The twisted SU(N) group. On the C *-algebra C(S μ U(N))

It is proved that C(S U(N)) is a type I C ^*-algebra.     

On superstring-inspired SU(3) × SU(2) × (U(1))2 models with SO(10) unification

Alternative compactification of the heterotic superstring can give rise to a residual four-dimensional SO(10) gauge symmetry for the observable sector. We consider a model with gauge group SU(3) × SU(2) × (U(1))², resulting from the Hosotani breaking of SO(10), study its further gauge symmetry breaking and calculate the particle spectrum. We find that all breakings can occur close to the weak scale; the top mass lies preferentially between 40 and 60 GeV, the second Z boson mass is O(200–400) GeV. The sparticle spectrum is quite heavy, apart possibly from a light chargino, whose mass can be as light as O(30) GeV.     

On the implementation of Sμ U(2) action in the irreducible representations of twisted canonical commutation relations

The natural S U(2) action on the creation and annihilation operators satisfying twisted canonical commutation relations (TCCR) is investigated. It is shown that the Fock representation is the only covariant irreducible representation of TCCR.Partially supported by the program RP.1.10.     

Lepton-flavor-violating pion decay π+→μ−νμ e + e + and SU(3)C ⊗ SU(3)L ⊗ U(1)N model

Within the minimal SU(3)_C ? SU(3)_L ? U(1)_N model, the lepton-flavor-violating decay π⁺→μ^?ν_μ e ⁺ e ⁺ is calculated without directly invoking lepton mixing. The branching ratio for this rare pion-decay mode is found to be much smaller than the current experimental upper limit. If the anomalous interactions are discarded, this result coincides with the result of the previous calculation.     

Irreducible Representation of Quantum SLq(3) Algebra (Ⅰ)

The explicit forms of the irreducible representation matricea for the quantum SLq(3) enveloping algebra are computed in analogy to the irreducible tensor technique in the classical SU(3) algebra.     

Irreducible Representation of Quantum SLq(3) Algebra(Ⅱ)

The explicit forms of the Clebech-Gordan coefficients for the quantum algebra SLq(3) are computed by our technique preeented in part Ⅰ.     

The phase structure of SU(2) × U(1)Y lattice gauge theory

Using analytic and Monte Carlo techniques, we determine the phase structure and nature of spontaneous symmetry breaking of the SU(2) × U(1)_Y electroweak gauge theory with fixed-length Higgs fields on a lattice. We find that it has two completely separated phases: (a) a disordered, symmetric phase and (b) a phase in which SU(2) × U(1)_Y is spontaneously broken to U(1)_em, which is realized in its deconfined Coulomb phase with massless photons. Exact analytic results and approximate series expansions are given for various special cases of the theory.     

The existence of a non-minimal solution to the SU (2) Yang-Mills-Higgs equations on ℝ3. Part I

This paper (Part I) and the sequel (Part II) prove the existence of a smooth, non-trivial, finite action solution to the SU (2) Yang-Mills-Higgs equations on ³ in the Bogomol'nyi-Prasad-Sommerfield limit. The proof uses a simple form of Morse theory known as Ljusternik-nirelman theory. Part I establishes that a form of Lusternik-nirelman theory is applicable to the SU (2) Yang-Mills-Higgs equations. Here, a sufficient condition for the existence of the aforementioned solution is derived. Part II contains the completed existence proof. There it is demonstrated that the sufficient condition of Part I is satisfied by the SU (2) Yang-Mills-Higgs equations.Research is supported in part by the Harvard Society of Fellows and the National Science Foundation under Grant PHY 79-16812     

The SU(3) β-functionat large β

MCRG results are presented for the SU(3) β-function obtained from optimized blockspin transformations at β = 6.9 and 7.2. At both couplings for the shiftΔβ, corresponding to a change of length scale by a factor 2, Δβ = 0.51 is found. Although the error is large, deviations from asymptotic scaling seem to be larger than expected on the basis of earlier calculations.     

Yukawa couplings in SU(3)×SU(2)×U(1)Y orbifold models

We analyze the Yukawa couplings of the first SU(3)×SU(2)×U(1)_Y orbifold models recently obtained. In these models the rank is naturally lowered due to the presence of a Fayet-Iliopoulos term associated with an “anomalous” U(1) in the four-dimensional theory. It is shown that the phenomenological viability of the models selects a favoured class of vacua. In particular, for the specific examples considered, some twisted fields with one moded oscillator acting, must acquire non-vanishing VEVs. However other possibilities may exist. We also find that all the baryon and lepton violating operators can be, in general, avoided in a completely natural way.     

SU(2)×SU(2) Electroweak Theory I: The B3 Field on the Physical Vacuum

Nonlinear optics confronts the U(1) theory of electrodynamics with the dilemma of the existence of nonlinear fields. The U(1) group is completely linear and Abelian and causes consideration of an SU(2) theory of electrodynamics. An SU(2) theory of electrodynamics, with a B ³ magnetic field, means that physics is forced to consider an SU(2) × SU(2) electroweak theory. It is then demonstrated that the B ³ field exists on the physical vacuum defined by the Higgs symmetry breaking of this extended electroweak theory.     

Structure of σ model in [1, 1] representation of SU(2) ⊗ SU(2) group

The spontaneous breakdown of symmetry of the-model in the [1, 1] representation of SU(2) SU(2) group is investigated. It is shown that the spontaneous breakdown is realized in all cases of squared mass ² in mass term in the Lagrangian ( ²>0, ²=0, ²<0), unlike the-model in [1/2, 1/2] representation, in which the spontaneous breakdown only for the case ²<0 manifests itself. Further, different but equivalent methods of obtaining the nonlinear realization for pions in the frame of an extended in such a way-model are demonstrated. Finally, it is sketched, that the obtained results can be generalized to all [N/2,N/2] representations of SU(2) SU(2) chiral group.Presented at the Symposium on Hadron-Hadron Scattering at High Energies, Liblice, Czechoslovakia, June 16–21, 1975.On leave of absence from theDept. of Theoretical Physics, Comenius University, Bratislava, Czechoslovakia.     

SU(3)_C×SU(2)_I×U(1)_Y复合轻子理论

假定HiggsYukawa耦合是宇称不守恒的唯一来源，通过取三代并引进超对称性，从而建立了一个SU（3）C×SU（2）I×U（1）Y复合轻子理论。     

Renormalization group equation and QCD coupling constant in?the?presence of?SU(3) chromo-electric field

We solve the renormalization group equation in QCD in the presence of a SU(3) constant chromo-electric field E ^a with arbitrary color index a=1,2,…,8 and find that the QCD coupling constant α _s depends on two independent Casimir/gauge invariants C ₁=[E ^a E ^a ] and C ₂=[d _abc E ^a E ^b E ^c ]² instead of one gauge invariant C ₁=[E ^a E ^a ]. The β function is derived from the one-loop effective action. This coupling constant may be useful to study hadron formation from color flux tubes/strings at high energy colliders and to study quark–gluon plasma formation at RHIC and LHC.     

弱电统一理论——SU(3)×U(1)模型

本文提出了一个对称性破缺前不仅左、右对称, 而且中微子(或反中微子)与荷电轻子、反轻子的弱作用也相同的SU(3)×U(1)模型. 这一模型无三角反常; 导出了sin²θ_w≤1/4; 在低能范围内与标准模型一致. 我们反轻子数推广为轻子荷. 证明了只有轻子荷才是严格守恒的, 各代轻子数分别守恒只能近似成立. 夸克不仅带有重子数、电荷, 而且也带有轻子荷. 本模型预言有μ_R→e_R+ν_eL+ν_μR, e^－+e^－→μ^－+μ^－等现象.     

An SU (3)_L×U(1)_X Electroweak Model

We studied an SU(3)_L×U(1)_X electroweak model. By requiring M2z1-M2w/ cos²θw to be less than experimental value we abtain a lower bound on M_Z′ The relation between M_Z′ and M_U (M_V) then gives a lower bound on M_U (M_V). We further consider the K_L－K_S mass difference due to Z′ exchange and obtain stronger lower bounds on M_Z′ and M_U (M_V).     

Measurement of the forward-backward asymmetry in the B→K*μ(+)μ(-) decay and first observation of the B(s)0→ϕμ(+)μ(-) decay

We reconstruct the rare decays B(+)→K(+)μ(+0μ(-0, B90)→K*(892)(0)μ(+)μ(-), and B(s)(0)→?(1020)μ(+)μ(-) in a data sample corresponding to 4.4 fb(-1) collected in pp collisions at √[s]=1.96 TeV by the CDF II detector at the Tevatron Collider. Using 121±16 B(+)→K(+)μ(+)μ(-) and 101±12 B(0)→K(*0)μ(+)μ(-) decays we report the branching ratios. In addition, we report the differential branching ratio and the muon forward-backward asymmetry in the B(+) and B(0) decay modes, and the K(*0) longitudinal polarization fraction in the B(0) decay mode with respect to the squared dimuon mass. These are consistent with the predictions, and most recent determinations from other experiments and of comparable accuracy. We also report the first observation of the B(s)(0)→?μ(+)μ(-) decay and measure its branching ratio BR(B(s)(0)→?μ(+)μ(-))=[1.44±0.33±0.46]×10(-6) using 27±6 signal events. This is currently the most rare B(s)(0) decay observed.     

Phenomenology of the hierarchical lepton mass spectrum in the flipped SU(5)×U(1) string model

A detailed phenomenological analysis of the lepton mass matrices and their implications in the low energy theory are discussed, within the recently proposed SU(5)×U(1) string model. The unification scale is highly constrained while the Yukawa couplings lie in a natural region. The flavour changing decays μ→eγ, μ→3e, μ→e are highly suppressed while the depletion in the in the flux of muon neutrinos reported by the Kamiokande is explained through ν_μ↔ν_τ oscillations.