Naturally heavy superpartners and a Little Higgs
  We construct an extension of the MSSM in which scalar superpartners can naturally be as heavy as 1 TeV. In the MSSM, the most significant fine tuning stems from the logarithmically enhanced top-stop loop contribution to the soft Higgs mass. We combine supersymmetry with the "simplest little Higgs" to render this loop finite, thereby removing the large logarithm even in models in which superpartner masses are generated at high scales such as in supergravity. Our model predicts an extended Higgs sector, superpartner masses near a TeV and little Higgs partners at a few TeV. 
Tuhin Roy, Martin Schmaltz