Natural ranges of supersymmetric signals

TL;DR

The paper analyzes the naturalness problem for supersymmetry in light of LEP2 bounds, using a Monte Carlo sampling approach to map how naturalness shapes the allowed sparticle spectra across minimal and non-minimal SUSY-breaking frameworks, including gauge mediation. It finds that b to s gamma remains a robust minimal SUSY signal across scenarios, even when a sizable fraction of colored superpartners exceed the TeV scale, and it quantifies the likelihood of various SUSY loop effects, both within minimal models and under non-minimal flavor structures. The work highlights how naturalness considerations constrain model-building and shape expectations for collider and flavor phenomenology, with notable implications for LFV processes like $\mu \to e\gamma$, EDMs, and CP-violating observables, as well as for upcoming experiments probing $a_\mu$ and $B$-physics. Overall, the study provides a framework to assess how accidental cancellations might reconcile SUSY with current bounds while outlining signatures that could reveal SUSY effects before the LHC, or motivate more natural, non-conventional constructions.

Abstract

The LEP2 experiments pose a serious naturalness problem for supersymmetric models. The problem is stronger in gauge mediation than in supergravity models. Particular scenarios, like electroweak baryogenesis or gauge mediation with light messengers, are strongly disfavoured. Searching a theoretical reason that naturally explains why supersymmetry has not been found poses strong requests on model building. If instead an unlikely (p\approx 5%) numerical accident has hidden supersymmetry to LEP2, we compute the naturalness distribution of values of allowed sparticle masses and supersymmetric loop effects. We find that b to s gamma remains a very promising signal of minimal supersymmetry even if there is now a 20% (4%) probability that coloured particles are heavier than 1 TeV (3 TeV). We study how much other effects are expected to be detectable.

Figures (8)

• Figure 1: The naturalness problem in a typical supersymmetric model. We plot the chargino mass in GeV as function of $\mu/M_2$, that is the only free parameter of the model under consideration. Values of $\wp$ marked in gray are unphysical, while color cmyk 0 0.46 0.50 0.3 light graycolor cmyk 0 0 0 1. regions have too light sparticles. Only the small white vertical band remain experimentally acceptable.
• Figure 2: Scatter plot with sampling density proportional to the naturalness probability. The area shaded in color cmyk 0 0.46 0.50 0.3 light graycolor cmyk 0 0 0 1. (color cmyk 0 0.50 0.70 0.25 dark graycolor cmyk 0 0 0 1.) in fig.s \ref{['fig:MassePallini']}a,b correspond to regions of each plane excluded at LEP2 (at LEP1), while the area shaded in color cmyk 0 0.46 0.50 0.3 light graycolor cmyk 0 0 0 1. in fig. \ref{['fig:MassePallini']}c has been excluded at Tevatron. The color cmyk 0 1. 1. 0.2 dark graycolor cmyk 0 0 0 1. (black) points correspond to sampling spectra excluded at LEP2 (at LEP1). Only the color cmyk 0.92 0 0.59 0.5 light graycolor cmyk 0 0 0 1. points in the unshaded area satisfy all the accelerator bounds. Points with unbroken electroweak symmetry are not included in this analysis.
• Figure 3: Naturalness distribution of sparticle masses in minimal supergravity. Allowed spectra contribute only with the small tails in color cmyk 0.92 0 0.59 0.5 dark graycolor cmyk 0 0 0 1.. The remaining 95% of the various bell-shaped distributions is given by points excluded at LEP2 (in color cmyk 0 1. 1. 0.2 medium graycolor cmyk 0 0 0 1.) or at LEP1 (in color cmyk 0 0.46 0.50 0.3 light graycolor cmyk 0 0 0 1.). On the vertical axes on each plot the particle masses in GeV are reported ($\tan\beta$ in the first plot). With 'squark' and 'slepton' me mean the lightest squark and slepton excluding the third generation ones, that have weaker accelerator bounds.
• Figure 4: Naturalness distribution of some illustrative supersymmetric particle masses (on the horizontal axis) in unified supergravity, under the hypothesis that supersymmetry has not be found at LEP2 due to a numerical accident. The three color cmyk 1. 1. 0.3 0 continuous linescolor cmyk 0 0 0 1. are the three gauginos ($M_N$, $M_\chi$ and $M_{\tilde{g}}$ from left to right). The color cmyk 1. 0 0 0.5 thin dashed linecolor cmyk 0 0 0 1. is the lightest slepton and the color cmyk 0 1. 1. 0.5 thick dashed linescolor cmyk 0 0 0 1. are the lightest stop (left) and squark (right). The color cmyk 0 0.63 0 0.3 dotted linescolor cmyk 0 0 0 1. are the light and charged higgs. The distribution of $\tan\beta$ is not shown because similar to the one in fig. \ref{['fig:MasseCampane']}.
• Figure 5: Contour plot of the fine-tuning parameter $\Delta$ in gauge mediation models in the plane $(M_{\rm GM},\eta)$ for $\mu<0$ (left) and $\mu>0$ (right). In the (color cmyk 0 1. 1. 0.5 dark graycolor cmyk 0 0 0 1., white, color cmyk 0.92 0 0.59 0.5 light graycolor cmyk 0 0 0 1.) area at the (left, center, right) of each picture the strongest experimental constraint is the one on the mass of the lightest (neutralino, right handed slepton, chargino). Values of $\eta$ in the gray area below the lower dashed lines and above the upper dashed lines are not allowed in models with only one SUSY-breaking singlet.