Graded Lie Algebra and the SU(3) L ⊗U(1) N Gauge Model (original) (raw)

Gauge bosons and fermions in SU(3)C x SU(4)L x U(1)X model with SU(2)H xU(1)AH symmetry

2009

We present a phenomenological study of neutral gauge bosons and fermions in an extended Standard model with SU(3)C x SU(4)L x U(1)X gauge symmetry.The model includes gauge bosons and fermions without exotic charges and is distinguished by the symmetry-breaking patern SU(4)L->SU(2)L x SU(2)H x U(1)AH. This introduces an extended electroweak symmetry group SU(2)L x SU(2)H at low energies.We recover the fermion spectra of an anomaly-free three-family 3-4-1 modelwithout exotic chargesfor U(1)X charge X = T3R+(B-L)/2.The interaction of physical neutral gauge bosons Zprime,Z double prime and exotic fermions are presented along with their masses and mixing angle.The electroweak constraints from oblique corections on the model are also calculated.

New Algebraic Unified Theory of Leptons and Quarks

Progress of Theoretical Physics, 1987

A new algebraic theory is developed to describe the characteristic features of leptons and quarks as a whole. A pair of master fields with up and down 'weak-isospin is introduced and postulated to obey the generalized Dirac equations with coefficient matrices which belong to an algebra, a triplet algebra, consisting of triple-direct-products of Dirac's I-matrices. The triplet algebra is decomposed into three subalgebras, in a non-intersecting manner, which describe respectively the external Lorentz symmetry, the internal colour symmetry and the degrees of freedom for fourfold-family-replication of fundamental fermionic particle modes. The master fields belonging to a 64 dimensional multi-spinor space form non-irreducible representations of the Lorentz group and represent fourfold-replications of families of spin 1/2 particles, each one of which accomodates triply-degenerate quark modes and singlet leptonic modes. Canonical quantization of master fields leads naturally to the renormalizable unified field theories of fundamental fermions with universal gauge interactions of local symmetries having the route of descent from SUc(4) x SUL(2) x SUR(2) to SUc(3) x SUL(2) x Uy(l).

SU(3)C⊗SU(3)L⊗U(1)X gauge symmetry from SU(4)PS⊗SU(4)L+R

Physical Review D, 2005

We consider an extension of the standard model gauge symmetry to a local gauge group SU(3) C ⊗SU(3) L ⊗U(1) X which is a subgroup of SU(4) PS ⊗ SU(4) L+R .The symmetry breaking pattern is SU(4) SU(3) ⊗U(1) for both weak SU(4) L+R and strong Pati-Salam SU(4) PS group. The SU(3) C ⊗U(1) B-L ⊗SU(3) L ⊗U(1) Y1 (3-3-1-1) local gauge symmetry breaks to SU(3) C ⊗SU(3) L ⊗U(1) X and generates a 3-3-1 model with threegeneration, anomaly-free fermions which transform as bifundamentals of (3-3-1-1). The 3-3-1 model is of Pleitez-Frampton type but SU(3) L gauge bosons (B-L = 0) do not include bilepton gauge boson.The neutral gauge bosons include γ, Z, Z / and a fourth, heavy gauge boson Z // which decouples from rest but can decay to ordinary fermions. An analysis for two-body decays of neutral Z / gauge boson is presented .From Yukawa interactions, the masses of all exotic fermions are obtained in the TeV region .This restricts Z / decays to exotic fermions The Z / is also found to be leptophobic and decays mainly to quarks.

A Geometric Basis for the Standard-Model Gauge Group

International Journal of Modern Physics, 2001

A geometric approach to the standard model in terms of the Clifford algebra C 7 is advanced. A key feature of the model is its use of an algebraic spinor for one generation of leptons and quarks. Spinor transformations separate into left-sided ("exterior") and right-sided ("interior") types. By definition, Poincaré transformations are exterior ones. We consider all rotations in the sevendimensional space that (1) conserve the spacetime components of the particle and antiparticle currents and (2) do not couple the right-chiral neutrino. These rotations comprise additional exterior transformations that commute with the Poincaré group and form the group SU (2) L , interior ones that constitute SU (3) C , and a unique group of coupled double-sided rotations with U (1) Y symmetry. The spinor mediates a physical coupling of Poincaré and isotopic symmetries within the restrictions of the Coleman-Mandula theorem. The four extra spacelike dimensions in the model form a basis for the Higgs isodoublet field, whose symmetry requires the chirality of SU (2). The charge assignments of both the fundamental fermions and the Higgs boson are produced exactly.

Unified Lepton-Hadron Symmetry and a Gauge Theory of the Basic Interactions

Physical Review D, 1973

An attempt is made to unify the fundamental hadrons and leptons into a common irreducible representation I of the same symmetry group G and to generate a gauge theory of strong, electromagnetic, and weak interactions. Based on certain constraints from the hadronic side, it is proposed that the group 6 is SU(4') x SU(4"), which contains a Han-Nambu-type SU(3') x SU{3")group for the hadronic symmetry, and that the representation I' is (4, 4*). There exist four possible choices for the lepton number L and accordingly four possible assignments of the hadrons and leptons within the (4, 4*). Two of these require nine Han-Nambu-type quarks, three "charmed" quarks, and the observed quartet of leptons. The other two also require the nine Han-Nambu quarks, plus heavy leptons in addition to observed leptons and only one or no "charmed" quark. One of the above four assignments is found to be suitable to generate a gauge theory of the weak, electromagnetic, and SU(3") gluonlike strong interactions from a selection of the gauges permitted by the model. The resulting gauge symmetry is SU(2')z x U(1) x SU(3")z,+z. The scheme of all three interactions is found to be free from Adler-Bell-Jackiw anomalies. The normal strong interactions arise effectively as a consequence of the strong gauges SU{3")z, z. Masses for the gauge bosons and fermions are generated suitably by a set of 14 complex Higgs fields. The neutral neutrino and AS =0 hadron currents have essentially the same strength in the present model as in other SU(2)L, x U(1) theories. The mixing of strongand weak-gauge bosons (a necessary feature of the model) leads to parity-violating nonleptonic amplitudes, which may be observable depending upon the strength of SU(3") symmetry breaking. The familiar hadron symmetries such as SU{3') and chiral SU(3')& xSU(3')z are broken only by quark mass terms and by the electromagnetic and weak interactions, not by the strong interactions. The difficulties associated with generating gauge interactions in the remaining three assignments are discussed in Appendix A. Certain remarks are made on the question of proton and quark stability in these three schemes,

SYSTEMATIC STUDY OF THE SU(3) c ⊗SU(4) L ⊗U(1) X GAUGE SYMMETRY

Modern Physics Letters A, 2007

We carry a systematic study of possible extensions of the standard model based on the gauge group SU (3) c ⊗SU (4) L ⊗U (1) X . We consider both models with particles with exotic electric charges and models which do not contain exotic electric charges neither in the gauge boson sector nor in the fermion sector. For the first case an infinite number of models can, in principle, be constructed, while the restriction to non-exotic electric charges only allows for eight different anomaly-free models. Four of them are three-family models in the sense that anomalies cancel by an interplay between the three families, and another two are one-family models where anomalies cancel family by family as in the standard model. The remaining two are two-family models.

Lie Algebras in Particle Physics

American Journal of Physics, 1982

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