A discrete R-symmetry often appears as an exact gauge symmetry in the low energy effective theory of superstring theories. We search for such discrete Rsymmetries from a phenomenological point of view and find that Z 9R and Z 18R are candidates of the nonanomalous R-symmetry in the case of the minimal supersymmetric standard model. We also find Z 4R and Z 20R in the case that quarks and leptons are embedded in the SU(5) GUT multiplets. Interesting is that in the latter case all the solutions predict some extra matter multiplets and we find that the simplest choice of the extra matters is to take a pair of 5 and 5 * of SU(5) GUT whose mass is of order the SUSY breaking scale ∼ 1 TeV. We emphasize that the presence of such extra matters is testable in future hadron collider experiments.
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 twoloop 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 ∆m K and ǫ 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 ∆m K and ǫ K are sufficiently suppressed without spoiling naturalness, even if the flavorviolating 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 ∆m K naturally, but evading the bound from ǫ K requires the CP phase smaller than 10 −2 .
Considering that the soft SUSY breaking scalar masses come from a vacuum expectation value of the D-term for an external gauge multiplet, the renormalization of the scalar masses is related to the gauge anomaly. Then, if the external gauge symmetry is anomaly-free and has no kinetic mixing with the other U(1) gauge symmetries, the scalar masses are non-renormalized at all orders assuming that the gaugino masses are negligibly small compared with the scalar masses. Motivated by this, we construct models where the sfermion masses for the first-two generations are much heavier than the other superparticles in the minimal SUSY standard model in a framework of the anomalous U(1) mediated SUSY breaking. In these models we have to introduce extra chiral multiplets with the masses as large as those for the first-two generation sfermions. We find that phenomenologically desirable patterns for the soft SUSY breaking terms can be obtained in the models.
We discuss the anomalous U͑1͒ gauge symmetry as a mechanism of generating the grand-unification ͑GU͒ scale. We conclude that unification to a simple group cannot be realized unless some parameters are ''tuned,'' and that models with product gauge groups are preferred. We consider the ''R-invariant natural unification'' model with gauge groups SU(5) GUT ϫU(3) H . In this model the doublet-triplet splitting problem is solved and the unwanted GU theory ͑GUT͒ relation m s ϭm is avoided maintaining m b ϭm . Moreover, R invariance suppresses the dangerous proton decays induced by dimension four and five operators. ͓S0556-2821͑99͒01219-9͔ PACS number͑s͒: 12.10.Dm, 12.15.Ff, 12.60.Jv M * ⌺Ј 2 , ͑2͒where parameters, 's, are assumed to be of order unity. There is a desirable SUSY vacuum which breaks SU͑5͒ down to SU(3) C ϫSU(2) L ϫU(1) Y , 1 There are several attempts to generate the hierarchy M GUT /M * ͓4͔.2 The last term is necessary to give masses for (3,2 Ã ) and (3 Ã ,2) components in ⌺Ј, since (3,2 Ã ) and (3 Ã ,2) in ⌺ are absorbed into broken gauge bosons.
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