Superpotential Couplings Research Articles

Unitarity constraints on grand unified models.

We present a simplified method for the calculation of low-energy unitarity constraints on grand unified broken-supersymmetric models based on the Goldstone-boson equivalence theorem for high-energy scattering in gauge theories, the fermion-boson equivalence theorem for supersymmetric theories, and the evolution of couplings under the renormalization group. We apply the method to the flipped SU(5)\ifmmode\times\else\texttimes\fi{}U(1) superstring model, obtain high-energy unitarity constraints at the grand unified scale ${M}_{G}=4\ifmmode\times\else\texttimes\fi{}{10}^{16}$ GeV, and then use the renormalization-group equations to evolve the constraints to the low-energy mass scale ${M}_{W}$. We investigate the peculiarities of the renormalization-group flow and the existence of critical surfaces at which the scalar superpotential couplings diverge at ${M}_{G}$. We find upper bounds on the superpotential couplings at low energies and use these to establish absolute upper bounds on the top-quark mass, ${m}_{t}\ensuremath{\lesssim}200$ GeV, and on the lightest neutral-Higgs-boson mass, ${M}_{{H}_{1}^{0}}\ensuremath{\lesssim}155$ GeV in the SU(5)\ifmmode\times\else\texttimes\fi{}U(1) model. We also obtain an upper bound on ${M}_{{H}_{1}^{0}}$ as a function of ${m}_{t}$ which shows that ${M}_{{H}_{1}^{0}}\ensuremath{\lesssim}125$ GeV for favored values of the ratios of Higgs vacuum expectation values.

Some exact results on the superpotential from Calabi-Yau compactifications

We prove that certain superpotential couplings in compactified string theories are given exactly by the values calculated at sigma-model tree level. In particular, the 27 3 coupling in (2,2) compactifications is a coupling of this sort. We explicitly check our results by examining the couplings in an exactly soluble model proposed by Gepner as a particular point in the moduli space of (2,2) compactifications on Y 4; 5. We thus determine the exact values of the normalized 27 3 couplings for any value of the radius of Y 4; 5.

An improved flipped SU(5)×U(1) model from the four-dimensional string

We discuss a four-dimensional string model whose effective field theory is a supersymmetric flipped SU(5)×U(1) GUT with the following properties. • - The quark and lepton mass matrices have a hierarchical structure and all Cabibbo-Kobayashi-Maskawa mixing angles can be non-zero. • - There is a natural splitting of Higgs doublets and triplets. • - A novel seesaw mechanism gives light left-handed neutrinos. • - The gauge group is reduced to the standard model SU(3) C×SU(2) L×U(1) Y at a large mass scale close to M P . Extensive use is made of non-renormalizable superpotential couplings which may arise from couplings to identifiable massive modes, and are restricted by an R symmetry and the requirements of flatness is some field directions.

On the particle spectrum of E(6) superstrings

The allowed parameter space of a superstring-inspired supergravity model with one additional neutral gauge boson Z′ is investigated in detail, under the assumption that no intermediate scale exists and that the supersymmetry breaking in the visible sector can be parameterized by m 0, m 1 2 and A as in usual supergravity models. It is shown that the model allows for large Yukawa couplings and thus a relatively small supersymmetry breaking scale. Additional superpotential couplings which do not involve Higgs superfields allow to reduce slepton and squark masses even further. Therefore, sparticle masses can lie well within the range of the SLC, Tevatron, and LEP even if the Z′-boson is very heavy. Bounds on the masses of exotic fermions and the total decay width of the Z′ are also given.

Problems for superstring models with vacuum expectation values for conjugate sneutrinos

Superstring models compactified on Calabi-Yau manifolds contain two new neutral scalars in each 27 generation of chiral supermultiplets. We consider implications of a vacuum expectation value for one of the neutral scalars, the conjugates neutrino ν L c :〈0|; ν L c |;0〉  y . Apart from a coupling from a coupling which generates a Dirac neutrino mass and which must be small [⪅ O(10 −9)], its only superpotential interaction is with D Ld L, so there would be D-d mixing if y ≠ 0. The fact that m d is not much less than m e or m u then tells us that y ⪅ O (few TeV). When the four-dimensional gauge group has rank 5, a pseudo-Goldstone boson, a ν , arises if y ≠ 0, and the D-d mixing would then induce the decay K → π + a ν at an unacceptable rate. Regardless of the gauge group rank, we show that the combined constraints on D-d mixing, and on the flavour-changing neutral currents it would induce, are sufficient to rule out D Ld L c ν L c superpotential coupling large enough to produce 〈0|; ν L c |;0〉 ≠ 0 . These problems are avoided in models with a rank-5 gauge group and 〈0|; ν L c |;0〉 ⪅ 40 KeV .

A modest proposal for generating Yukawa couplings from gauge interactions

We propose that the quark and lepton Yukawa superpotential couplings to Higgs supermultiplets arise from non-perturbative gauge interactions. This is possible in models with an SU( N) × G gauge group. We present a three-generation model based on SU(8) × G, and indicate how such a scenario could lead to a realistic hierarchy of quark and lepton masses.