Supersymmetric unification without low energy supersymmetry and signatures for fine-tuning at the LHC

Abstract

The cosmological constant problem is a failure of naturalness and suggests that a fine-tuning mechanism is at work, which may also address the hierarchy problem. An example — supported by Weinberg's successful prediction of the cosmological constant — is the potentially vast landscape of vacua in string theory, where the existence of galaxies and atoms is promoted to a vacuum selection criterion. Then, low energy SUSY becomes unnecessary, and supersymmetry — if present in the fundamental theory — can be broken near the unification scale. All the scalars of the supersymmetric standard model become ultraheavy, except for a single finely tuned Higgs. Yet, the fermions of the supersymmetric standard model can remain light, protected by chiral symmetry, and account for the successful unification of gauge couplings. This framework removes all the difficulties of the SSM: the absence of a light Higgs and sparticles, dimension five proton decay, SUSY flavor and CP problems, and the cosmological gravitino and moduli problems. High-scale SUSY breaking raises the mass of the light Higgs to ~ 120−150 GeV. The gluino is strikingly long lived, and a measurement of its lifetime can determine the ultraheavy scalar mass scale. Measuring the four Yukawa couplings of the Higgs to the gauginos and higgsinos precisely tests for high-scale SUSY. These ideas, if confirmed, will demonstrate that supersymmetry is present but irrelevant for the hierarchy problem — just as it has been irrelevant for the cosmological constant problem — strongly suggesting the existence of a fine-tuning mechanism in nature.