1208.1737 (Chris Wymant)

Optimising Stop Naturalness    [PDF]

Chris Wymant

In supersymmetric models the average stop mass $\MS$ is well known to contribute both to the lightest Higgs boson mass $m_{h}$ and to the level of unnaturalness in radiative electroweak-symmetry breaking (REWSB). The same is true of the stop trilinear mixing term $A_t$, though its role in naturalness receives rather less attention. We address this issue in this note by using Lagrange constrained maximisation to optimise radiative corrections to $m_{h}$ for a constant REWSB term $\delta m_{H_u}^2$ in the MSSM. The ratio $A_t^2/\MS^2$ is robustly predicted to be close to maximal mixing: $\sim5-6$. Experimental uncertainties alone (on the top and Higgs masses) may prevent any inference of the $\MS^2$ associated with a given Higgs mass, mixing parameter and $\tan\beta$. We also emphasise that a fair comparison of how easily different models can reach a particular $m_{h}$ should attempt to maximise $m_{h}$ with respect to some upper-bounded measure of naturalness, and not simply compare stop masses. For example with respect to the leading-log $\delta m_{H_u}^2$, maximal-mixing scenarios are as natural as no-mixing scenarios with stops twice as heavy.

View original: http://arxiv.org/abs/1208.1737