Left-Right Non-Linear Dynamical Higgs

All the possible CP-conserving non-linear operators up to the p⁴-order in the Lagrangian expansion are analysed here for the left-right symmetric model in the non-linear electroweak chiral context coupled to a light dynamical Higgs. The low energy effects will be triggered by an emerging new physics field content in the nature, more specifically, from spin-1 resonances sourced by the straightforward extension of the SM local gauge symmetry to the larger local group SU(2)_L×SU(2)_R×U(1)_B-L. Low energy phenomenology will be altered by integrating out the resonances from the physical spectrum, being manifested through induced corrections onto the left handed operators. Such modifications are weighted by powers of the scales ratio implied by the symmetries of the model and will determine the size of the effective operator basis to be used. The recently observed diboson excess around the invariant mass 1.8 TeV-2 TeV entails a scale suppression that suggests to encode the low energy effects via a much smaller set of effective operators.     

Z2 × Z2 Discrete Symmetry in the Left-Right Symmetric Model SU(2)L × SU(2)R × U(l)B-L

From the point that the Higgs fields can be regarded as the gauge fields on a discrete group, we construct a gauge theory of the leftright symmetric model SU(2)_L × SU(2)_R × U(1)_B-L (LRSM) over Z₂ ⊙ Z₂ discrete symmetry.     

The Anomaly Coupling of Axigluon and Technicolor Neutral Pseudo Goldstone Bosons

By gauging the anomaly terms according to the gauge group SU(3)_cl x SU(3)_cr × SU(2)_l × U(l)_Y in the technicolor theory, we obtain various possibld anomaly vertices involving technicolor pseudo Goldstone boson and gauge boson (γ, Z, g, g_A). We estimate the decay rates of g_A → gP⁰, g_A → P_A⁰³γ and g_A → P_A⁰³Z.     

Semi-simple unification on T/Z12 orientifold in the type IIB supergravity

The semi-simple unification model based on SU(5)_GUT×U(3)_H gauge group is an interesting extension of the minimal SU(5)_GUT grand unification theory (GUT), since it solves the two serious problems in the standard GUT: the triplet–doublet splitting problem and the presence of dangerous dimension five operators for proton decay. Here, the extra U(3)_H gauge interaction plays a crucial role on the GUT breaking. In this Letter, we show that the full multiplet structure of the U(3)_H sector required for the desired GUT breaking is reproduced naturally on T⁶/Z₁₂ orientifold in the type IIB supergravity with a D3–D7 system. The SU(5)_GUT vector multiplet lives on D7-branes and the U(3)_H sector resides on D3-branes. We also show that various interesting features in the original SU(5)_GUT×U(3)_H model are explained in the present brane-world scenario. A possible extension to the type IIB string theory is also discussed.     

Supersymmetric left-right model and its tests in linear colliders

We investigate phenomenological implications of a supersymmetric left-right model based on SU(2)_L × SU(2)_R × U(1)_B–L gauge symmetry testable in the next generation linear colliders. We concentrate in particular on the doubly charged SU(2)_R triplet higgsino , which we find very suitable for experimental search. We estimate its production rate in e⁺e⁻, e⁻e⁻, e⁻γ and γγ collisions and consider its subsequent decays. These processes have a clear discovery signature with a very low background from other processes.     

STRING THEORY WITH THREE FAMILIES OF CHIRAL FERMIONS

A heterotic string theory is constructed by compactifying directly from 26 to 4 dimensions via a smooth manifold T²²/G. In the low energy limit, there are three families of chiral fermions with exactly the same quantum numbers as thatin the standard supersymmetric SU(3)×SU(2)×XU(1) model. They couple to supergravity and supergauge fields with the gauge symmetry SU(3)_F×SU(3)_c×SU(3)_L×U(1)_YR×U(1)_I3R.     

Derivation of the Bosonic Part of the Electroweak Chiral Lagrangian from a General Underlying Technicolor Theory

Bosonic part of SU(2)_L\otimes U(1)_Y effective chiral Lagrangian for electroweak symmetry breaking is derived from an underlying technicolor theory with no approximation. The underlying theory is assumed to be the most general gauge theory without fundamental scalars. A condensate is required to exist in the theory which breaks SU(2)_L\otimes U(1)_Y dynamically to U(1)_em and the anomaly of the theory caused by gauge interaction must be cancelled. The formulation offers general definitions in terms of underlying theory for the low energy constants in effective chiral Lagrangian.     

SOME DISCUSSIONS OF POSSIBLE MECHANISM OF Z0→l+l-γ

The possible mechanisms for anomalous decay Z⁰→l⁺l^-γ are discussed. The mechanism with anomaious ZZ_Y vertex is investipted indetail. It is pointed out that this vertex may appear via some effective Lagrangian which can be derived from an SU(2)×U (1) gauge invariant effective Lagrangian after the spontaneous symmetry breaking. The predictions based on this mechanism are consistent with recent experiments and can be verified experimentally. This mechanism is consistent with a composite model of Z⁰ with radius 10^-15 cm.     

Four-Particle Entangled State Representation and Its Squeezing Transformation

The four-particle EPR entangled state | p,χ₂,χ₃,χ₄〉is constructed. The corresponding quantum mechanical operator with respect to the classical transformation p→e^λ₁p, χ₂→ e^λ₂χ₂, χ₃→e^λ₃χ₃, and χ₄→e^λ₄χ₄ in the state |p,χ₂ ,χ₃ ,χ₄〉is investigated, and the four-mode realization of the SU(1,1) Lie algebra as well as the corresponding squeezing operators are presented.     

The bose form of two-dimensional quantum chromodynamics

By means of a special choice of gauge QCD₂ [SU(N)] with one flavor of quarks is recast into the Bose form. Weak (g m) and strong (gm) coupling regimes are studied. The former is shown to be the SU(N)-symmetric confining phase in which bound states possess stringlike configurations with strings being represented by electric vortex lines; the ordinary mesons and baryons appear as longitudinal modes of electric strings. The strong coupling regime describes the Higgs phase with the residual symmetry [U(1)]^N−1 S_N where the left and right factors are the maximal abelian subgroup of SU(N) and the permutation group of N quarks, respectively; the particle spectrum consists of S_N multiplets and the [Uw(1)]^N−1 charges are trapped.     

The mass-scale of supersymmetry breaking and proton decay

A fundamental mass-scale is associated with the transition of supersymmetric SU(3)_c×SU(2)_L×U(1) to the ordinary SU(3)_c×SU(2)_L×U(1) symmetry of elementary particle interactions. The renormalisation of the gauge coupling in a supersymmetric SU(5) grand unification leads to the mass-scale of supersymmetry breaking to be of order 10¹² GeV if the lifetime of the proton is taken to be 10³⁰ y and is lowered to the mass-scale of ordinary electroweak interactions if the proton lives longer than 10³⁰ y. It is lower than 10¹² GeV if the contribution of light scalars is taken into account. The predictions of the weak angle sin²θ (M_W) are in excellent agreement with experiment.     

Exact Solutions of the Morse-like Potential,Step-Up and Step-Down Operators via Laplace Transform Approach

We intend to realize the step-up and step-down operators of the potential V (x) = V₁ e ^2βx + V₂ e ^βx. It is found that these operators satisfy the commutation relations for the SU(2) group. We find the eigenfunctions and the eigenvalues of the potential by using the Laplace transform approach to study the Lie algebra satisfied the ladder operators of the potential under consideration. Our results are similar to the ones obtained for the Morse potential (β → -β).     

CONFINEMENT PROPERTIES OF PURE GAUGE FIELCS ON COSET SPACE OF THE NON-ABELIAN CHIRAL GROUP

In this paper the method of lattlce gauge theories is applied to the investigation of the effect of coset pure gauge fields of the non-Abelian chiral group on the confinement properties of a system. In particular, the current-current propagator of the coset G/H=SU(2)_L×(2)_r/SU(2) model is calculated. Then it IS found that the pure gauge fields-on coset space only offer a perimeter law factor which does not change the confinement properties of a physical system.     

Renormalization group analysis and the top quark mass in the SU(4) × O(4) string model

We perform a two-loop renormalization group analysis for the gauge couplings in the SU(4) × O(4) model. We use the string theory prediction for the unification scale and the experimentally acceptable low energy values for ₃ and sin² θ_w, to determine the magnitudes of the various symmetry breaking scales as well as the value of the common gauge coupling at the unification scale. We solve the coupled differential system for the gauge and top and bottom Yukawa couplings, and determine the top mass as a function of two parameters which could be chosen to be the ratio of the Higgs VEV's that give masses to the up and down quarks and the value of the top coupling at the unification scale. We find a relatively heavy top quark mass which lies in the range 130m_t180 GeV.     

An orbifold compactification with three families from twisted sectors

We obtain a three generational SU(3)_c×SU(3)_w×U(1)⁴×[SO(12)×U(1)²]′ model from an orbifold construction with the requirement that three generations arise from twisted sectors. There exist supersymmetric vacua realizing the standard model. In one example the anomalous U(1) breaks the gauge symmetry down to SU(3)_c×SU(3)_w×U(1)_y×SO(12)′.     

An Interacting Gauge Field Theoretic Model for Hodge Theory: Basic Canonical Brackets

We derive the basic canonical brackets amongst the creation and annihilation operators for a two （1 ＋ 1）- dimensional （2D） gauge field theoretic model of an interacting Hodge theory where a U（1） gauge field （Aμ） is coupled with the fermionic Dirac fields （ψ and ψ）. In this derivation, we exploit the spin-statistics theorem, normal ordering and the strength of the underlying six infinitesimal continuous symmetries （and the concept of their generators） that are present in the theory. We do not use the definition of the canonical conjugate momenta （corresponding to the basic fields of the theory） anywhere in our whole discussion. Thus, we conjecture that our present approach provides an alternative to the canonical method of quantization for a class of gauge field theories that are physical examples of Hodge theory where the continuous symmetries （and corresponding generators） provide the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level.     

Symplectic Geometry,Hopf Algebraic Structures of Classical and Quantum q-Deformations of SU(2) Algebra

By deforming the symplectic structure on S², we get the q-deformation of SU(2) algebra at classical level, SU_q,h→0(2), in a Hamiltonian approach. Furthermore, we construct a set of operators on the line bundle over the deformed symplectic manifo1d.S_q² such that they form SU_q,h→0(2) in Lie brackets and set up a nontrivial Hopf algebra with a parameter q only in such a classical Hamiltonian system. We also show that the deformations from S_q² to S_q² are a set of quasiconformal transformations. The quantization via geometric approach of the system gives rise to the quantum q-deformed algebra SU_q,h(2), wnich has a Hopf algebraic structure with two independent parameters q and h.     

Two-loop renormalization of tanβ and its gauge dependence

Renormalization of two-loop divergent corrections to the vacuum expectation values (v₁,v₂) of the two Higgs doublets in the minimal supersymmetric standard model, and their ratio tanβ=v₂/v₁, is discussed for general R_ξ gauge fixings. When the renormalized (v₁,v₂) are defined to give the minimum of the loop-corrected effective potential, it is shown that, beyond the one-loop level, the dimensionful parameters in the R_ξ gauge fixing term generate gauge dependence of the renormalized tanβ. Additional shifts of the Higgs fields are necessary to realize the gauge-independent renormalization of tanβ.     

A Lattice Study of the Glueball Spectrum

Glueball Spectrum is studied using an improved gluonic action on asymmetric lattices in the pure SU(3) gauge theory.The smallest spatial lattice spacing is about 0.08 fm which makes the extrapolation to the continuum limit more reliable.In particular.attention is paid to the scalar glueball mass which is known to have problems in the extrapolation.Converting our lattice results to physical units using the scale set by the static quark potential,we obtain the following results for the glueball masses:MG(0 )=1730(90)MeV for the scalar glueball mass and MG(2 )=2400(95)MeV for the tensor glueball.     

On the link between strong and weak coupling expansions for the SU(2) lattice gauge theory

The intermediate region between the strong and weak coupling expansions of SU(2) lattice gauge theory is analyzed by inverting the strong coupling series of the average plaquette energy E_p(J).

Taking into account the weak coupling behaviour too, we get Padé approximants for J(E_p) valid in the whole physical region. The zeros of pJ/pE_p are mapped into singularities of E_p(J); they occur for complex values of J and give rise to a peak in the specific heat in fair agreement with the Monte Carlo simulation data. The variable E_p is further used to analyze the strong coupling expansions for the roughening indicator, the string tension and the mass gap.