Naturalness and superpartner masses or when to give up on weak scale supersymmetry

Naturalness in low-scale SUSY models and "non-linear" MSSM

In MSSM models with various boundary conditions for the soft breaking terms ([Formula: see text]) and for a Higgs mass of 126 GeV, there is a (minimal) electroweak fine-tuning [Formula: see text] to [Formula: see text] for the constrained MSSM and [Formula: see text] for non-universal gaugino masses. These values, often regarded as unacceptably large, may indicate a problem of supersymmetry (SUSY) breaking, rather than of SUSY itself. A minimal modification of these models is to lower the SUSY breaking scale in the hidden sector ([Formula: see text]) to few TeV, which we show to restore naturalness to more acceptable levels [Formula: see text] for the most conservative case of low [Formula: see text] and ultraviolet boundary conditions as in the constrained MSSM. This is done without introducing additional fields in the visible sector, unlike other models that attempt to reduce [Formula: see text]. In the present case [Formula: see text] is reduced due to additional (effective) quartic Higgs couplings proportional to the ratio [Formula: see text] of the visible to the hidden sector SUSY breaking scales. These couplings are generated by the auxiliary component of the goldstino superfield. The model is discussed in the limit its sgoldstino component is integrated out so this superfield is realized non-linearly (hence the name of the model) while the other MSSM superfields are in their linear realization. By increasing the hidden sector scale [Formula: see text] one obtains a continuous transition for fine-tuning values, from this model to the usual (gravity mediated) MSSM-like models.

Multi-TeV scalars are natural in minimal supergravity

For a top quark mass fixed to its measured value, we find natural regions of minimal supergravity parameter space where all squarks, sleptons, and heavy Higgs scalars have masses far above 1 TeV and are possibly beyond the reach of the Large Hadron Collider at CERN. This result is simply understood in terms of "focus point" renormalization group behavior and holds in any supergravity theory with a universal scalar mass that is large relative to other supersymmetry breaking parameters. We highlight the importance of the choice of fundamental parameters for this conclusion and for naturalness discussions in general.