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.
A non anomalous horizontal U (1)H gauge symmetry can be responsible for the fermion mass hierarchies of the minimal supersymmetric standard model. Imposing the consistency conditions for the absence of gauge anomalies yields the following results: i) unification of leptons and down-type quarks Yukawa couplings is allowed at most for two generations. ii) The µ term is necessarily somewhat below the supersymme-try breaking scale. iii) The determinant of the quark mass matrix vanishes, and there is no strong CP problem. iv) The superpotential has accidental B and L symmetries. The prediction mup = 0 allows for an unambiguous test of the model at low energy. One of the most successful ideas in modern particle physics is that of local gauge symmetries. A huge amount of data is beautifully explained in terms of the standard model (SM) gauge group G SM = SU (3) C × SU (2) L × U (1) Y. Identifying this symmetry required a lot of experimental and theoretical efforts, since SU (2) L × U (1) Y is hidden and color is confined. Today we understand particle interactions but we do not have any deep clue in understanding other elementary particle properties, like fermion masses and mixing angles. The SM can only accommodate but not explain these data. Another puzzle is why CP is preserved by strong interactions to an accuracy < 10 −9. One solution is to postulate that one quark is massless, but within the SM there are no good justifications for this. Adding supersymmetry does not provide us with any better understanding of these issues. In contrast, it adds new problems. A bilinear coupling for the down-type and up-type Higgs superfields µφ d φ u is allowed both by supersymmetry and by the gauge symmetry. However, phenomenology requires that µ should be close to the scale where these symmetries are broken. With supersymmetry, several operators that violate baryon (B) and lepton (L) numbers can appear. However , none of the effects expected from these operators has ever been observed. Since a few of them can induce fast proton decay, they must be very suppressed or absent. Relying on the gauge principle, in this paper we attempt to gain insight into these problems. We extend minimally G SM with a non anomalous horizontal Abelian U (1) H factor. An unambiguous prediction of the non anomalous U (1) H is a massless up-quark. This represents the crucial low energy test of our framework. Shall future lattice computations rule out m up = 0 [1], the whole idea will have to be abandoned. To explain the fermion mass pattern we follow the approach originally suggested by Froggatt and Nielsen (FG) [2]. U (1) H forbids most of the fermion Yukawa couplings. The symmetry is spontaneously broken by the vacuum expectation value (VEV) of a SM singlet field S, giving rise to a set of effective operators that couple the SM fermions to the electroweak Higgs field. The hierarchy of fermion masses results from the dimensional hierarchy among the various higher order operators. This idea was recently reconsidered by several groups, both in the context...
The doublet-triplet splitting problem in supersymmetric grand unified theories is elegantly solved in a supersymmetric SO(10) GUT ×SO(6) H model. In this model, the gauginos in the supersymmetric standard model do not respect the usual GUT gaugino mass relation. We point out that in spite of non-unified gaugino masses there is one nontrivial relation among gaugino masses in the model. Thus, it can be used to test the model in future experiments.
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