Natural Effective Supersymmetry
  Much heavier sfermions of the first-two generations than the other superparticles provide a natural explanation for the flavor and CP problems in the supersymmetric standard model (SUSY SM). However, the heavy sfermions may drive the mass squareds for the light third generation sfermions to be negative through two-loop renormalization group (RG) equations, breaking color and charge. Introducing extra matters to the SUSY SM, it is possible to construct models where the sfermion masses are RG invariant at the two-loop level in the limit of vanishing gaugino-mass and Yukawa-coupling contributions. We calculate the finite corrections to the light sfermion masses at the two-loop level in the models. We find that the finite corrections to the light-squark mass squareds are negative and can be less than (0.3-1)% of the heavy-squark mass squareds, depending on the number and the parameters of the extra matters. We also discuss whether such models realized by the U(1)_X gauge interaction at the GUT scale can satisfy the constraints from \Delta m_K and \epsilon_K naturally. When both the left- and right-handed down-type squarks of the first-two generations have common U(1)_X charges, the supersymmetric contributions to \Delta m_K and \epsilon_K are sufficiently suppressed without spoiling naturalness, even if the flavor-violating supergravity contributions to the sfermion mass matrices are included. When only the right-handed squarks of the first-two generations have a common U(1)_X charge, we can still satisfy the constraint from \Delta m_K naturally, but evading the bound from \epsilon_K requires the CP phase smaller than 10^{-2}. 
Junji Hisano, Kiichi Kurosawa, Yasunori Nomura