The quasi-fixed Minimal Supersymmetric Standard Model

The infra-red fixed points are determined for all the parameters of the MSSM. They dominate the renormalisation group running when the top-Yukawa is in the quasi-fixed point regime (i.e. large at the GUT scale). We examine this behaviour analytically, by solving the full set of one-loop renormalisation group equations in the approximation that the electroweak contributions are negligible, and also numerically. We find the quasi-fixed points for the top-quark trilinear couplings; A_Uα3=A_U3α=−0.59m_g independently of the input parameters at the unification scale. All the remaining parameters are significantly focused towards their true fixed points at the weak scale. We examine how this increases the predictivity of the MSSM in this regime.     

Baryogenesis and Electric Dipole Moments in Minimal Supersymmetric Standard Model

We briefly review the issues related to electroweak baryogenesis in minimal supersymmetric standard model (MSSM). The constraints from electric dipole moments of electron and neutron are emphasized.     

The decayH 2 0 →gg within the Minimal Supersymmetric Standard Model

I present a detailed SUSY QCD calculation of the decay rate of the lightest Higgs bosonH ₂ ⁰ into two gluons, where all quarks and scalar quarks are taken within the relevant loop diagrams. I include the mixing of all the scalar partners of the left and right handed quarks and show that their contribution is more than several tens of per cent compared to the quark contribution in the MSSM for some SUSY parameter space. Furthermore the MSSM fermionic contribution is enhanced by several factors for large tanβ and large Higgs masses. As a result, the two gluon decay rate ofH ₂ ⁰ is much larger than the two gluon decay rate of an equal mass standard model Higgs boson. I further compare the decay mode ofH ₂ ⁰ →gg to the similar decay modes ofH ₂ ⁰ →cc andH ₂ ⁰ →bb including one loop QCD corrections and show that in some casesΓ(H ₂ ⁰ →gg) is even higher thanΓ(H ₂ ⁰ →cc), although still much smaller thanΓ(H ₂ ⁰ →bb).     

The Effects from the Complex Parameters on t→ch0 Within the Minimal Supersymmetric Standard Model

We investigate the effects from complex parameters on the branching ratio (BR) of the flavor changing raredecay t → ch0 contributed by the electroweak interactions in the framework of the minimal supersymmetric standardmodel with complex parameters. We study the dependence of the BR on the possible relevant additional parameterswhich could be the original sources inducing CP-violation, I.e., the complex phase angles φμ and φAb in squark andchargino sectors and δ13 appearing in Cabibbo-Kobayashi-Maskawa matrix. We find that these parameters influencethe BR obviously and the effects induced by φμ and φAb are much larger than by δ13. With the different chosen valuesof the complex parameters, the BR is in the range between 10-10 and 10-8, depending mainly on the phase angles of the higgsino mass parameter μ and the trilinear coupling Ab.     

Supersymmetric two-boson equation: Bilinearization and solutions

A bilinear formulation for the supersymmetric two-boson equation is derived. As applications, some solutions are calculated for it. We also construct a bilinear Bäcklund transformation.     

Instantons,fermion mass generation and supercomplementarity

We consider the possibility that hypercolor instantons can provide fermion masses in preon models of quark and leptons. After discussing the basic ideas of this mechanism in a non-supersymmetric preon model we consider a supersymmetric, QCD-like preon model. We work within the so-called complementarity picture and show the equivalence between the mass term of the elementary fermions, generated by a vacuum expectation value of a elementary scalar, and the mass term of the composite fermions, generated by the hypercolor instantons.     

Critical Points and Supersymmetric Vacua, III: String/M Models

A fundamental problem in contemporary string/M theory is to count the number of inequivalent vacua satisfying constraints in a string theory model. This article contains the first rigorous results on the number and distribution of supersymmetric vacua of type IIb string theories compactified on a Calabi-Yau 3-fold X with flux. In particular, complete proofs of the counting formulas in Ashok-Douglas [AD] and Denef-Douglas [DD1] are given, together with van der Corput style remainder estimates.Supersymmetric vacua are critical points of certain holomorphic sections (flux superpotentials) of a line bundle over the moduli space of complex structures on X × T ² with respect to the Weil-Petersson connection. Flux superpotentials form a lattice of full rank in a 2 b ₃(X)-dimensional real subspace . We show that the density of critical points in for this lattice of sections is well approximated by Gaussian measures of the kind studied in [DSZ1,DSZ2,AD,DD1].Research partially supported by DOE grant DE-FG02-96ER40959 (first author) and NSF grants DMS-0100474 (second author) and DMS-0302518 (third author).     

New Realization of N=2 Supersymmetric QuantumMechanics and Shape Invariance

The new supercharges are constructed and the weight function is defined to study the N=2 one-dimensional supersymmetric quantum mechanics. Several examples are discussed in the new realization.     

Supersymmetric Yang-Mills,octonionic instantons and triholomorphic curves

In four-dimensional gauge theory there exists a well-known correspondence between instantons and holomorphic curves, and a similar correspondence exists between certain octonionic instantons and triholomorphic curves. We prove that this latter correspondence stems from the dynamics of various dimensional reductions of ten-dimensional supersymmetric Yang-Mills theory. More precisely we show that the dimensional reduction of the (5+1)-dimensional supersymmetric sigma model with hyper-Kähler (but otherwise arbitrary) target X to a four-dimensional hyper-Kähler manifold M is a topological sigma model localising on the space of triholomorphic maps M -+ X (or hyperinstantons). When X is the moduli space M_k of instantons on a four-dimensional hyper-Kdhler manifold K, this theory has an interpretation in terms of supersymmetric gauge theory. In this case, the topological sigma model can be understood as an adiabatic limit of the dimensional reduction of ten-dimensional supersymmetric Yang-Mills on the eight-dimensional manifold M × K of holonomy Sp(1) × Sp(1) ⊂ Spin(7), which is a cohomological theory localising on the moduli space of octonionic instantons.     

Supersymmetric σ-models,twistors, and the Atiyah-Hitchin metric

The Legendre transform and its generalizations, originally found in supersymmetric σ-models, are techniques that can be used to givelocal constructions of hyperkähler metrics. We give a twistor space interpretation to the generalizations of the Legendre transform construction. The Atiyah-Hitchin metric on the moduli space of two monopoles is used as a detailed example.     

Infrared quasi-fixed point structure of the fermion masses in the standard model: The two-loop analysis

In the standard model, the renormalization group equation for the Yukawa couplings has the infrared quasi-fixed point which determines the upper bound for the masses of fermions present in the theory. We analyse this effect within the two loop approximation and report the 15% increase of the quark bound compared to the one loop results. We notice and investigate the strong dependence of the bound on the precise value of the Weinberg angle. The detailed study of the Yukawa coupling evolution is also included.     

Gauge coupling unification,the GUT scale,and magic fields

We consider field sets that do not form complete SU(5) multiplets, but exactly preserve the one-loop MSSM prediction for α₃(MZ)${\alpha }_3(M_Z)$ independently of the value of their mass. Such fields can raise the unification scale in different ways, through a delayed convergence of the gauge couplings, a fake unified running below the GUT scale, or a postponed unification after a hoax crossing at a lower scale. The α₃(MZ)${\alpha }_3(M_Z)$ prediction is independent of the mass of the new fields, while the GUT scale often is not, which allows to vary the GUT scale. Such “magic” fields represent a useful tool in GUT model building. For example, they can be used to fix gauge coupling unification in certain two step breakings of the unified group, to suppress large KK thresholds in models with extra dimensions, or they can be interpreted as messengers of supersymmetry breaking in GMSB models.     

Square-roots,internal symmetries,and fermion field quantization

It is observed that the complex square-root of the hermitian matrix σ^μ p _μ associated with a physical four-momentum admits Lorentz-independent unitary transformations that may be related to the internal symmetries of hadrons. An operator-valued square-root of the Hilbert space inner product in relativistic one-electron theory brings in fermion field quantization conditions as a direct concomitant of its linearity and hermicity properties.     

N=2超对称量子力学的新实现和形状不变性

构造新的超荷和定义权重函数,并研究了N=2一维超对称量子力学.在新的实现中讨论了若干实例.     

Instability of layered quantum liquids: 3. New phase in fermion superlattices

Starting with a layered interacting Fermi liquid we describe a possible origin of high-T _c superconductivity. We argue that for a electron densityN smaller than a critical densityN _c many-body effects are very large in layered electron systems leading, to an attraction of electrons in neighboring planes. This attraction leads to pairing of two electrons. The paired electrons are bosons, which undergo a Bose-Einstein condensation and form a Schafroth superconductor (local pairing) with a boson densityN _B expressed asT _c N _B N[1-(N/N _c )^1/2]. This superconductor is characterized by a short coherence length. We compare our theoretical results for the critical temperatureT _c , the pressure effect coefficient and the isotope effect coefficient with experimental results and find good agreement.     

Supersymmetric string theories,superconformal algebras and exceptional groups

We study the relation between extended space-time supersymmetry and extended worldsheet symmetries within the context of four-dimensional heterotic string theories. It is shown how these symmetries follow from an underlying E₇ and E₈ symmetry which also explains the appearance of extra U(1) gauge bosons. Supersymmetry transformation aalways act within a given multiplet of E₇ and E₈.