Supersymmetry, Naturalness, and Signatures at the LHC

TL;DR

The paper argues that electroweak naturalness in the MSSM with minimal matter can be achieved if the top A-term is large and the μB term is small, yielding light stops and Higgsinos and predicting a Higgsino-like LSP with three nearly degenerate states. It develops a largely model-independent mass-determination strategy based on dilepton endpoints and kinematic variables, and demonstrates its viability through realistic Monte Carlo simulations of LHC signals. The authors show that a Higgsino LSP yields distinctive dilepton signatures and that key superpartner masses can be extracted with percent-level accuracy, enabling discrimination among SUSY-breaking scenarios such as mixed moduli–anomaly mediation. They also explore how these natural spectra connect to dark matter and offer concrete procedures to test the underlying theory using collider data and cosmological observations.

Abstract

Weak scale supersymmetry is often said to be fine-tuned, especially if the matter content is minimal. This is not true if there is a large A term for the top squarks. We present a systematic study on fine-tuning in minimal supersymmetric theories and identify low energy spectra that do not lead to severe fine-tuning. Characteristic features of these spectra are: a large A term for the top squarks, small top squark masses, moderately large tanβ, and a small μparameter. There are classes of theories leading to these features, which are discussed. In one class, which allows a complete elimination of fine-tuning, the Higgsinos are the lightest among all the superpartners of the standard model particles, leading to three nearly degenerate neutralino/chargino states. This gives interesting signals at the LHC -- the dilepton invariant mass distribution has a very small endpoint and shows a particular shape determined by the Higgsino nature of the two lightest neutralinos. We demonstrate that these signals are indeed useful in realistic analyses by performing Monte Carlo simulations, including detector simulations and background estimations. We also present a method that allows the determination of all the relevant superparticle masses without using input from particular models, despite the limited kinematical information due to short cascades. This allows us to test various possible models, which is demonstrated in the case of a model with mixed moduli-anomaly mediation. We also give a simple derivation of special renormalization group properties associated with moduli mediated supersymmetry breaking, which are relevant in a model without fine-tuning.

Figures (24)

• Figure 1: Minimal values of $m_{\tilde{t}} \equiv (m_{Q_3}^2)^{1/2} = (m_{U_3}^2)^{1/2}$ giving $M_{\rm Higgs} \mathrel{\hbox{$>$$\sim$}} 114.4~{\rm GeV}$ as a function of $A_t/m_{\tilde{t}}$. The other parameters are fixed to be $500~{\rm GeV}$ for the gaugino and sfermion masses other than $m_{Q_3}^2$ and $m_{U_3}^2$, $(500~{\rm GeV}) (A_t/m_{\tilde{t}})$ for the $A$ parameters other than $A_t$, $\tan\beta = 15$, $\mu = +170~{\rm GeV}$, and $m_A = 250~{\rm GeV}$.
• Figure 2: Contours of $\Delta^{-1}$ on the $m_0$-$M_{1/2}$ plane for the constrained mSUGRA with $A_0 = 0$ (left) and $A_0 = -3|m_0|$ (right). The sign of $\mu$ is chosen to be positive. The constraints from direct superparticle search, the Higgs boson mass bound, and the stau LSP are also shown.
• Figure 3: Contours of $\Delta^{-1}$ on the $m_0$-$M_{1/2}$ plane in the mSUGRA model with $\mu = 190~{\rm GeV}$ and $m_A = 250~{\rm GeV}$ fixed at the weak scale and $A_0 = -3|m_0|$ at $M_{\rm unif}$ (left). Contours of $\Delta^{-1}$ on the $m_{\tilde{q}}$-$M_{1/2}$ plane with $\mu > 0$ and $m_{\tilde{l}}^2 = (500~{\rm GeV})^2$, $A_0 = -|m_{\tilde{q}}|$ and $m_H^2 \equiv m_{H_u}^2 = m_{H_d}^2 = (100~{\rm GeV})^2$ at $M_{\rm unif}$, where $m_{\tilde{q}}^2$ and $m_{\tilde{l}}^2$ are the squark and slepton masses, respectively (right). In both cases $\tan\beta = 15$.
• Figure 4: Contours of $\Delta^{-1}$ on the $M_{\rm mess}$-$F/M_{\rm mess}$ plane for the minimal gauge mediation models with $n_{\rm mess} = 1$ (left) and $n_{\rm mess} = 4$ (right) pairs of messenger fields in the ${\bf 5} + {\bf 5}^*$ representation. The instability bound implies the region in which the messenger fields are tachyonic, $F/|M_{\rm mess}|^2 > 1$. The Higgs sector parameters are fixed as $\tan\beta = 15$ and $\mu > 0$.
• Figure 5: Characteristic spectra for the superparticles which give the correct scale for electroweak symmetry breaking without significant fine-tuning. The spectrum in (a) arises typically in a high scale supersymmetry breaking scenario with $\Delta^{-1} \approx 10\%$, while that in (b) arises in a theory where supersymmetry is broken by boundary conditions, or moduli contributions, with small (effective) $M_{\rm mess}$.