Supersymmetry, naturalness, and signatures at the CERN LHC

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 $\tan \beta$, and a small $\mu$ parameter. 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.