The Well-Tempered Neutralino

TL;DR

Arkani-Hamed, Delgado, and Giudice address the challenge that LEP constraints make the thermal relic density a finely-tuned outcome in low-energy SUSY, rather than a robust prediction. They introduce the well-tempered neutralino as the boundary state between pure Bino and Higgsino or Bino and Wino, capable of reproducing the observed dark-matter density in realistic parameter spaces, and they derive analytic and numerical results for these mixtures, including the impact of high-energy boundary conditions. A key contribution is showing how conventional high-scale scenarios, notably anomaly mediation and gaugino unification, can realize the well-tempered condition via threshold corrections when mu is large, with Split Supersymmetry providing a natural framework (SMS) where this occurs. The work outlines distinctive collider and EDM phenomenology, such as quasi-degenerate neutralinos/charginos and gluino-related signals, making well-tempered neutralinos a testable bridge between dark matter and high-scale SUSY-breaking structure.

Abstract

The dark-matter prediction is usually considered as one of the successes of low-energy supersymmetry. We argue that, after LEP constraints are taken into account, the correct prediction for the dark-matter density, at a quantitative level, is no longer a natural consequence of supersymmetry, but it requires special relations among parameters, highly sensitive to small variations. This is analogous to the problem of electroweak-symmetry breaking, where the correct value of the Z mass is obtained only with a certain degree of fine tuning. In the general parameter space of low-energy supersymmetry, one of the most plausible solution to reproduce the correct value of the dark-matter density is the well-tempered neutralino, which corresponds to the boundary between a pure Bino and a pure Higgsino or Wino. We study the properties of well-tempered neutralinos and we propose a simple limit of split supersymmetry that realizes this situation.

Figures (5)

• Figure 1: The three bands show the contribution to $\Omega h^2$ from pure Bino LSP with $0.3<M_1/m_{{\tilde{e}}_R}<0.9$ (red band), Higgsino LSP with $1.5<m_{\tilde{t}}/\mu<\infty$ (blue band) and Wino LSP with $1.5<m_{{\tilde{\ell}}_L}/M_2<\infty$ (green band).
• Figure 2: The parameters of the well-tempered $\tilde{B}$/$\tilde{H}$ consistent with the dark-matter constraint within 2$\sigma$. We have taken $\tan\beta=2$, $m_H=115\hbox{\rm,GeV}$, and heavy supersymmetric scalars, and chosen the convention $M_1>0$. We have considered only $|\mu|>100\hbox{\rm,GeV}$, to satisfy the experimental limit on chargino masses.
• Figure 3: The bands show the parameters of the well-tempered $\tilde{B}$/$\tilde{W}$ consistent with the dark-matter constraint within 2$\sigma$. We have taken heavy supersymmetric scalars.
• Figure 4: The relation between $\mu$, $m_A$ and $m_{3/2}$ necessary to obtain a well-tempered $\tilde{B}$/$\tilde{W}$ with $0<(|M_2|-|M_1|)/|M_2|<0.1$, assuming gaugino masses from anomaly mediation.
• Figure 5: The ratio $M_{\tilde{g}}/|M_2|$ between the gluino pole mass and the gaugino mass as a function of $\tilde{m} /|M_2|$ for $\tan\beta =1$, assuming the well-tempered $\tilde{B}$/$\tilde{W}$ relation in the negative-$\mu$ branch ($M_1=M_2$) and the positive-$\mu$ branch ($M_1=-M_2$). The curves start from the minimum value of $\tilde{m} /|M_2|$ determined by eq. (\ref{['flop']}).