Fine tuning as an indication of physics beyond the MSSM

TL;DR

This paper explores how higher dimensional operators can significantly reduce the fine tuning required in the MSSM to achieve the electroweak scale, suggesting the presence of new physics at high scales.

Contribution

It provides analytical formulas for electroweak fine-tuning in the MSSM with higher dimensional operators, including quantum corrections, and discusses implications for new physics.

Findings

Fine tuning can be reduced to Delta<10 with new physics.

New physics scale M_* can be 30-65 times the Higgsino mass.

States like gauge singlets or SU(2) triplets may generate these operators.

Abstract

We investigate the amount of fine tuning of the electroweak scale in the presence of new physics beyond the MSSM, parametrized by higher dimensional operators. We show that these significantly reduce the MSSM fine tuning to Delta<10 for a Higgs mass between the LEPII bound and 130 GeV, and a corresponding scale M_* of new physics as high as 30 to 65 times the Higgsino mass. If the fine-tuning criterion is indeed of physical relevance, the findings indicate the presence of new physics in the form of new states of mass of O(M_*) that generated the effective operators in the first instance. At small $\tan\beta$ these states can be a gauge singlet or a SU(2) triplet. We derive analytical results for the EW scale fine-tuning for the MSSM with higher dimensional operators, including the quantum corrections which are also applicable to the pure MSSM case in the limit the coefficients of the higher dimension operators vanish. A general expression for the fine-tuning is also obtained for an arbitrary two-Higgs doublet potential.