Supersymmetric naturalness beyond MSSM

Archil Kobakhidze,Matthew Talia

doi:10.1007/jhep08(2019)105

Abstract

The experiments at the Large Hadron Collider (LHC) have pushed the limits on masses of supersymmetric particles beyond the ∼TeV scale. This compromises naturalness of the simplest supersymmetric extension of the Standard Model, the minimal supersymmetric Standard Model (MSSM). In this paper we advocate that perhaps the current experimental data are actually hinting towards the physics beyond MSSM. To illustrate this, we treat the MSSM as a low-energy limit of a more fundamental yet unspecified theory at a scale Λ, and compute the fine-tuning measure Δ for generic boundary conditions with soft SUSY breaking parameters and various cut-off scales. As a general trend we observe reduction in fine-tuning together with lowering Λ. In particular, perfectly natural [Δ ≲ mathcal{O} (10)] theories with a multi-TeV spectrum of supersymmetric particles that are consistent with all current observations can be obtained for Λ ∼ mathcal{O} (100)TeV. The lowering of the fine-tuning for large cut-off scales can also be observed in theories exhibiting special quasi-fixed point behaviour for certain parameters. Our observations call for a more thorough exploration of possible alternative ultraviolet completions of MSSM.

Highlights

JHEP08(2019)105 as well as the effects of higher-dimensional irrelevant operators which are expected to be important at energies Λ
As a general trend we observe the reduction of fine-tuning with lowering Λ from ∆ ∼ O(100) to ∆ ∼ O(10), which may hint towards physics beyond the minimal supersymmetric Standard Model (MSSM) at a scale ∼ 100 TeV.1
The effective running parameters evaluated at the cut-off scale Λ we identify as the “fundamental” parameters of the effective MSSM

Summary

Supersymmetric naturalness

We consider the MSSM as an effective low-energy approximation of an unspecified ultraviolet theory with a cut-off scale Λ. One assumes that the physics beyond the MSSM enters at a low enough scale Λ such that the “fundamental” parameters do not evolve significantly when running down to low energies In this case, if the fundamental theory is such that no significant fine tuning is required to satisfy the minimization condition (2.2), the RG running cannot destabilize the relation (2.2). Upon computing the beta-functions for yt and g3 up to one-loop and without electroweak contribution, one finds an infrared stable point at yt2/g32 = 7/18 of the corresponding RG equations This procedure has been carried out for other couplings and soft-masses in the MSSM [8,9,10]. We allow more generic variation of fundamental parameters at the high energy scale Λ rather than focusing on model-dependent correlations (such as in grand unified theories) among them

Parameter scan

MSSM quasi infrared fixed-point and fine-tuning

Conclusions