ as well the Higgs mass parameters $m_{H_u},m_{H_d},\mu$ and trilinear $A_t$ at the scale $M_{SS}$ obtained from the running below the unification scale $M_C$.
• Figure 5: Higgs mass versus SUSY breaking scale $M_{SS}$ for $\mu=-M/2$. Up: for various values of the scalar mass parameter $m$ in units of the gaugino mass $M$; Down: for various values of the trilinear $A$ parameter.