Yukawa Coupling Unification Research Articles

String scale unification in an SU(6) × SU(2) GUT

We construct and analyze an SU (6) × SU (2) GUT. The model is k = 1 string embedable in the sense that we employ only chiral representations allowed at the k = 1 level of the associated Kač-Moody Algebra. Both cases SU (6) × SU (2) L and SU (6) × SU (2) R are realized. The model is characterized by the SU (6) × SU (2) → SU (4) × SU (2) × SU (2) breaking scale M X , and the SU (4) × SU (2) × SU (2) → SU (3) C × SU (2) L × U (1) Y breaking scale M R . The spectrum bellow M R includes an extra pair of charge- 1 3 colour-triplets of mass M I ≤ M R that does not couple to matter fields and, possibly, an extra pair of isodoublets. Above M X the SU (6) and SU (2) gauge couplings always unify at a scale which can be taken to be the string unification scale M s ∼ 5 × 10 17 GeV. The model has Yukawa coupling unification since quarks and leptons obtain their masses from a single Yukawa coupling. Neutrinos obtain acceptably small masses through a see-saw mechanism. Coloured triplets that couple to matter fields are naturally split from the coexisting isodoublets without the need of any numerical fine tuning.

B−τunification and neutrino masses in SU(5) extensions of the MSSM with radiative electroweak breaking

We make a complete analysis of the Yukawa coupling unification in SU(5) extensions of the MSSM in the framework of the radiative symmetry-breaking scenario. Both logarithmic and finite threshold corrections of sparticles have been included in the determination of the gauge and Yukawa couplings at ${M}_{Z}.$ The effect of the heavy masses of each model in the renormalization group equations is also included. We find that in the minimal SU(5) model $b$-$\ensuremath{\tau}$ Yukawa unification can be achieved for too large a value of ${\ensuremath{\alpha}}_{s}.$ On the other hand, the Peccei-Quinn version of the missing doublet model, with the effect of the right-handed neutrino also included, exhibits $b$-$\ensuremath{\tau}$ unification in excellent agreement with all low energy experimental data. Unification of all Yukawa couplings is also discussed.

An extension of the standard model with a single coupling parameter

We show that it is possible to find an extension of the matter content of the standard model with a unification of gauge and Yukawa couplings reproducing their known values. The perturbative renormalizability of the model with a single coupling and the requirement to accommodate the known properties of the standard model fix the masses and couplings of the additional particles. The implications on the parameters of the standard model are discussed.

The Nonminimal Supersymmetric Standard Model at Large tan β

We present a comprehensive analysis of the Nonminimal Supersymmetric Standard Model (NMSSM) for large values of tan β, the ratio of the vacuum expectation values of the two Higgs doublets, which arise when we impose the constraint of the unification of Yukawa couplings in the model. In this limit, we show that the vacuum expectation value of the singlet is forced to be large, of the order of 10 TeV. The singlet decouples from the lightest CP-even neutral Higgs boson and the neutralinos. We compare our results with the corresponding particle spectrum of the Minimal Supersymmetric Standard Model in the same limit. With the exception of the lightest Higgs boson, the particle spectrum in the model turns out to be heavy. The Higgs boson mass, after the inclusion of radiative corrections, is found to be in the neighborhood of ~ 130 GeV.

Precision corrections in the minimal supersymmetric standard model

In this paper we compute one-loop corrections to masses and couplings in the minimal supersymmetric standard model. We present explicit formulae for the complete corrections and a set of compact approximations which hold over the unified parameter space associated with radiative electroweak symmetry breaking. We illustrate the importance of the corrections and the accuracy of our approximations by scanning over the parameter space. We calculate the supersymmetric one-loop corrections to the W-boson mass, the effective weak mixing angle, and the quark and lepton masses, and discuss implications for gauge and Yukawa coupling unification. We also compute the one-loop corrections to the entire superpartner and Higgs-boson mass spectrum. We find significant corrections over much of the parameter space, and illustrate that our approximations are good to O(1%) for many of the superparticle masses.

Gauge and Yukawa Coupling Unification in Models with Gauge-Mediated Supersymmetry Breaking [Phys. Rev. Lett. 78, 1002 (1997)

Gauge and Yukawa Coupling Unification in Models with Gauge-Mediated Supersymmetry Breaking [Phys. Rev. Lett. 78, 1002 (1997)

Heavy SUSY Higgs bosons at e + e - linear colliders

The production mechanisms and decay modes of the heavy neutral and charged Higgs bosons in the Minimal Supersymmetric Standard Model are investigated at future e +e − colliders in the TeV energy regime. We generate supersymmetric particle spectra by requiring the MSSM Higgs potential to produce correct radiative electroweak symmetry breaking, and we assume a common scalar mass m0, gaugino mass m1/2 and trilinear coupling A, as well as gauge and Yukawa coupling unification at the Grand Unification scale. Particular emphasis is put on the low tan β solution in this scenario where decays of the Higgs bosons to Standard Model particles compete with decays to supersymmetric charginos/neutralinos as well as sfermions. In the high tan β case, the supersymmetric spectrum is either too heavy or the supersymmetric decay modes are suppressed, since the Higgs bosons decay almost exclusively into b and τ pairs. The main production mechanisms for the heavy Higgs particles are the associated AH production and H +H− pair production with cross sections of the order of a few fb.

Gauge and Yukawa Coupling Unification in Models with Gauge-Mediated Supersymmetry Breaking

We examine gauge and Yukawa coupling unification in models with gauge-mediated supersymmetry breaking. We work consistently to two-loop order, and include all weak, messenger and unification-scale threshold corrections. We find that successful unification requires unification-scale threshold corrections that are in conflict with the minimal SU(5) model, but are consistent with the modified missing doublet SU(5) model for small tan beta, and large tan beta with mu>0.

Four-generation low energy supersymmetry with a light top quark

A supersymmetric model with four generations is proposed, in which the top quark is approximately degenerate in mass with the W ± gauge boson, m t ∼/ m w , leading to values of R b in better agreement with the present experimental data than in the Standard Model. The model shares many of the good features of the minimal supersymmetric extension of the Standard Model (MSSM), such as the unification of gauge and Yukawa couplings at a common high energy scale. The model differs from the MSSM by re-interpreting the Tevatron “top-quark” events as the production of the fourth generation quark t′, which decays dominantly to bW + The top quark decays primarily into supersymmetric particles, t → t ̃ X ̃ 1 , with t ̃ → c X ̃ 1 0 thereby evading previous searches, Light supersymmetric particles are predicted to lie in the mass range between 25 and 70 GeV, which together with the fourth generation leptons provide a rich spectrum of new physics which can be probed at LEP-2 and the Tevatron.

Mutual consideration of b → sγ and μ → eγ in supersymmetric SO(10) grand unification

We compare the branching ratios for b → sγ and μ → eγ in terms of constraining the parameter space in supersymmetric SO(10) grand unification models where supersymmetry is broken softly near the Planck scale by generationally symmetric operators. We observe two general cases. One with small tan β = 2 and the other one with large tan β having third generation Yukawa coupling unification at the GUT scale. We show that for small tan β the branching ratio constraints allow only a smaller region of parameter space for μ > 0 compared to μ < 0 for gluino mass ≲ 500 GeV. With large tan β, we find acceptable regions of parameter space with |μ| ≲ 1 TeV only for μ < 0. The dominant constraint on large tan β with μ > 0 parameter space is found to be given by the b → sγ branching ratio, while for large tan β with μ < 0 it is found to be given by the μ → eγ branching ratio. In many of these acceptable regions, we find that the μ → eγ branching ratio is predicted to be within one order of magnitude of its current experimental bound. We also show that the usually neglected gluino mediated diagrams in b → sγ can not be ignored in some regions of parameter space, especially for large tan β scenarios when the gluino mass is near its lower experimental bound.

Viable t- b- τ Yukawa unification in SUSY SO(10)

The supersymmetric SO(10) GUT with t- b- τ Yukawa coupling unification has problems with correct electroweak symmetry breaking, experimental constrains (especially b → sγ) and neutralino abundance, if the scalar masses are universal at the GUT scale. We point out that non-universality of the scalar masses at the GUT scale generated both by (1) renormalization group running from the Planck scale to the GUT scale and (2) D-term contribution induced by the reduction of the rank of the gauge group, has a desirable pattern to make the model phemenologically viable (in fact the only one which is consistent with experimental and cosmological constraints). At the same time the top quark mass has to be either close to its quasi IR-fixed point value or below ∼ 170 GeV. We also briefly discuss the spectrum of superpartners which is then obtained.

Lepton flavour violations in SO(10) with large tan β

In supersymmetric SO(10) with large tan β and Yukawa coupling unification λ t = λ b = λ t , we compute the rates for lepton flavour violating processes. Experiments in progress or foreseen for μ → eγ, μ → e conversion (and the dipole moment of the electron) are shown to provide very significant tests of the theory for all slepton masses up to about 1 TeV.

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.

Implications of non-universality of soft terms in supersyrnmetric grand unified theories

Most discussions of supersymmetric grand unified theories assume universality of the soft supersymmetry breaking terms at the grand scale. We point out that the behaviour of these theories might change significantly in the presence of non-universal soft terms. Particularly in SO(10)-like models with a large value of tan β (and assuming Yukawa coupling unification for the third generation) we observe a decisive change of predictions, allowing the presence of relatively fight gauginos as well as small supersymmetric corrections to the b-quark mass. Some results remain rather stable, including the μ-M 1 2 correlation. Models with small tan β seem to be less affected by non-universality which mainly leads to the new possibility of small m 0 (i.e. the squark and slepton soft mass parameter), excluded in the universal case.

Electroweak symmetry breaking with non-universal scalar soft terms and large tan β solutions

We discuss radiative electroweak symmetry breaking with non-universal scalar masses at the GUT scale. Large tan β solutions are investigated in detail and it is shown that qualitatively new (as compared to the universal case) solutions exist, with much less correlation between soft terms. We identify two classes of non-universalities which give solutions with A o ⋍ B o ⋍ M 1 2 ⋍ O(M z) and with μ ⪢ M Z or μ ⋍ O(M Z) , respectively. In each case, after imposing gauge and Yukawa coupling unification, we discuss the predictions for m t , m b and the spectrum of supersymmetric particles. One striking consequence is the possibility of light charginos and neutralinos which in the second option can be higgsino-like. Cosmological constraint on the relic abundance of the lightest neutralino is also included.

Infrared fixed points and fixed lines in the top-bottom-tau sector in supersymmetric grand unification

The two-loop “top-down” renormalization group flow for the top, bottom and tau Yukawa couplings, from μ = M GUT ⋍ O(10 16 GeV) to μ ⋍ m t , is explored in the framework of supersymmetric grand unification; reproduction of the physical bottom and tau masses is required. Instead of following the recent trend of implementing exact Yukawa coupling unification i) a search for infrared (IR) fixed lines and fixed points in the m t pole −tan β plane is performed and ii) the extent to which these imply approximate Yukawa unification is determined. In the m t pole −tan β plane two IR fixed lines, intersecting in an IR fixed point, are located. The more attractive fixed line has a branch of almost constant top mass, m t pole ⋍ 168–180 GeV (close to the experimental value), for the large interval 2.5 ≲ tan β ≲ 55; it realizes tau-bottom Yukawa unification at M GUT approximately. The less attractive fixed line as well as the fixed point at m t pole ⋍ 170 GeV, tan β ⋍ 55 implement approximate top-bottom Yukawa unification at all scales μ. The renormalization group flow is attracted towards the IR fixed point by way of the more attractive IR fixed line. The fixed point and lines are distinct from the much quoted effective IR fixed point m t pole ⋍ O(200 GeV) sin β.

Implications of [formula omitted] for supersymmetry searches and model-building

Assuming that the actual values of M t at FNAL and of Γ(Z → b b ̄ )/Γ(Z → hadrons) at LEP are within their current 1σ reported ranges, we present a No-Lose Theorem for superpartner searches at LEP II and an upgraded Tevatron. We impose only two theoretical assumptions: the Lagrangian is that of the Minimal Supersymmetric Standard Model (MSSM) with arbitrary soft-breaking terms, and all couplings remain perturbative up to scales ∼ 10 16 GeV; there are no assumptions about the soft supersymmetry breaking parameters, proton decay, cosmology, etc. In particular, if the LEP and FNAL values hold up and supersymmetry is responsible for the discrepancy with the Standard Model prediction of Γ(Z → b b ̄ ) , then we must have charginos and/or top squarks observable at the upgraded machines (for LEP the superpartner threshold is below √ s = 140 GeV). Furthermore, little deviation from the Standard Model is predicted within “super-unified” supersymmetry, so these models predict that the discrepancy between experiment and the Standard Model prediction for Γ(Z → b b ̄ ) will fade with time. Finally, it appears to be extremely difficult to find any unified MSSM model, regardless of the form of soft supersymmetry breaking, that can explain Γ(Z → b b ̄ ) for large tan β; in particular, no model with t b τ Yukawa coupling unification appears to be consistent with the experiments.

Predictive fermion mass matrix Ansa-umltze in nonsupersymmetric SO(10) grand unification.

We investigate the status of predictive fermion mass ansatzes which make use of the grand unification scale conditions $m_e=m_d/3$, $m_\mu =3m_s$, and $\mid V_{cb}\mid =\sqrt{m_{c}/m_{t}}$ in non-supersymmetric SO(10) grand unification. The gauge symmetry below an intermediate symmetry breaking scale $M_I$ is assumed to be that of the standard model with either one Higgs doublet or two Higgs doublets . We find in both cases that a maximum of 5 standard model parameters may be predicted within $1\sigma$ experimental ranges. We find that the standard model scenario predicts the low energy $\mid V_{cb}\mid$ to be in a range which includes its experimental mid-value 0.044 and which for a large top mass can extend to lower values than the range resulting in the supersymmetric case. In the two Higgs standard model case, we identify the regions of parameter space for which unification of the bottom quark and tau lepton Yukawa couplings is possible at grand unification scale. In fact, we find that unification of the top, bottom and tau Yukawa couplings is possible with the running b-quark mass within the $1\sigma$ preferred range $m_b=4.25\pm 0.1\, GeV$ provided $\alpha_{3c}(M_Z)$ is near the low end of its allowed range. In this case, one may make 6 predictions which include $\mid V_{cb}\mid$ within its $90\%$ confidence limits. However unless the running mass $m_b>4.4\, GeV$, third generation Yukawa coupling unification requires the top mass to be greater than

Yukawa coupling unification with supersymmetric threshold corrections.

Radiative corrections to the down-type fermion masses at the supersymmetric threshold are enhanced by the ratio of vacuum expectation values, $tan\ensuremath{\beta}$. This can have a strong impact on the unification of Yukawa couplings in supersymmetric grand unified theories. We present an example of such a model with a horizontal gauge symmetry that naturally explains the fermion mass hierarchy and the small mixing angles of the Kobayashi-Maskawa matrix. The unification of the lepton and the down-quark Yukawa couplings is achieved without introducing large Higgs multiplets.

Top-down approach to unified supergravity models

We introduce a new approach for studying unified supergravity models. In this approach all the parameters of the grand unified theory (GUT) are fixed by imposing the corresponding number of low energy observables. This determines the remaining particle spectrum whose dependence on the low energy observables can now be investigated. We also include some SUSY threshold corrections that have previously been neglected. In particular the SUSY threshold corrections to the fermion masses can have a significant impact on the Yukawa coupling unification.