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The intermediate scale MSSM, the Higgs mass and F-theory unification

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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 × 1010 GeV at an intermediate scale and a unification scale M c  ≃ 3 × 1014 GeV. As a direct consequence one also predicts the vanishing of the quartic Higgs SM self-coupling at M SS  ≃ 1011 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 × 1014GeV 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 ≃ 1012 GeV which could solve the strong CP problem and provide for the observed dark matter. The price to pay for these attractive features is to assume that the hierarchy problem is solved due to anthropic selection in a string landscape.

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  1. Departamento de Física Teórica, Universidad Autónoma de Madrid, Cantoblanco, 28049, Madrid, Spain

    L. E. Ibáñez & I. Valenzuela

  2. Instituto de Física Teórica UAM-CSIC, Universidad Autónoma de Madrid, Cantoblanco, 28049, Madrid, Spain

    L. E. Ibáñez, F. Marchesano, D. Regalado & I. Valenzuela

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Ibáñez, L.E., Marchesano, F., Regalado, D. et al. The intermediate scale MSSM, the Higgs mass and F-theory unification. J. High Energ. Phys. 2012, 195 (2012). https://doi.org/10.1007/JHEP07(2012)195

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