Is Electroweak Symmetry Breaking Still Natural in the MSSM?

TL;DR

This paper examines the naturalness of electroweak symmetry breaking in the MSSM considering recent LHC constraints, proposing a new measure that allows for larger  to still be natural.

Contribution

It introduces a novel measure of naturalness based on the separation between the radiative symmetry breaking scale and the average stop mass, challenging previous assumptions.

Findings

Electroweak symmetry breaking can be natural with large .

The key measure is the separation between the radiative breaking scale and the stop mass.

Large  does not necessarily imply unnaturalness.

Abstract

The absence of any signal of supersymmetry (SUSY) at the LHC has raised the SUSY particle mass scale compared to $Z$ boson mass $M_Z$. We investigate the naturalness of the electroweak symmetry breaking after considering radiative symmetry breaking along with 125 GeV Higgs mass. We find that the important quantity to measure the naturalness of the hierarchy between the SUSY scale and $M_Z$ is the separation between the radiative symmetry breaking scale, i.e., where $m_{H_u}^2+\mu^2$ turns negative for large $\tan\beta$ case ($\mu$ is the Higgsino mass and $m_{H_u}$ is the SUSY breaking up-type Higgs boson mass) and the average stop mass. Using this measure, one can show that the electroweak symmetry breaking can be natural even if $\mu$ is large contrary to the prevailing claim that $\mu$ is needed to be small to maintain the naturalness.