Strong unification

We investigate the possibility that unification occurs at strong coupling. We show that, despite the fact the couplings pass through a strong coupling regime, accurate predictions for their low energy values are possible because the couplings of the theory flow to infrared fixed points. We determine the low-energy QCD coupling in a favoured class of strong coupling models and find it is reduced from the weak coupling predictions, lying close to the experimentally measured value. We extend the analysis to the determination of quark and lepton masses and show that (even without Grand Unification) the infra-red fixed point structure may lead to good predictions for the top mass, the bottom to tau mass ratio and tan β. Finally we discuss the implications for the unification scale finding it to be increased from the MSSM value and closer to the heterotic string prediction.     

Unified models at intermediate energy scales and Kaluza–Klein excitations

We discuss the possibility of intermediate gauge coupling unification in unified models of string origin. Useful relations of the β-function coefficients are derived, which ensure unification of couplings when Kaluza–Klein excitations are included above the compactification scale. We apply this procedure to two models with SU(3)×SU(3)_L×SU(3)_R and SU(4)×O(4) gauge symmetries.     

Fractional charges and the renormalization group in theSU(4)×O(4) string model

We study the renormalization group equations of the gauge couplings in theSU(4)×O(4)～SU(4)×SU(2) _L ×SU(2_ _R string model, derived in the context of the free fermionic formulation of the four dimensional superstring. We calculate the effective string unification scale taking into account string threshold corrections and we consider the consequences of then _L andn _R fractionally charged states, sitting in the (1, 2, 1) and (1, 1, 2) representations correspondingly, of the gauge symmetry of the model. Some of these states become massive at a very high scale, when a number of singlet fields acquire vev's. However, many of them (the precise number depends on the specific choice of the flat direction) remain in the massless spectrum. We consider various cases and find that, for specific choices of flat directions, the physical parameters of the model, like the grand unification scale and the low energy parameters sin²θ _W and α₃, depend only on the differencen _?=n_L-n_R. We study more general cases where remnants of the exotic doublets remain below theSU(4) breaking scale. We also solve the coupled differential system of the renormalization group equations for the gauge and the Yukawa couplings and estimate the range of the top quark mass which is found to lie in the range 140 GeV<m _t<190GeV.     

Predictions of SUSY masses in the minimal supersymmetric grand unified theory

The Minimal Supersymmetric Standard Model (MSSM) distinguishes itself from other GUT's by a successful prediction of many unrelated phenomena with a minimum number of parameters. Among them: a) Unification of the gauge couplings constants; b) Unification of the b-quark and τ-lepton masses; c) Proton stability; d) Electroweak symmetry breaking at a scale far below the unification scale and the corresponding relation between the gauge boson masses and the top quark mass. A combined fit of the free parameters in the MSSM to these low energy constraints shows that the MSSM model can satisfy these constraints simultaneously. From the fitted parameters the masses of the as yet unobserved superpartners of the SM particles are predicted, the top mass is constrained to a range between 140 and 200 GeV, and the second order QCD coupling constant is required to be between 0.108 and 0.132. The complete second order renormalization group equations for the gauge and Yukawa couplings are used and analytical solutions for the neutral gauge boson, the Higgs masses and the sparticle masses are derived, taking into account the one-loop corrections to the Higgs potential.     

Gravitational correction to running of gauge couplings

We calculate the contribution of graviton exchange to the running of gauge couplings at lowest non-trivial order in perturbation theory. Including this contribution in a theory that features coupling constant unification does not upset this unification, but rather shifts the unification scale. When extrapolated formally, the gravitational correction renders all gauge couplings asymptotically free.     

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.     

The Coupling Constants for an Electroweak Model with an SU(4)PS\otimes SU(4)EW Unification Symmetry

We introduce the sequence of spontaneous symmetry breaking of a coupling between Pati-Salam and electroweak symmetries SU(4)_PS\otimes SU(4)_EW in order to establish a mathematically consistent relation among the coupling constants at grand unification energy scale. With the values of baryon minus lepton quantum numbers of known quarks and leptons, by including right-handed neutrinos, we can find the mixing angle relations at different energy levels up to the electromagnetic U(1)_EM scale.     

Gauge coupling unification with extra dimensions and correction due to higher dimensional operators

We study the gauge coupling unification with extra dimensions. We take into account corrections due to the higher dimensional operators. We show the prediction of ₃(M_Z) is sensitive to such corrections, even if cΦ/M=O(0.01). We also discuss the b−τ Yukawa unification.     

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.     

Emergent O(4) symmetry at the phase transition from plaquette-singlet to antiferromagnetic order in quasi-two-dimensional quantum magnets

Recent experiments [Guo et al., Phys. Rev. Lett. 124 206602(2020)] on thermodynamic properties of the frustrated layered quantum magnet SrCu_2(BO_3)_2-the Shastry–Sutherland material-have provided strong evidence for a lowtemperature phase transition between plaquette-singlet and antiferromagnetic order as a function of pressure. Further motivated by the recently discovered unusual first-order quantum phase transition with an apparent emergent O(4) symmetry of the antiferromagnetic and plaquette-singlet order parameters in a two-dimensional "checkerboard J-Q" quantum spin model[Zhao et al., Nat. Phys. 15 678(2019)], we here study the same model in the presence of weak inter-layer couplings. Our focus is on the evolution of the emergent symmetry as the system crosses over from two to three dimensions and the phase transition extends from strictly zero temperature in two dimensions up to finite temperature as expected in SrCu_2(BO_3)_2.Using quantum Monte Carlo simulations, we map out the phase boundaries of the plaquette-singlet and antiferromagnetic phases, with particular focus on the triple point where these two ordered phases meet the paramagnetic phase for given strength of the inter-layer coupling. All transitions are first-order in the neighborhood of the triple point. We show that the emergent O(4) symmetry of the coexistence state breaks down clearly when the interlayer coupling becomes sufficiently large, but for a weak coupling, of the magnitude expected experimentally, the enlarged symmetry can still be observed at the triple point up to significant length scales. Thus, it is likely that the plaquette-singlet to antiferromagnetic transition in SrCu_2(BO_3)_2 exhibits remnants of emergent O(4) symmetry, which should be observable due to additional weakly gapped Goldstone modes.     

Gauge coupling renormalisation with several U(1) factors

We examine the renormalisation of gauge coupling constants in theories with a G × U(1)^N gauge group (which appears to be the gauge symmetry of many possible superstring vacua). In general, the abelian gauge bosons mix among themselves, so a correct renormalisation requires including this mixing in the evolution of the gauge couplings. We present general results and note that the mixing is scale independent to all orders if the renormalization group trajectory passes through a unification point. We discuss the cases of one loop and two loops explicitly. An example, based on a possible superstring-inspired model, is given.     

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     

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     

Prediction of sinθW in a conformal approach to coupling unification

The possibility that nonsupersymmetric conformal field theories softly broken below 100 TeV may provide an alternative to conventional grand unification is explored. We consider a low energy theory presumed to be of this type arising from the type IIB superstring compactified on a AdS₅×S₅/Γ space whose gauge group and the particle content are severely restricted by the compactification process. We present an example of a resulting SU(4)_C×SU(2)_L×SU(2)_R with three generations, which leads to coupling unification and a prediction for sin²θ_W0.227 and other phenomenology generally consistent with observations.     

Gauge couplings in four-dimensional type I string orbifolds

We compute threshold effects to gauge couplings in four-dimensional _N orientifold models of type I strings with GN = 2 and GN = 1 supersymmetry, and study their dependence on the geometric moduli. We also compute the tree-level (disk) couplings of the open sector gauge fields to the twisted closed string moduli of the orbifold in various models and study their effects and that of the one-loop threshold corrections on gauge coupling unification. We interpret the results from the (supergravity) effective theory point of view and comment on the conjectured heterotic-type I duality.     

耦合形貌对Si4团簇电子输运影响的第一性原理计算

运用密度泛函理论与非平衡格林函数相结合的方法,对Si₄团簇与Au （100）-3×3两电极以顶位-顶位、顶位-空位、空位-空位三种形貌相连构成的Au-Si₄-Au纳米结点的拉伸过程进行第一性原理模拟,计算不同构型纳米结点在不同距离的电导和结合能.讨论耦合形貌、距离对结点电导的影响,结合能的计算表明三种不同耦合形貌结点存在稳定平衡结构,其平衡电导分别为0.71 G₀、0.96 G₀和2.44 G₀,且在-1.2 V~1.2 V的电压范围内,三种不同耦合形貌结点稳定结构表现出类似金属的导电特性,其I-V关系都近似为直线.计算结果表明Si₄团簇与电极的耦合形貌、两极距离对纳米结点电子输运有重要影响.     

Light Dirac neutrinos in left-right symmetric and horizontal gauge models

We describe a scheme to generate light Dirac neutrinos. It uses a heavy symmetry-breaking scale to avoid introducing very small couplings or vacuum expectation values. We show how the scheme can be applied to left-right symmetric and to horizontal gauge models with four generations of fermions. In these models neutrino oscillations occur only between pairs of generations (e.g. ν_e−ν_τ oscillations can occur with no ν_μ−ν_e or ν_μ−ν_τ oscillations).     

Mechanism of ferromagnetism in(Fe,Co)-codoped 4H-SiC from density functional theory

First-principles calculations are performed to investigate the electronic structures and magnetic properties of(Fe, Co)-codoped 4H-SiC using the generalized gradient approximation plus Hubbard U method. We find that 4H-SiC doped with an isolated Fe atom and an isolated Co atom produces a total magnetic moment of 5.98 μ_B and 6.00 μ_B respectively. We estimate T_C of about 263.1 K for the(Fe, Co)-codoped 4H-SiC system. We study ferromagnetic and antiferromagnetic coupling in(Fe, Co)-codoped 4H-SiC. Ferromagnetic behavior is observed.The strong ferromagnetic couplings between local magnetic moments can be attributed to p–d hybridization between Fe, Co and neighboring C. However, the(Fe, Co, V_(Si))-codoped 4H-SiC system shows antiferromagnetic coupling when an Si vacancy is introduced in the same 4H-SiC supercell. The results may be helpful for further study on transition metal-codoped systems.     

Combined fit of low energy constraints to minimal supersymmetry and discovery potential at LEP II

Within the Constrained Minimal Supersymmetric Standard Model (CMSSM) it is possible to predict the low energy gauge couplings and masses of the 3. generation particles from a few parameters at the GUT scale. In addition the MSSM predicts electroweak symmetry breaking due to large radiative corrections from Yukawa couplings, thus relating theZ ⁰ boson mass to the top quark mass. From ax ² analysis, in which these constraints can be considered simultaneously, one can calculate the probability for each point in the MSGUT parameter space. The recently measured top quark mass prefers two solutions for the mixing angle in the Higgs sector: tanβ in the range between 1 and 3 or alternatively tanβ≈25?50. For both cases we find a uniquex ² minimum in the parameter space. From the corresponding most probable parameters at the GUT scale, the masses of all predicted particles can be calculated at low energies using the RGE, albeit with rather large errors due to the logarithmic nature of the running of the masses and coupling constants. Our fits include full second order corrections for the gauge and Yukawa couplings, low energy threshold effects, contributions of all (s)particles to the Higgs potential and corrections tom _b from gluinos and higgsinos, which exclude (in our notation) positive values of the mixing parameterμ in the Higgs potential for the large tanβ region. Further constraints can be derived from the branching ratio for the radiative (penguin) decay of theb-quark intosγ and the lower limit on the lifetime of the universe, which requires the dark matter density due to the Lightest Super-symmetric Particle (LSP) not to overclose the universe. For the low tanβ solution these additional constraints can be fulfilled simultaneously for quite a large region of the parameter space. In contrast, for the high tanβ solution the correct value for theb→sγ rate is obtained only for small values of the gaugino scale and electroweak symmetry breaking is difficult, unless one assumes the minimal SU(5) to be a subgroup of a larger symmetry group, which is broken between the Planck scale and the unification scale. In this case small splittings in the Yukawa couplings are expected at the unification scale and electroweak symmetry breaking is easily obtained, provided the Yukawa coupling for the top quark is slightly above the one for the bottom quark, as expected e.g. if the larger symmetry group would be SO(10). For particles, which are most likely to have masses in the LEP II energy range, the cross sections are given for the various energy scenarios at LEP II. For low tanβ the production of the lightest Higgs boson, which is expected to have a mass below 103 GeV, is the most promising channel, while for large tanβ the production of charginos and/or neutralinos covers the preferred parameter space.