One Loop Predictions of the Finely Tuned SSM

TL;DR

This paper investigates a finely tuned supersymmetric Standard Model with decoupled scalars, examining whether high-scale SUSY can be probed through low-energy observables. It derives and solves the one-loop leading-log renormalization group equations for the Higgs quartic coupling and four gaugino-Higgs Yukawa couplings, along with the $\mu$ term and gaugino masses, starting from the SUSY-breaking scale $M_s$. The authors predict a Higgs mass in the range $m_h \approx 140$–$165$ GeV for $M_s=10^9$ GeV and show that the gaugino Yukawa couplings run significantly, enabling a determination of $M_s$ if these couplings are measured to about 10% accuracy at future colliders; the Higgs mass and $\tan\beta$ measurements can further refine $M_s$ estimates. The work highlights a testable, high-scale SUSY scenario where precise coupling measurements at colliders could reveal the SUSY-breaking scale and provide a striking signal for the model.

Abstract

We study the finely tuned SSM, recently proposed by Arkani-Hamed and Dimopoulos, at the one loop level. The runnings of the four gaugino Yukawa couplings, the mu term, the gaugino masses, and the Higgs quartic coupling are computed. The Higgs mass is found to be 130 - 170 GeV for M_s > 10^6 GeV. If the Yukawa coupling constants are measured at the 1% level, this can determine the SUSY breaking scale to within an order of magnitude. Measuring the relationships between the couplings to this accuracy provides a striking signal for this model.

Figures (4)

• Figure 1: The Higgs mass as a function of the SUSY breaking scale $\log_{10}(M_s/\text{GeV})$. The upper bands are for $\tan\beta(M_s) = 50$ and the lower ones are $\tan\beta(M_s) = 1$. The width of each grey band is the experimental uncertainty, mainly due to $m_t$. The width of each black band is the uncertainty when expected improvements from a future linear collider are taken into account.
• Figure 2: The ratio $\kappa(m_t)$/$\kappa(M_s)$ as a function of $M_s$ for fixed $\tan\beta(M_s)=5$.
• Figure 3: The solid line shows $\tan\beta_{\text{low}}(m_t)$ as a function of $M_s$. The dashed line is for $\tan\beta'_{\text{low}}(m_t)$. Here $\tan\beta(M_s) = 5$.
• Figure 4: The gaugino masses and $\mu$ evaluated at $m_t$ as a function of $M_s$ for fixed $\tan\beta(M_s) = 5$.