Natural effective supersymmetry

Much heavier sfermions of the first-two generations than the other superpar ticles provide a natural explanation for the flavor and CP problems in the supersymmetric Standard Model (SUSY SM). However, the heavy sfermions may d rive the mass squareds for the light third generation sfermions to be negat ive through two-loop renormalization group (RG) equations, breaking color a nd charge. Introducing extra matters to the SUSY SM, it is possible to cons truct models where the sfermion masses are RG invariant at the two-loop lev el in the limit of vanishing gaugino-mass and Yukawa-coupling contributions . We calculate the finite corrections to the light sfermion masses at the t wo-loop level in the models. We find that the finite corrections to the lig ht-squark mass squareds are negative and can be less than (0.3-1)% of the h eavy-squark mass squareds, depending on the number and the parameters of th e 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-t ype squarks of the first-two generations have common U(l)(X) charges, the s upersymmetric contributions to Delta m(K) and epsilon(K) are sufficiently s uppressed without spoiling naturalness, even if the flavor-violating superg ravity 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 ). (C) 2000 Elsevier Science B.V. All rights reserved.