Supersymmetric Unification Research Articles

The CKM Matrix and Its Origin

In the context of the supersymmetric unification model in which the massless sector contains extra particles beyond those in the minimal supersymmetric standard model, we obtain mixings between quarks (leptons) and the extra particles which are closely intertwined with Yukawa hierarchies. With the assumption that the unification gauge group $G$ includes $SU(2)_R$, it is shown that the non-trivial texture of the CKM matrix originates from the extra-particle mixings. The CKM matrix of quarks emerges as a consequence of the mixings between the down-type quarks and colored Higgses, both of which are $SU(2)_L$-singlets. On the other hand, the CKM matrix of leptons is due to the mixings stemming from the seesaw mechanism with the hierarchical Majorana mass matrix of right-handed neutrinos.

The high-2 HERA anomaly and supersymmetric unification

We discuss an initial condition on the superpotential couplings of an SU(5) theory which allows the R-violating term L d^c Q but avoids the simultaneous presence of L L e^c + d^c d^c u^c. This same condition keeps under control the products of pairs of different couplings lambda_{ijk} L_i d^c_j Q_k, which are more strongly constrained by flavour-changing-neutral-current limits. In our view, this observation makes relatively more plausible the interpretation of the high-Q^2 Hera anomaly, if real, as caused by squark production.

Supersymmetric unification with radiative breaking ofRparity

We show how $R$ parity can break spontaneously as a result of radiative corrections in unified $N=1$ supergravity models. We illustrate this with a concrete rank-four unified model, where the spontaneous breaking of $R$ parity is accompanied by the existence of a physical Majoron. We determine the resulting supersymmetric particle mass spectrum and show that $R$-parity-breaking signals may be detectable at CERN LEP 200.

Gauge coupling unification and the top mass in string models with SU (4) × O (4) symmetry

We discuss the low energy implications of gauge coupling unification at the string scale, taking into account string threshold corrections in the SU (4) × O (4) model. We express sin 2 θ W and a 3 as functions of the calculable string threshold differences and discuss simple examples of spectra which retain the successful predictions of the supersymmetric unification. Using further the low energy data and reasonable values of the common gauge coupling at the string scale, we obtain the range of the threshold corrections. Finally, we study the top Yukawa coupling ( h t ) evolution whose initial value is determined in terms of the common gauge coupling at the string scale. We find that h t reaches its (quasi) infra-red fixed point at the weak scale and discuss the implications on the top mass.

Dicyclic horizontal symmetry and supersymmetric grand unification.

It is shown how to use as horizontal symmetry the dicyclic group ${Q}_{6}\ensuremath{\subset}\mathrm{SU}(2)$ in a supersymmetric unification SU(5)\ensuremath{\bigotimes}SU(5)\ensuremath{\bigotimes}SU(2) where one SU(5) acts on the first and second families, in a horizontal doublet, and the other acts on the third. This can lead to acceptable quark masses and mixings, with an economic choice of matter supermultiplets, and charged lepton masses can be accommodated.

Electric dipole moments as signals of supersymmetric unification

If supersymmetric unification is true, we show how the combined effort of several experiments under way to try to measure an electric dipole moment of the electron or of the neutron has a significant chance not only of producing a positive signal but also of providing crucial information to understand the physical origin of the signal itself.

Flavor mixing signals for realistic supersymmetric unification.

The gauge interactions of any supersymmetric extension of the standard model involve new flavor mixing matrices. The assumptions involved in the construction of minimal supersymmetric models, both $SU(3) \times SU(2) \times U(1)$ and grand unified theories, force a large degree of triviality on these matrices. However, the requirement of realistic quark and lepton masses in supersymmetric grand unified theories forces these matrices to be non-trivial. This leads to important new dominant contributions to the neutron electric dipole moment and to the decay mode $p \to K^o\mu^+$, and suggests that there may be important weak scale radiative corrections to the Yukawa coupling matrix of the up quarks. The lepton flavor violating signal $\mu \to e\gamma$ is studied in these theories when $\tan\beta$ is sufficiently large that radiative effects of couplings other than $\lambda_t$ must be included. The naive expectation that large $\tan\beta$ will force sleptons to unacceptably large masses is not borne out: radiative suppressions to the leptonic flavor mixing angles allow regions where the sleptons are as light as 300 GeV, provided the top Yukawa coupling in the unified theory is near the minimal value consistent with $m_t$.

Violations of lepton flavour and CP in supersymmetric unified theories

As a consequence of the large top quark Yukawa coupling, supersymmetric unified theories with soft supersymmetry breaking terms generated at the Planck scale predict lepton flavour and CP violating processes with significant rates. The flavour violating parameters of the low energy theory are derived in both SU(5) and SO(10) theories, and are used to calculate the rate for μ → eγ. The sensitivity of the search for μ → eγ is compared with that for μ → e conversion in atoms, τ → μγ and the electric dipole moment of the electron. The experimental search for these processes is shown to provide a very significant test of supersymmetric unification, especially in SO(10) but also in SU(5).

Grand unification scale effects in supersymmetric unification.

We write a Monte Carlo program allowing arbitrary splitting among GUT scale particles consistent with experimental constraints for both the minimal supersymmetric model and the missing doublet model. The resulting correlations among the low energy parameters are discussed and several advantages of the missing doublet model are pointed out.

Precision corrections to supersymmetric unification

We compute the full set of weak-scale gauge and Yukawa threshold corrections in the minimal supersymmetric standard model, including all finite (non-logarithmic) corrections, which we show to be important. We use our results to examine the effects of unification-scale threshold corrections in the minimal and missing-doublet SU(5) models. We work in the context of a unified mass spectrum, with scalar mass M 0 and gaugino mass M 1 2 , and find that in minimal SU(5) with squark masses less than one TeV, successful gauge and Yukawa coupling unification requires M 1 2 ⪡ M 0 and M 0 ⋍ 1 TeV. In contrast, we find that the missing-doublet model permits gauge and Yukawa unification for a wide range of supersymmetric masses.

Left-right symmetry and supersymmetric unification.

The existence of an SU(3) X SU(2)_L X SU(2)_R X U(1) gauge symmetry with g_L = g_R at the TeV energy scale is shown to be consistent with supersymmetric SO(10) grand unification at around 1O^{16} GeV if certain new particles are assumed. The additional imposition of a discrete Z_2 symmetry leads to a generalized definition of R parity as well as highly suppressed Majorana neutrino masses. Another model based on SO(10) X SO(10) is also discussed.

Electric dipole moments as a test of supersymmetric unification

In a class of supersymmetric grand unified theories, including those based on the gauge group SO(10), there are new contributions to the electric dipole moments of the neutron and electron, which arise as a heavy top quark effect. These contributions arise from CKM-like phases, not from phases of the supersymmetry breaking operators, and can be reliably computed in terms of the parameters of the weak scale supersymmetric theory. For the expected ranges of these parameters, the electric dipole moments of the neutron and the electron are predicted to be close to present experimental limits.

Signals for supersymmetric unification

Using the Yukawa couplings of the minimal supersymmetric SU(5) model, the rates for μ → eγ, μ → e conversion, μ → 3 e and τ → μγ are computed. For a selectron mass of 100 GeV, and without exploring the full parameter space, we find rates which are one order of magnitude beneath present experimental bounds. It is argued that these relatively large rates have a wide applicability, so that lepton flavor violating signals provide a more general test of supersymmetric unification than can be obtained from either proton decay or neutrino masses.

Supersymmetric unification without proton decay

We present a supersymmetric grand unification scheme based on the gauge group SU(3) c × SU(3) L × SU(3) R in which the proton and the lightest supersymmetric particle are stable, neutrinos are necessarily massive, and the observed baryon asymmetry originates in the lepton sector. Such models are also consistent with the measured value of sin 2 θ W as well as unification of the gauge couplings.

Gravitational smearing of minimal supersymmetric unification predictions.

A short and mean paper.

Minimal supersymmetric unification predictions

We re-examine the predictions for the gauge couplings in the minimal extension of the standard model which result from the assumption that the model comes from a unified theory with a single scale of breaking. The effects of thresholds are considered both at the unification scale and at the low-energy scale of the new supersymmetric states. The latter are found to be particularly important and are analysed using the supergravity spectrum corresponding to common scalar and gaugino masses plus other soft supersymmetry breaking terms corrected by gauge and Yukawa radiative corrections. The analysis is extended to include the prediction for the W-boson mass coming from the radiatively induced spontaneous symmetry breaking of the standard model. The requirement that this be within the measured value without fine tuning strongly limits the magnitude of the supersymmetry breaking scale and the resulting predictions for the detailed mass spectrum of the supersymmetric states and the Higgs bosons. The bottom quark mass is also determined using the full two-loop renormalisation group equation with the unification prediction m b = m τ at the compactification scale.

Phenomenological consequences of a direct fifth force coupling to photons.

The possible consequences of a mixing between the photon field and the vector component of a fifth-force field are considered, using an effective phenomenological model based on the coupling term ${F}_{\ensuremath{\mu}\ensuremath{\nu}}{G}^{\ensuremath{\mu}\ensuremath{\nu}}$, which may be motivated in the context of multidimensional and supersymmetric unification schemes. Various constraints on the strength of this coupling, following from observational data, are discussed.

Limits on photino and squark masses from proton lifetime in supergravity models.

It is shown that the current experimental lower limit on the proton lifetime via p..-->..nu-barK/sup +/ puts severe constraints on the photino and squark masses in supersymmetric unification. For Higgs-triplet masses approx. <10/sup 16/ GeV (as required to maintain the gauge hierarchy in supergravity models) the Kamioka data imply that squarks would be so heavy as not to be observable at the Fermilab Tevatron (and probably not observable even at the Superconducting Super Collider) for photinos heavier than approx.10 GeV. (W-ino and gluino signals would then still be possible signals of supersymmetry.) For very light photinos, a region of squark mass accessible to the Tevatron is still possible, due to an ''accidental'' cancellation of the low-lying and high-lying W-ino contribution to the decay amplitude.

Fourfold gradings of superalgebras and structures equations describing extended superspaces

We show how to construct Z 2 × Z 2 and Z 4 gradings of a large class of superalgebras. The classification of such gradings for d = 4, d = 5 and d = 7 anti-de Sitter extended superalgebras is given. It is also shown how the fourfold gradings determine the supersymmetric unification of two bosonic geometries, describing space-time and internal degrees of freedom.

Supersymmetric unification and cosmology

We discuss the cosmological implications of a model of supersymmetric unification by Witten. Because the unification phase transition occurs with a low critical temperature, we estimate the final baryon number to be negligible.