A new (string motivated) approach to the little hierarchy problem

We point out that in theories where the gravitino mass, M3/2, is in the range (10-50) TeV, with soft-breaking scalar masses and trilinear couplings of the same order, there exists a robust region of parameter space where the conditions for electroweak symmetry breaking (EWSB) are satisfied without large imposed cancellations. Compactified string/M-theory with stabilized moduli that satisfy cosmological constraints generically require a gravitino mass greater than about 30 TeV and provide the natural explanation for this phenomenon. We find that even though scalar masses and trilinear couplings (and the soft-breaking B parameter) are of order (10-50) TeV, the Higgs vev takes its expected value and the μ parameter is naturally of order a TeV. The mechanism provides a natural solution to the cosmological moduli and gravitino problems with EWSB.