Naturalness Implications of LEP Results

TL;DR

Kane and King address naturalness in light of LEP results without enforcing universal soft SUSY-breaking inputs. They show that the dominant fine-tuning sensitivity arises from the SU(3) gaugino mass $M_3(0)$, allowing a relatively light gluino ($m_{ ilde g} \\lesssim 350$ GeV) or specific correlations with the Higgs sector (e.g., $m_{H_U}(0) \\approx 2 M_3(0)$) to mitigate tuning. The LEP Higgs constraint, especially at low $ an\beta$, interplays with stop masses through radiative corrections, linking Higgs mass bounds to gluino thresholds and fine-tuning. Using a non-universal MSSM framework (MRM) with RG running, the authors provide both analytic and numerical evidence that non-universal gaugino masses or relations among soft terms can significantly reduce tuning, offering concrete directions for collider tests and implications for high-scale physics.

Abstract

We analyse the fine-tuning constraints arising from absence of superpartners at LEP, without strong universality assumptions. We show that such constraints do not imply that charginos or neutralinos should have been seen at LEP, contrary to the usual arguments. They do however imply relatively light gluinos $(m_{\tilde g} \lsim 350 GeV)$ and/or a relation between the soft-breaking SU(3) gaugino mass and Higgs soft mass $m_{H_U}$. The LEP limit on the Higgs mass is significant, especially at low $\tan β$, and we investigate to what extent this provides evidence for both a lighter gluino and correlations between soft masses.

Figures (2)

• Figure 1: The Higgs mass $m_h$ (in GeV) (solid) and fine-tuning parameter $\Delta_{\mu(0)}$ (dashes) as a function of $\tan \beta$. The upper to lower curves correspond to $M_3(0)=200,150,100$ GeV. Apart from the gluino mass we use universal parameters $m_0=100$ GeV, $M_{1,2}(0)=200$ GeV in each case. Note the large decrease in the measure of fine-tuning as $M_3(0)$ decreases.
• Figure 2: The Higgs mass $m_h$ (in GeV) (solid) and fine-tuning parameters (dashes) $\Delta_{\mu(0)}$, $\Delta_{M_3(0)}$, $\Delta_{m_{H_U}^2(0)}$ as a function of $\tan \beta$, for two parameter sets. The first parameter set corresponds to $M_3(0)=m_0=100$ GeV, $M_{1,2}(0)=200$ GeV and the second parameter set has all parameters unchanged apart from a larger second Higgs mass parameter $m_{H_U}(0)=200$ GeV. The $m_h$, $\Delta_{\mu(0)}$ curves are obviously identified by comparison to Figure \ref{['tanb1']}. In fact the uppermost values of $m_h$, $\Delta_{\mu(0)}$ in this Figure correspond exactly to the lowermost values in Figure \ref{['tanb1']} which also uses the first parameter set here; note the change of scale for $\tan \beta$. The four remaining dashed lines correspond to $\Delta_{M_3(0)}$ (higher pair) and $\Delta_{m_{H_U}^2(0)}$ (lower pair), where now $m_{H_U}(0)=200$ GeV gives the upper curve of each pair. Observe here that by increasing $m_{H_U}(0)$ relative to $M_3(0)$ there is an additional decrease in the fine-tuning parameter $\Delta_{\mu(0)}$ which is particularly relevant for small $\tan \beta$ where it may be needed.