The fine-tuning price of LEP

Abstract

We quantify the amount of fine tuning of input parameters of the Minimal Supersymmetric Extension of the Standard Model (MSSM) that is needed to respect the lower limits on sparticle and Higgs masses imposed by precision electroweak measurements at LEP, measurements of $b\to X_sγ$, and searches at LEP 2. If universal input scalar masses are assumed in a gravity-mediated scenario, a factor of $\gappeq180$ is required at $\tanβ\sim1.65$, decreasing to $\sim20$ at $\tanβ\sim10$. The amount of fine tuning is not greatly reduced if non-universal input scalar Higgs masses are allowed, but may be significantly reduced if some theoretical relations between MSSM parameters are assumed.

Figures (5)

• Figure 1: The price of fine tuning for tan$\beta = 1.65$, assuming universal input scalar masses at the supergravity scale. Panel (a) displays the regions of the $(\mu, M_2)$ plane that are allowed by LEP 2, and the restricted regions permitted when the other constraints discussed in the text are implemented. The other panels display the ranges of the fine-tuning parameter $\Delta$ obtained as functions of (b) the Higgs mixing parameter $\mu$, (c) the input gaugino mass parameter $M_{1/2}$, (d) the ratio of the universal scalar mass $m_0$ to $M_{1/2}$, (e) the CP-odd neutral Higgs mass $M_A$, and (f) the lightest neutral Higgs mass $M_h$.
• Figure 2: As for Fig. 1, but for the value $\tan\beta = 2.5$. Black stars in panel (a) correspond to points with $\Delta<100$.
• Figure 3: As for Figs. 1 and 2, but for the value $\tan\beta = 10$. Black stars in panel (a) again correspond to points with $\Delta<100$.
• Figure 4: Compilation of the minimal values of the fine-tuning parameter $\Delta$ as a function of tan$\beta$. The left panel is for the case of universal scalar masses, with the current constraints from LEP, $b\rightarrow X_s\gamma$, etc., shown as a solid line. The dashed line is for the constraints that were available after the initial runs of LEP 1, and the dotted line indicates what might be the situation if no evidence for sparticles or MSSM Higgs bosons is found with future upgrades of LEP 2. The right panel shows the corresponding lower limits on $\Delta$ for the case of non-universal Higgs masses, using the same conventions for the lines.
• Figure 5: As for Fig. 1, but now with non-universal input scalar masses for the Higgs multiplets: $m^2_{H_i} \neq m^2_0$, $i = 1,2$. In panel (a), only points with $\Delta_{max}<500$ are displayed.