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

TL;DR

This paper investigates an intermediate-scale MSSM within F-theory unification, predicting a Higgs mass consistent with LHC hints, and discusses proton decay suppression and dark matter implications.

Contribution

It proposes a specific intermediate SUSY-breaking scale in F-theory SU(5) unification, linking Higgs mass predictions, proton decay suppression, and axion dark matter.

Findings

M_{SS} ~ 5 x 10^{10} GeV consistent with unification

Higgs self-coupling vanishes near 10^{11} GeV, matching LHC hints

Proton decay suppressed by hypercharge flux deformation

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/(4\pi)^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.