Connecting (Supersymmetry) LHC Measurements with High Scale Theories
  If supersymmetry is discovered at the LHC, the measured spectrum of superpartner masses and couplings will allow us to probe the origins of supersymmetry breaking. However, to connect the collider-scale Lagrangian soft parameters to the more fundamental theory from which they arise, it is usually necessary to evolve them to higher scales. The apparent unification of gauge couplings restricts the possible forms of new physics above the electroweak scale, and suggests that such an extrapolation is possible. Even so, this task is complicated if the low scale spectrum is not measured completely or precisely, or if there is new physics at heavy scales beyond the reach of collider experiments. In this work we study some of these obstacles to running up, and we investigate how to get around them. Our main conclusion is that even though such obstacles can make it very difficult to accurately determine the values of all the soft parameters at the high scale, there exist a number of special combinations of the soft parameters that can avoid these difficulties. We also present a systematic application of our techniques in an explicit example. 
Gordon L. Kane, Piyush Kumar, David E. Morrissey, Manuel Toharia