Quasifixed-point scenario in a modified nonminimal supersymmetric standard model

The modified next-to-minimal supersymmetric standard model is the simplest model that is obtained as an extension of the minimal supersymmetric standard model and which is compatible with the LEP II experimental constraint on the mass of the lightest Higgs boson at tan β～1. The renormalization of Yukawa coupling constants and of the parameters of a soft breakdown of supersymmetry is investigated within this model. The possibility of unifying the Yukawa coupling constants for the b quark and the τ lepton at the Grand Unification scale M _X is studied. The spectrum of particles is analyzed in the vicinity of a quasifixed point where solutions to the renormalization-group equations are concentrated at the electroweak scale.     

Particle spectrum in the modified nonminimal supersymmetric standard model in the strong Yukawa coupling regime

A theoretical analysis of solutions of renormalization group equations in the minimal supersymmetric standard model, which lead to a quasi-fixed point has shown that the mass of the lightest Higgs boson in these models does not exceed 94 ± 5 GeV. This implies that a considerable part of the parameter space in the minimal supersymmetric model is in fact eliminated by existing LEPII experimental data. In the nonminimal supersymmetric standard model the upper bound on the mass of the lightest Higgs boson reaches its maximum in the strong Yukawa coupling regime when the Yukawa constants are substantially greater than the gauge constants on the grand unification scale. In the present paper the particle spectrum is studied using the simplest modification of the nonminimal supersymmetric standard model which gives a self-consistent solution in this region of parameter space. This model can give m _h ～ 125 GeV even for comparatively low values of β ≥ 1.9. The spectrum of Higgs bosons and neutralinos is analyzed using the method of diagonalizing mass matrices proposed earlier. In this model the mass of the lightest Higgs boson does not exceed 130.5 ± 3.5 GeV.     

Improved predictions for intermediate and heavy supersymmetry in the MSSM and beyond

For a long time, the minimal supersymmetric standard model (MSSM) with light masses for the supersymmetric states was considered as the most natural extension of the Standard Model of particle physics. Consequently, a valid approximation was to match the MSSM to the precision measurement directly at the electroweak scale. This approach was also utilized by all dedicated spectrum generators for the MSSM. However, the higher the supersymmetric (SUSY) scale is, the bigger the uncertainties which are introduced by this matching. We point out important consequences of a two-scale matching, where the running parameters within the SM are calculated at \(M_Z\) and evaluated up to the SUSY scale, where they are matched to the full model. We show the impact on gauge coupling unification as well as the SUSY mass spectrum. Also the Higgs mass prediction for large supersymmetric masses has been improved by performing the calculation within an effective SM. The approach presented here is now also available in the spectrum generator SPheno. Moreover, also SARAH was extended accordingly and gives the possibility to study these effects now in many different supersymmetric models.     

Top compositeness and precision unification

The evolution of standard model gauge couplings is studied in a nonsupersymmetric scenario in which the hierarchy problem is resolved by Higgs compositeness above the weak scale. It is argued that massiveness of the top quark combined with precision tests of the bottom quark imply that the right-handed top must also be composite. If, further, the standard model gauge symmetry is embedded into a simple subgroup of the unbroken composite-sector flavor symmetry, then precision coupling unification is shown to occur at approximately 10(15) GeV, to a degree comparable to supersymmetric unification.     

Comparison of grand unified theories with electroweak and strong coupling constants measured at LEP

Using the renormalization group equations one can evolve the electroweak and strong coupling constants, as measured at LEP, to higher energies in order to test the ideas of grand unified theories, which predict that the three coupling constants become equal at a single unification point. With data from the DELPHI Collaboration we find that in the minimal non-supersymmetric standard model with one Higgs doublet a single unification point is excluded by more than 7 standard deviations. In contrast, the minimal supersymmetric standard model leads to good agreement with a single unification scale of 10^16.0±0.3 GeV. Such a large scale is compatible with the present lower limits on the proton lifetime. The best fit is obtained for a SUSY scale around 1000 GeV and limits are derived as function of the strong coupling constant. The unification point is sensitive to the number of Higgs doublets and only the minimal SUSY model with two Higgs doublets is compatible with GUT unification, if one takes the present limits on the proton lifetime into account.     

Standard model on D-branes

I briefly outline previous work on getting the (supersymmetric) standard model from string theory, and then describe two ecent attempts using D-branes. The first uses D3-and D7-branes and gives a supersymmetric standard model with extra vector-like matter and an intermediate unification scale. The second uses intersecting D4-branes and yields a non-supersymmetric spectrum with TeV-scale unification.     

Neutrino masses, mixing angles and the unification of couplings in the MSSM

In the light of the gathering evidence for neutrino oscillations, coming in particular from the Super-Kamiokande data on atmospheric neutrinos, we re-analyze the unification of gauge and Yukawa couplings within the minimal supersymmetric extension of the Standard Model (MSSM). Guided by a range of different grand-unified models, we stress the relevance of large mixing in the lepton sector for the question of bottom-tau Yukawa coupling unification. We also discuss the dependence of the favoured value of on the characteristics of the high-energy quark and lepton mass matrices. In particular, we find that, in the presence of large lepton mixing, Yukawa unification can be achieved for intermediate values of that were previously disfavoured. The renormalization-group sensitivity to the structures of different mass matrices may enable Yukawa unification to serve as a useful probe of GUT models. Received: 22 June 1999 / Published online: 10 December 1999     

Infrared quasifixed solutions in a nonminimal supersymmetric standard model

The constraints from LEPII on the mass of the lightest Higgs boson are such that, in the parameter space of the minimal supersymmetric standard model (MSSM), a considerable part of the region that corresponds to the scenario of an infrared fixed point is virtually ruled out by available experimental data. In a nonminimal supersymmetric standard model (NMSSM), the mass of the lightest Higgs boson takes its maximum value in the regime of strong Yukawa coupling, in which case the Yukawa coupling constants are much greater than the gauge coupling constants at the Grand Unification scale $(Y_i (0) \gg \tilde \alpha _i (0))$ . In this limiting case, solutions to the renormalization-group equations are attracted to Hill and infrared fixed lines or surfaces in the space of Yukawa coupling constants; for Y _i (0) → ∞, they are concentrated in the vicinities of quasifixed points. However, this attraction is quite weak. For this reason, solutions to the renormalization-group equations are grouped near some line on the Hill surface when all Y _i (0) are close to unity. Approximate solutions for the Yukawa coupling constants within the NMSSM are presented. In addition, the possibility of unifying the Yukawa coupling constants for the b quark and the τ lepton at the scale M _X is discussed.     

Quantum weakdynamics as an SU(3)_I gauge theory: Grand unification of strong and electroweak interactions

Quantum weakdynamics (QWD) as an gauge theory with the vacuum term is considered to be the unification of the electroweak interaction as an gauge theory. The grand unification of beyond the standard model is established by the group . The grand unified interactions break down to weak and strong interactions at a new grand unification scale, GeV, through dynamical spontaneous symmetry breaking (DSSB); the weak and strong coupling constants are the same, , at this scale. DSSB is realized by the condensation of scalar fields, postulated to be spatially longitudinal components of gauge bosons, instead of Higgs particles. Quark and lepton family generation, the Weinberg angle , and the Cabbibo angle are predicted. The electroweak coupling constants are , , , and ; there are symmetric isospin interactions. Received: 21 January 2001 / Published online: 21 November 2001     

Grand unified theories without the desert

We present a grand unified theory (GUT) that has GUT fields with masses of the order of a TeV, but at the same time preserves (at the one-loop level) the success of gauge-coupling unification of the minimal supersymmetric standard model (MSSM) and the smallness of proton decay operators. This scenario is based on a five-dimensional theory with the extra dimension compactified as in the Randall-Sundrum model. The MSSM gauge sector and its GUT extension live in the 5D bulk, while the matter sector is localized on a 4D boundary.the is a test again     

The weak mixing angle and unification mass in supersymmetric SU(5)

We consider the predictions for the weak mixing angle θ_W and the scale M of unification in a supersymmetric extension of SU(5), with particular emphasis on the sensitivity to the number of Higgs multiplets. In the one-loop approximation, we also calculate the ratio m_b/m_τ. We discuss generally the effects of an intermediate threshold between the weak interaction scale and M and estimate the sensitivity of θ_W and M to the scale of supersymmetry breaking.The evolution of the coupling constants of the supersymmetric SU(3) ? SU(2) ? U(1) effective gauge theory is described and the two-loop corrections to θ_{W and M} are calculated.     

Minimal grand unification model in an anthropic landscape

It has been recently pointed out by Arkani-Hamed and Dimopoulos that if the universe is a landscape of vacua, and if therefore fine-tuning is not a valid guidance principle for searching for physics beyond the standard model, supersymmetric unification only requires the fermionic superpartners. We argue that in that landscape scenario, the fermionic superpartners are not needed for unification, which can be achieved in SO(10) either via a direct breaking to the standard model at the grand unification scale or through an intermediate gauge symmetry. In most minimal SO(10) models, the proton lifetime is long enough to avoid the experimental bounds. These models are the truly minimal fine-tuned extensions of the standard model in the sense proposed by Davoudiasl et al.Received: 3 September 2004, Published online: 23 March 2005     

Third generation Yukawa couplings unification in supersymmetric SO(10) model

In the minimal supersymmetric standard model (MSSM) contained in SUSY SO(10), top-- Yukawa unification is achieved at the intermediate mass scale GeV using the recent world average experimental value of the top-quark mass, GeV, which has been directly established by CDF and D0 experiments at the Tevatron Collider. It is also observed that the Yukawa couplings unification scale can be further decreased by taking lower input values of the top-quark mass. This trend indicates the possible existence of an intermediate symmetry breaking scale in SUSY SO(10). The present finding does not agree with the earlier notion that the third generation Yukawa couplings unification should occur at the GUT scale . Received: 22 September 1997 / Revised version: 22 January 1998 / Published online: 24 March 1998     

Proton hexality in local grand unification

Proton hexality is a discrete symmetry that avoids the problem of too fast proton decay in the supersymmetric extension of the standard model. Unfortunately it is inconsistent with conventional grand unification. We show that proton hexality can be incorporated in the scheme of “Local Grand Unification” discussed in the framework of model building in (heterotic) string theory.     

Supersymmetric standard model from the heterotic string

We present a [FORMULA: SEE TEXT] orbifold compactification of the E8xE8 heterotic string which leads to the (supersymmetric) standard model gauge group and matter content. The quarks and leptons appear as three 16-plets of SO(10), whereas the Higgs fields do not form complete SO(10) multiplets. The model has large vacuum degeneracy. For generic vacua, no exotic states appear at low energies and the model is consistent with gauge coupling unification. The top quark Yukawa coupling arises from gauge interactions and is of the order of the gauge couplings, whereas the other Yukawa couplings are suppressed.     

Prediction for α3(Mz) in a string-inspired model

We apply the Renormalisation Group Evolution (RGE) to analyse the phenomenological implications of an extended supersymmetric model, for the value of the unification scale and the strong coupling at the electroweak scale. The model we consider is predicted to exist in Calabi–Yau string compactifications with Wilson line mechanism for E₆ symmetry breaking, contains additional matter beyond the MSSM spectrum and avoids the “doublet-triplet” splitting problem in the Higgs sector. The calculation is analytical in two-loop order and includes the effects of the heavy thresholds due to the additional matter considered. The value of α₃(M_z) can be brought within the experimental limits without a significant change of the unification scale from the MSSM prediction.     

Radiatively generated maximal mixing scenario for the Higgs boson mass and the least fine-tuned minimal supersymmetric standard model

We argue that given the experimental constraints on the Higgs boson mass the least fine-tuned parameter space of the minimal supersymmetric standard model is with negative top-squark masses squared at the grand unification scale. While the top-squark mass squared is typically driven to positive values at the weak scale, the contribution to the Higgs boson mass squared parameter from the running can be arbitrarily small, which reduces the fine-tuning of electroweak symmetry breaking. At the same time the top-squark mixing is necessarily enhanced and the maximal mixing scenario for the Higgs boson mass can be generated radiatively even when starting with negligible mixing at the unification scale. This highly alleviates constraints on possible models for supersymmetry breaking in which fine-tuning is absent.     

Particle physics implications of Wilkinson microwave anisotropy project measurements

We present an overview of the implications of the WMAP data for particle physics. The standard parameter set ∈, η and ξ characterising the inflaton potential can be related to the power-law indices characterising deviation of the CMB spectrum from the scale invariant form. Different classes of inflation potentials are in turn naturally associated with different unified schemes. At present WMAP does not exclude any but a few simple unified models. In particular, hybrid models favoured by supersymmetric unification continue to be viable. However future improvement in data leading to better determination of the ‘running’ of power-law indices should help to narrow the possibilities for unified models. The main conclusion is that WMAP is consistent with the paradigm of GUT scale (10¹⁶ GeV) inflation.     

Spreading of gauge coupling constants in minimal LR models

Minimal left-right (LR) models are often inconsistent with gauge unification at the Planck scale, as they imply too large a Weinberg angle. In (E₆) superstring-inspired models true gauge unification is nit required, and the absence of unification of coupling constants might be an indication of non-zero (string) renormalization effects. Here we perform a quantitative analysis of the necessary spreading of the gauge coupling constants in order to accommodate a realistic value of the Weinberg angle in minimal LR models motivated by the string.     

类矢标准模型中规范相互作用与引力的统一

提出在无轻子的超对称类矢标准模型中,在规范作用双圈修正和引力单圈弦修正下,研究规范耦合和引力之间的统一问题.结果表明,需要两个中间质量标度.其中低质量标度在未来实验室可到达的范围内,高的质量标度约为10¹⁶GeV.