The $G_2$-MSSM - An $M$ Theory motivated model of Particle Physics

TL;DR

This paper develops the $G_2$-MSSM, a concrete, M-theory–motivated model derived from compactifications on $G_2$ manifolds that stabilizes all moduli and generates a TeV-scale spectrum with Planck-scale input. The authors compute the soft SUSY-breaking parameters at the unification scale, showing heavy scalars and Higgsinos with suppressed tree-level gaugino masses, and they incorporate anomaly mediation and threshold effects to obtain a non-universal gaugino spectrum that typically yields a wino-like LSP when precision gauge unification is satisfied. RG evolution to the electroweak scale, decoupling of heavy scalars, and matching to the SM predict radiatively broken electroweak symmetry with a light Higgs around 120 GeV, while maintaining natural-like gauge coupling unification. Cosmologically, non-thermal production from moduli decay yields the observed dark matter abundance for a wino LSP, linking the moduli sector to dark matter, and yielding distinctive collider signatures such as multi-top-rich final states and short charged tracks from nearly degenerate charginos. Overall, the work provides a UV-complete, testable framework connecting high-scale M-theory dynamics to low-energy phenomenology and collider/cosmology signals, with explicit predictions for gaugino masses, LSP identity, and Higgs sector properties.

Abstract

We continue our study of the low energy implications of $M$ theory vacua on $G_2$ manifolds, undertaken in \cite{Acharya:2007rc,Acharya:2006ia}, where it was shown that the moduli can be stabilized and a TeV scale generated, with the Planck scale as the only dimensionful input. A well-motivated phenomenological model - the $G_2$-MSSM, can be naturally defined within the above framework. In this paper, we study some of the important phenomenological features of the $G_2$-MSSM. In particular, the soft supersymmetry breaking parameters and the superpartner spectrum are computed. The $G_2$-MSSM generically gives rise to light gauginos and heavy scalars with wino LSPs when one tunes the cosmological constant. Electroweak symmetry breaking is present but fine-tuned. The $G_2$-MSSM is also naturally consistent with precision gauge coupling unification. The phenomenological consequences for cosmology and collider physics of the $G_2$-MSSM will be reported in more detail soon.

Figures (6)

• Figure 1: The absolute value of the gaugino masses at the unification scale are plotted as functions of threshold correction to the gauge kinetic function $\delta$ for $Q-P=3$, $P_{\mathrm{eff}}=83$, $m_{3/2}$=20 TeV and $\alpha_{unif}^{-1}=26.5$.
• Figure 2: Gaugino Masses at low scales (include correction (\ref{['Eq:gaugino-correction']})) as a function of $\delta$ for the case with cosmological constant tuned to zero ($P_{\mathrm{eff}} = 83$), $Q-P=3$, $V_7=10.8$, $C_2=1$ and $\alpha_{unif}^{-1}=26.5$.TOP: Plot for positive $\mu$. BOTTOM: Plot for negative $\mu$.
• Figure 3: Plot of the ratio of the Higgs mass and the $Z$ mass as a function of the gravitino mass.
• Figure 4: Plot of $L^{2/3}$ as a function of integer $q$ from $2$ to $50$. Different curves correspond to different choices of $\omega$ as marked in the plot.
• Figure 5: Gaugino Mass spectra vs $m_{3/2}$ compatible with gauge unification for $P_{\mathrm{eff}}=83$, $C_{2}=5$ and $\mu >0$. The red, green and blue lines correspond to gaugino mass $M_{1}$, $M_{2}$ and $M_{3}$ respectively.