A low Fermi scale from a simple gaugino-scalar mass relation

F Brümmer,W Buchmüller

doi:10.1007/jhep03(2014)075

Abstract

In supersymmetric extensions of the Standard Model, the Fermi scale of electroweak symmetry breaking is determined by the pattern of supersymmetry breaking. We present an example, motivated by a higher-dimensional GUT model, where a particular mass relation between the gauginos, third-generation squarks and Higgs fields of the MSSM leads to a Fermi scale smaller than the soft mass scale. This is in agreement with the measured Higgs boson mass. The mu parameter is generated independently of supersymmetry breaking, however the mu problem becomes less acute due to the little hierarchy between the soft mass scale and the Fermi scale as we will argue. The resulting superparticle mass spectra depend on the localization of quark and lepton fields in higher dimensions. In one case, the squarks of the first two generations as well as the gauginos and higgsinos can be in the range of the LHC. Alternatively, only the higgsinos may be accessible at colliders. The lightest superparticle is the gravitino.

Highlights

JHEP03(2014)075 choose it smaller than the typical soft SUSY breaking parameters, say, of the order of the electroweak scale
We present an example, motivated by a higher-dimensional GUT model, where a particular mass relation between the gauginos, third-generation squarks and Higgs fields of the MSSM leads to a Fermi scale smaller than the soft mass scale
To obtain proper electroweak symmetry breaking at large tan β, the loop-corrected up-type Higgs soft mass needs to be of the same order as μ at the scale where the MSSM is matched to the Standard Model, requiring an accidental cancellation between the tree-level and radiative contributions to this parameter

Summary

Electroweak symmetry breaking with a little hierarchy

The scalar potential for the MSSM Higgs fields depends on the higgsino mass μ, which is a parameter of the superpotential, and the soft supersymmetry breaking parameters m2Hu, m2Hd and Bμ,. The known value of mb leads to an upper bound on tan β, while the known value of mt implies that the top Yukawa coupling is large, and that a relation such as m 2Hu = 0 will be spoiled by large loop corrections These two arguments point towards a soft mass scale MS which is not too far above the electroweak scale; the 126 GeV Higgs mass further fixes the ‘little hierarchy’ to amount to 1–2 decades. The μ problem is still present, but somewhat alleviated when allowing for a little hierarchy between MS and the Fermi scale (as seems to be forced upon us by LHC data)

Supersymmetry breaking in higher-dimensional GUTs

Prospects for phenomenology and outlook