The Intermediate Scale MSSM, the Higgs Mass and F-theory Unification

TL;DR

The paper investigates an intermediate-scale MSSM within F-theory $SU(5)$ unification, arguing that gauge coupling unification and SUSY-breaking from closed-string flux select an intermediate $M_{SS}\approx5\times10^{10}$ GeV and a unification scale $M_c\approx3\times10^{14}$ GeV. It links this structure to a vanishing SM Higgs quartic coupling near $M_{SS}$, compatible with a 124–126 GeV Higgs, and proposes a natural axion with $F_a\sim2\times10^{12}$ GeV as DM. Proton decay constraints are softened by hypercharge-flux-induced wavefunction deformations that suppress $X,Y$-mediated operators, while a potential light Higgs triplet sector offers additional but controlled decay channels. The framework also yields a set of cosmological and neutrino mass implications, and contrasts with Split-SUSY scenarios, highlighting testable predictions in proton decay and axion experiments. Overall, the work presents a cohesive, string-m-theory–inspired route to reconcile unification, Higgs physics, and DM without low-energy SUSY, at the cost of embracing a landscape-driven hierarchy explanation.

Abstract

Even if SUSY is not present at the Electro-Weak scale, string theory suggests its presence at some scale M_{SS} below the string scale M_s to guarantee the absence of tachyons. We explore the possible value of M_{SS} consistent with gauge coupling unification and known sources of SUSY breaking in string theory. Within F-theory SU(5) unification these two requirements fix M_{SS} ~ 5 x 10^{10} GeV at an intermediate scale and a unification scale M_c ~ 3 x 10^{14} GeV. As a direct consequence one also predicts the vanishing of the quartic Higgs SM self-coupling at M_{SS} ~10^{11} GeV. This is tantalizingly consistent with recent LHC hints of a Higgs mass in the region 124-126 GeV. With such a low unification scale M_c ~ 3 x 10^{14} GeV one may worry about too fast proton decay via dimension 6 operators. However in the F-theory GUT context SU(5) is broken to the SM via hypercharge flux. We show that this hypercharge flux deforms the SM fermion wave functions leading to a suppression, avoiding in this way the strong experimental proton decay constraints. In these constructions there is generically an axion with a scale of size f_a ~ M_c/(4π)^2 ~ 10^{12} GeV which could solve the strong CP problem and provide for the observed dark matter. The prize to pay for these attractive features is to assume that the hierarchy problem is solved due to anthropic selection in a string landscape.

Figures (7)

• Figure 1: Scheme of an F-theory $SU(5)$ GUT. The six extra dimensions are compactified on $B_3$ whereas the $SU(5)$ degrees of freedom are localized on a 4-cycle submanifold $S$. The gauge bosons live on the bulk of $S$ but the chiral multiplets are localized on complex matter curves. At the intersection of two matter curves with a Higgs curve a Yukawa coupling develops.
• Figure 2: Constraints on $M_{SS}$ and $M_c$ from gauge coupling unification (black line) and closed string flux induced SUSY breaking (red line). The vertical (blue) band shows the region of $M_{SS}$ at which the SM Higgs coupling $\lambda$ vanishes for a Higgs mass in the range $124-126$ GeV and $m_t=173.2$ GeV, as extracted from ref.Giudice:2011cgEliasMiro:2011aa. The horizontal line shows the value of the axion decay constant for the selected unification mass $M_c$.
• Figure 3: The string dilaton coupling constant versus $M_{SS}$ for consistent gauge coupling unification. Left: With an MSSM content in the region $M_{SS}-M_c$; Right: With an additional vector-like triplet set $D+{\overline D}$ in that region.
• Figure 4: Structure of scales and the running of the gauge and Higgs coupling constants in this scheme.
• Figure 5: Renormalization of tan$\beta$ in the region $M_{SS}-M_c$ as a function of $M_{SS}$ for three values of the top quark mass.