A possible minimal gauge–Higgs unification

A possible minimal model of the gauge–Higgs unification based on the higher dimensional spacetime M ⁴⊗(S ¹/Z ₂) and the bulk gauge symmetry SU(3) _C ⊗SU(3) _W ⊗U(1) _X is constructed in some detail. We argue that the Weinberg angle and the electromagnetic current can be correctly identified if one introduces the extra U(1) _X above and a bulk scalar triplet. The VEV of this scalar as well as the orbifold boundary conditions will break the bulk gauge symmetry down to that of the standard model. A new neutral zero-mode gauge boson Z′ exists that gains mass via this VEV. We propose a simple fermion content that is free from all the anomalies when the extra brane-localized chiral fermions are taken into account as well. The issues on recovering a standard model chiral-fermion spectrum with the masses and flavor mixing are also discussed, where we need to introduce the two other brane scalars which also contribute to the Z′ mass in the similar way as the scalar triplet. The neutrinos can get small masses via a type I seesaw mechanism. In this model, the mass of the Z′ boson and the compactification scale are very constrained being, respectively, given in the ranges: 2.7 TeV<m _Z′<13.6 TeV and 40 TeV<1/R<200 TeV.     

A Condensed Matter Interpretation of SM Fermions and Gauge Fields

We present the bundle (Aff(3)⊗ℂ⊗Λ)(ℝ³), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each (ℂ⊗Λ)(ℝ³) describes an electroweak doublet. The Dirac equation has a doubler-free staggered spatial discretization on the lattice space (Aff(3)⊗ℂ)(ℤ³). This space allows a simple physical interpretation as a phase space of a lattice of cells. We find the SM SU(3) _c ×SU(2) _L ×U(1) _Y action on (Aff(3)⊗ℂ⊗Λ)(ℝ³) to be a maximal anomaly-free gauge action preserving E(3) symmetry and symplectic structure, which can be constructed using two simple types of gauge-like lattice fields: Wilson gauge fields and correction terms for lattice deformations. The lattice fermion fields we propose to quantize as low energy states of a canonical quantum theory with ℤ₂-degenerated vacuum state. We construct anticommuting fermion operators for the resulting ℤ₂-valued (spin) field theory. A metric theory of gravity compatible with this model is presented too.     

Obtaining the Gauge Invariant Kinetic Term for a SU(n) U ⊗ SU(m) V Lagrangian

We propose a generalized way to formally obtain the gauge invariance of the kinetic part of a field Lagrangian over which a gauge transformation ruled by an SU(n) _U ⊗ SU(m) _V coupling symmetry is applied. As an illustrative example, we employ such a formal construction for reproducing the standard model Lagrangian. This generalized formulation is supposed to contribute for initiating the study of gauge transformation applied to generalized SU(n) _U ⊗ SU(m) _V symmetries as well as for complementing an introductory study of the standard model of elementary particles.     

Separability of two-qubit state in terms of local invariants

The separability condition for the two-qubit mixed state is formulated in terms of a system of inequalities in invariants of the adjoint SU(2) ⊗ SU(2) action on the space of density matrices, i.e., positive semidefinite 4 × 4 Hermitian matrices.     

Pion and kaon electromagnetic form factors in a SUL(3) ⊗ SUR(3) effective Lagrangian

A SU(2) effective Lagrangian is extended to a SU _L(3) ⊗SU _R(3) by including the vector and axial vector meson. With this effective Lagrangian, electromagnetic form factors of charged pion and kaon are calculated in both time- and space-like regions. The pseudoscalar meson loops are taken into account. Good agreement with experimental data is obtained for those form factors and charged pseudoscalar meson radii. Decay widths of ρ→ππ and φ→K ⁺ K ^- are also calculated and shown to agree with experimental data very well. Received: 20 December 1999 / Accepted: 12 October 2000     

A SU(4)⊗O(3) scheme for nonstrange baryons

We show that nonstrange baryon resonances can be classified according to multiplets of SU(4)⊗O(3). We identify spectral regularities and degeneracies that allow us to predict the high-spin spectrum from 2 to 3GeV.     

On unified field theories,dynamical torsion and geometrical models: II

We analyze in this letter the same space-time structure as that presented in our previous reference (Part. Nucl., Lett. 2010. V. 7, No. 5, P. 299–307), but relaxing now the condition a priori of the existence of a potential for the torsion. We show through exact cosmological solutions from this model, where the geometry is Euclidean R ⊗ O ₃ ∼ R ⊗ SU(2), the relation between the space-time geometry and the structure of the gauge group. Precisely this relation is directly connected with the relation between the spin and torsion fields. The solution of this model is explicitly compared with our previous ones and we find that: (i) the torsion is not identified directly with the Yang-Mills type strength field, (ii) there exists a compatibility condition connected with the identification of the gauge group with the geometric structure of the space-time: this fact leads to the identification between derivatives of the scale factor with the components of the torsion in order to allow the Hosoya-Ogura ansatz (namely, the alignment of the isospin with the frame geometry of the space-time), and (iii) of two possible structures of the torsion the “tratorial” form (the only one studied here) forbids wormhole configurations, leading only to cosmological space-time solution in eternal expansion.     

SU(3) classification of p-wave ηπ and π systems

An exotic meson, the π₁(1400) with J ^PC = 1^{- +}, has been seen to decay into a p-wave ηπ system. If this decay conserves flavor SU(3), then it can be shown that this exotic meson must be a four-quark state ( qˉq + qˉq) belonging to a flavor ˉ10 representation of SU(3). In contrast, the π₁(1600) with a substantial decay mode into π is likely to be a member of a flavor octet. Received: 27 March 2002 / Accepted: 8 August 2002 / Published online: 10 December 2002 RID="b" ID="b"e-mail: klempt@iskp.uni-bonn.de Communicated by V. Vento     

Family unification inSU(6) L ⊗U(1) Y

Electroweak and horizontal interactions are unified with the groupSU(6) _L U(1) _Y for three generations. The horizontal gauge group suggested from low energy phenomenology isSU(2) _H . This model does not contain exotic quarks, but exotic leptons are needed in order to make it anomaly-free. The breaking of the symmetry gives, in a natural way, heavy masses for exotic leptons and a BCS mass matrix for the up quarks, which implies that at tree level only the top quark gets a mass of orderM _W . The see-saw mechanism generates tiny masses for the three known neutrinos. The remaining of the known fermion masses are light, because they can be generated only as radiative corrections.     

Large N 2D Yang-Mills Theory and Topological String Theory

We describe a topological string theory which reproduces many aspects of the 1/N expansion of SU(N) Yang-Mills theory in two spacetime dimensions in the zero coupling (A= 0) limit. The string theory is a modified version of topological gravity coupled to a topological sigma model with spacetime as target. The derivation of the string theory relies on a new interpretation of Gross and Taylor's “Ω^-1 points ”. We describe how inclusion of the area, coupling of chiral sectors, and Wilson loop expectation values can be incorporated in the topological string approach. Received: 3 March 1994 / Accepted: 2 February 1995     

Unified Field Theoretical Models from Generalized Affine Geometries II

The space-time structure of the new Unified Field Theory presented in previous reference (Int. J. Theor. Phys. 49:1288–1301, 2010) is analyzed from its SL(2C) underlying structure in order to make precise the notion of minimal coupling. To this end, the framework is the language of tensors and particularly differential forms and the condition a priory of the existence of a potential for the torsion is relaxed. We shown trough exact cosmological solutions from this model, where the geometry is Euclidean R⊗O ₃∼R⊗SU(2), the relation between the space-time geometry and the structure of the gauge group. Precisely this relation is directly connected with the relation of the spin and torsion fields. The solution of this model is explicitly compared with our previous ones and we find that: (i) the torsion is not identified directly with the Yang Mills type strength field, (ii) there exists a compatibility condition connected with the identification of the gauge group with the geometric structure of the space-time: this fact lead the identification between derivatives of the scale factor a(τ) with the components of the torsion in order to allows the Hosoya-Ogura ansatz (namely, the alignment of the isospin with the frame geometry of the space-time), (iii) this compatibility condition precisely mark the fact that local gauge covariance, coordinate independence and arbitrary space time geometries are harmonious concepts and (iv) of two possible structures of the torsion the “tratorial” form (the only one studied here) forbids wormhole configurations, leading only, cosmological instanton space-time in eternal expansion.     

Mass operator in theSU(3)-symmetric strong coupling theory with pseudoscalar mesons

In this paper theSU(3)-symmetric model of a static baryon octet source interacting with pseudoscalar meson octet fields by the coupling of Yukawa type is considered in the strong coupling limit. Using the result derived earlier that the isobaric states form the basis of the unitary irreducible representation of the dynamical group G=T ₂₄ [SU(3) SU(2)], the mass operator is specified by the kinetic part of the Hamiltonian as a particular element of the universal enveloping algebra of the symmetry groupSU(3) SU(2) acting in the space of isobaric states.     

Detection of heavy Majorana neutrinos and right-handed bosons

The SU _c (3) ⊗ SU _L (2) ⊗ SU _R (2) ⊗ U(1) left-right (LR) symmetric model explains the origin of the parity violation in weak interactions and predicts the existence of additional gauge bosons W _R and Z′. In addition, heavy right-handed Majorana neutrino states N arise naturally within the LR symmetric model. The states N could be partners of light neutrino states, related to their nonzero masses through the seesaw mechanism. This makes the searches for W _R , Z′, and N interesting and important. In the framework of the minimal LR model, we study the possibility to observe signals from N and W _R production in pp collisions after three years of running at low LHC luminosity. We show that their decay signals can be identified with a small background, especially in the case of same-sign leptons in the final state. For the integral LHC luminosity of L _t = 30 fb⁻¹, the 5σ discovery of W _R boson and heavy Majorana neutrinos N _e with masses up to 4 TeV and up to 2.4 TeV, respectively, is found to be possible. The text was submitted by the authors in English.     

Colour gluons and scaling in a unified gauge model

Deep inelastic weak and electromagnetic processes are considered within the parton framework taking the partons to be integrally charged quarks and coloured gluons. Despite the participation of the spin-one gluons in these processes, scaling is shown to be maintained by treating the problem in a unified gauge model based on the groupSU (3)_colour⊗SU _L (2)⊗U(1). This is a consequence of the vector-dominance type of couplings between the gluons and the weak or electromagnetic vector bosons which are induced by the spontaneous breakdown of gauge symmetry. As a further consequence it is found that in the asymptotic region far above the gluon masses the colour octet parts of the weak and electromagnetic currents of the quarks are damped so that, in particular, the integrally charged quarks behave as fractionally charged quarks in this region.     

Quaternionic-valued Gravitation in 8D, Grand Unification and Finsler Geometry

A unification model of 4D gravity and SU(3)×SU(2)×U(1) Yang-Mills theory is presented. It is obtained from a Kaluza-Klein compactification of 8D quaternionic gravity on an internal CP ²=SU(3)/U(2) symmetric space. We proceed to explore the nonlinear connection formalism used in Finsler geometry to show how ordinary gravity in D=4+2 dimensions has enough degrees of freedom to encode a 4D gravitational and SU(5) Yang-Mills theory. This occurs when the internal two-dim space is a sphere S ². This is an appealing result because SU(5) is one of the candidate GUT groups. We conclude by discussing how the nonlinear connection formalism of Finsler geometry provides an infinite hierarchical extension of the Standard Model within a six dimensional gravitational theory due to the embedding of SU(3)×SU(2)×U(1)⊂SU(5)⊂SU(∞).     

Classification of Subsystems for Local Nets¶with Trivial Superselection Structure

Let ℱ be a local net of von Neumann algebras in four spacetime dimensions satisfying certain natural structural assumptions. We prove that if ℱ has trivial superselection structure then every covariant, Haag-dual subsystem ℬ is of the form ℱ₁ ^G ⊗I for a suitable decomposition ℱ=ℱ₁⊗ℱ₂ and a compact group action. Then we discuss some application of our result, including free field models and certain theories with at most countably many sectors. Received: 26 January 2000 / Accepted: 28 September 2000     

SU(2,2¦N) · 〈N′〉 superunified theory

We establish a superspaceU for supergauge actions, a conformal supergroupSU(2,2¦N), and a conformal extendedSU(2,2¦N) supergravity theory. Using the Lagrangian Higgs evolution mechanism under the supergroupSU(2,2¦N) SU(N) acting on the superspaceU, we advance anSU(2,2¦N)SUN superunified theory of a superunited system, discuss the Lagrangian evolution of the superunified theory, and give the fiber bundle geometry of all the above mechanisms.     

Complex quantum group,dual algebra and bicovariant differential calculus

The method used to construct the bicovariant bimodule in ref. [CSWW] is applied to examine the structure of the dual algebra and the bicovariant differential calculus of the complex quantum group. The complex quantum group Fun _q (SL(N, C)) is defined by requiring that it contains Fun _q (SU(N)) as a subalgebra analogously to the quantum Lorentz group. Analyzing the properties of the fundamental bimodule, we show that the dual algebra has the structure of the twisted product Fun _q (SU(N))Fun _q (SU(N)) _reg ^* . Then the bicovariant differential calculi on the complex quantum group are constructed.     

Group theoretical aspects ofU B(6) ⊗U F(20) symmetry limits of IBFM related to theU B(5) andO B(6) limits of IBM

TheU ^B(6)⊗U ^F(20) Bose-Fermi dynamical symmetry of interacting boson-fermion model arises when the odd nucleon occupies single particle orbits withj=1/2, 3/2, 5/2, and 7/2. The subgroup structures ofU ^B(6)⊗U ^F(20) related to theU ^B(5) andO ^B(6) limits of sdIBM (U ^B(6)) are analysed. Broadly speaking,U ^B(6)⊗U ^F(20) admitsU ^BF(5)⊗U _s ^F (4), Spin^BF(5)⊗U _k ^F (5) andU ^BF(5)⊗U _s ^F (2) limits withU ^B(5) core and Spin^BF(6),O ^BF(5)⊗U _s ^F (4), Spin^BF(6)⊗U _k ^F (5) andO ^BF(6)⊗U _s ^F (2) limits withO ^B(6) core respectively. For each of these seven symmetry limits, group chains, quantum numbers labelling the basis states, generators and Casimir operators for the various subgroups and energy formulas are given. Recoupling coefficients (reduced Wigner coefficients) for constructing wavefunctions of low-lying states are tabulated and these will allow (together with sdIBMU ^B(5) andO ^B(6) limit results) one to calculateB(E2)’s,B(M1)’s, one and two nucleon transfer strengths etc. in the seven symmetry limits. Experimental examples for theU ^B(6)⊗U ^F(20) symmetry limits are briefly discussed.