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

TL;DR

This paper formulates a quantitative naturalness framework for the MSSM by introducing a fine-tuning measure $\gamma$ that gauges how sensitively the $Z$-boson mass and other observables depend on fundamental parameters. Using a 1-loop effective potential and RG running to enforce radiative electroweak symmetry breaking, the authors scan a 4+1 dimensional parameter space under collider and precision constraints to map natural regions. They find that naturalness can accommodate weak-scale stability even if LEP II or the Tevatron see no superpartners, but not if squarks and gluinos lie beyond LHC reach; the most natural spectra typically lie below the TeV scale with $m_{\tilde{\chi}^\pm}$ around 50 GeV and $m_{\tilde{q}}$, $m_{\tilde{g}}$ in a few hundred GeV, though upper bounds can extend to several hundred GeV for certain sparticles. The results imply that natural SUSY scenarios often yield sparticles accessible at current or near-future colliders, emphasizing the role of naturalness in guiding collider searches and interpreting null results.

Abstract

Superpartner masses cannot be arbitrarily heavy if supersymmetric extensions of the standard model explain the stability of the gauge hierarchy. This ancient and hallowed motivation for weak scale supersymmetry is often quoted, yet no reliable determination of this upper limit on superpartner masses exists. In this paper we compute upper bounds on superpartner masses in the minimal supersymmetric model, and we identify which values of the superpartner masses correspond to the most natural explanation of the hierarchy stability. We compare the most natural value of these masses and their upper limits to the physics reach of current and future colliders. As a result, we find that supersymmetry could explain weak scale stability naturally even if no superpartners are discovered at LEP II or the Tevatron (even with the Main Injector upgrade). However, we find that supersymmetry cannot provide a complete explanation of weak scale stability, if squarks and gluinos have masses beyond the physics reach of the LHC. Moreover, in the most natural scenarios, many sparticles, for example, charginos, squarks, and gluinos, lie within the physics reach of either LEP II or the Tevatron. Our analysis determines the most natural value of the chargino (squark) ((gluino)) mass consistent with current experimental constraints is $\sim$ 50 (250) ((250)) GeV and the corresponding theoretical upper bound is $\sim$ 250 (700) ((800)) GeV.