Triplet Representation Research Articles

Spontaneous breaking of the lepton number and invisible majoron in a 3-3-1 model

In this work we implement the spontaneous breaking of lepton number in version II of the 3-3-1 models and study their phenomenological consequences. The main result of this work is that our majoron is invisible even though it belongs to a triplet representation by the 3-3-1 symmetry.

Tomographic representation of spin and quark states

We present a short review of the general principles of constructing tomograms of quantum states. We derive a general tomographic reconstruction formula for the quantum density operator of a system with a dynamical Lie group. In the reconstruction formula, the multiplicity of irreducible representation in Clebsch–Gordan decomposition is taken into account. Various approaches to spin tomography are discussed. An integral representation for the tomographic probability is found and a contraction of the spin tomogram to the photon-number tomography distribution is considered. The case of SU(3) tomography is discussed with the examples of quark states (related to the simplest triplet representations) and octet states.

Search for Higgs bosons and new particles decaying into two photons at [formula omitted] GeV

A search for the resonant production of high mass photon pairs associated with a leptonic or hadronic system has been performed using a data sample of 57.7 pb −1 collected at an average center-of-mass energy of 182.6 GeV with the OPAL detector at LEP. No evidence for contributions from non-Standard Model physics processes was observed. The observed candidates are used to place limits on B(H 0→ γγ) assuming a Standard Model production rate for Higgs boson masses up to 92 GeV, and on the production cross section for a scalar resonance decaying into di-photons up to a mass of 170 GeV. Upper limits on the product of cross section and branching ratios, σ( e + e −→ XY)×B( X→γγ)×B( Y→f f ̄ ) , as low as 70 fb are obtained over the range 10< M X<170 GeV for the case where 10< M Y<160 GeV and M X+ M Y>90 GeV, independent of the nature of Y provided it decays to a fermion pair and has negligible width. Higgs scalars which couple only to gauge bosons at Standard Model strength are ruled out up to a mass of 90.0 GeV at the 95% confidence level. Limits are also placed on non-minimal Higgs sectors having triplet representations.

PROBING EXOTIC HIGGS SECTORS IN ℓ-ℓ- COLLISIONS

I review extended Higgs sectors and constraints thereon arising from ρ=1, gauge-coupling unification and b→sγ. The couplings and decays of the Higgs boson eigen-states are outlined for triplet representations. Direct experimental probes of exotic Higgs bosons are reviewed with a focus on the important role that would be played by an e-e- or μ-μ- collider.

Triplet geometric representation: a novel scale, translation and rotation invariant feature representation based on geometric constraints for recognition of 2D object features

We present a novel representation for scale, translation and rotation independent recognition of 2D object features based on the invariance properties of the included angles of a triangle which we exploit to construct signature histograms of local shape. We describe the practical implementation of this new technique together with its properties, and present a statistical quantification of performance in the presence of: fragmentation, additive noise and clutter. The scale-invariant properties are assessed, the results of which imply a fundamental limit on scale-invariant recognition from a single model.

A Class of Quantum Integrable Models Associated with the Infra-red Limit of Massive Chern–Simons Theory

We study the infra-red limit of non-abelian Chern–Simons gauge theory perturbed by a non-topological, albeit gauge invariant, mass term. It is show that, in this limit, we may construct an infinite class of integrable quantum mechanical models which, for the case of SU(2) group, are labelled by the angular momentum eigenvalue. The first non-trivial example in this class is obtained for the triplet representation and it physically describes the gauge invariant coupling of a non-abelian Chern–Simons particle with a particle moving onS3—the SU(2) group manifold. In addition to this, the model has a fascinating resemblance to the Landau problem and may be regarded as a non-abelian and a non-linear generalisation of the same defined on the three-sphere with the uniform magnetic field replaced by an angular momentum field. We explicitly solve for some eigenstates of this model in a closed form in terms of some generalised orthogonal polynomials. In the process, we unravel some startling connections with Anderson's chain models which are important in the study of disordered systems in condensed matter physics. We also sketch a method which allows us, in principle, to find the energy eigenvalues corresponding to the above eigenstates of the theory if the Lyapunov exponents of the transfer matrix of the infinite chain model involved are known.

Dibaryon states containing two different types of heavy quarks.

In a recent series of papers we have shown that including heavy quarks in the dibaryon sector can lead to configurations stable against decay into two baryons. In this study we extend our previous work by a study of all the physical ${\mathit{Q}}^{2}$${\mathit{q}}^{4}$ [Q denotes a heavy quark and q denotes a member of the SU(3${)}_{\mathit{F}}$ triplet representation] systems in a solvable chromomagnetic model. We propose a number of new heavy states which could be stable under strong interactions.

Naturalness problems for rho =1 and other large one-loop effects for a standard-model Higgs sector containing triplet fields.

Extensions of the Higgs sector of the standard model (SM) that employ only doublet and singlet Higgs-field representations are not the only ones that guarantee \ensuremath{\rho}=1 at the tree level. Higgs sectors containing triplet (and higher) representations can be constructed in such a way that there is a tree-level custodial SU(2) symmetry yielding \ensuremath{\rho}=1. However, this custodial SU(2) is inevitably violated at the one-loop level. We explore the implications of this violation in the context of a Higgs sector containing triplet fields. In particular, we show that it leads to one-loop corrections to \ensuremath{\rho} and to certain mixings among the Higgs bosons and gauge bosons of the model that are quadratically divergent, thereby creating a new naturalness problem for \ensuremath{\rho} and for certain Higgs-boson couplings. This new class of naturalness problems first arises for a Higgs sector with triplet representations, making such a sector an interesting case study. A priori, deviations from \ensuremath{\rho}=1 induced at one loop are of arbitrary magnitude and sign. We demonstrate that the fine-tuning required to keep one-loop corrections to \ensuremath{\rho} and the Higgs-boson couplings small is similar in nature to that required in the SM to keep the SM Higgs-boson mass in the perturbative regime.

Pseudospin symmetry and new collective modes of the Hubbard model.

The Hubbard model possesses a SU(2) pseudospin symmetry, which contains the U(1) phase symmetry as a subgroup. The existence of such symmetry leads to interesting experimental consequences if the U(1) phase symmetry is spontaneously broken, i.e., if the ground state is superconducting. In this case, there must exist a pair of massive collective modes which together with the usual Goldstone mode form a triplet representation of the psuedospin group. These collective modes are collisionless and couple directly to external charge disturbances with wave number \ensuremath{\pi} and can therefore be detected experimentally as sharp resonances.

Top-quark decay in models with Higgs triplets.

It is well known that if the charged Higgs scalar (${H}^{\ifmmode\pm\else\textpm\fi{}}$) is lighter than the top quark ($t$) then the decay $t\ensuremath{\rightarrow}b{H}^{+}$ will dominate over the usual charged-current decays via the $W$ in the two-Higgs-doublet extension of the standard model. We show that in models with Higgs fields in triplet representations, the fine-tuning of the ratio of triplet to doublet vacuum expectation values required by constraints on the $\ensuremath{\rho}$ parameter naturally leads to competitive charged-Higgs-boson and $W$ decay modes for the $t$ quark if its mass is below ${M}_{W}+{m}_{b}\ensuremath{\simeq}85$ GeV. In these models we show that the branching fraction for $t\ensuremath{\rightarrow}b\ensuremath{\tau}\ensuremath{\nu}$ is always enhanced whereas the corresponding branching fraction for $t\ensuremath{\rightarrow}\mathrm{bl}\ensuremath{\nu}$ is suppressed. Universality violation is one of the best probes of this scenario.

Quark confinement with dynamical fermions in higher representations

We study the static interquark potential on a hypercubic lattice in pure gauge theory and with dynamical fermions in triplet and octet representation. Our computation shows that octet fermions in contraryto triplet fermions have no effect on the linear confinement behavior of the quark-antiquark potential. This fact gives interesting insight into the confinement mechanism of supersymmetric Yang-Mills theories if octet fermions are interpreted as a simple model for gluinos.

See-saw neutrino masses induced by a triplet of leptons

Neutrinos can acquire mass through the see-saw mechanism by extending the lepton sector of the Standard Model. The most generalSU(2)L assignments allowed for the exotic leptons are the singlet and triplet representations. A model is constructed involving a triplet of exotic leptons. In this model lepton number is broken. Therefore lepton number violating processes, in particular those involving the lepton triplet, could provide distinctive experimental signatures.

Is the fourth generation a weak SU(2) triplet?

The possibility of additional fermions in non-standard weak SU (2) ⊗ U (1) representations is investigated. If only one additional Higgs multiplet is allowed, then the additional fermion representation must be a Y=0 triplet with the additional Higgs fields belonging to a Y=2 triplet representation. The additional charged fermions have a characteristic signature, and they can reduce the theoretically predicted ratio R= N( P P → W→ ev) N ( P P → Z→ e + e −) in accordance with the experimental value.

Ground state of spin liquids, hole-hole attraction and high-T csuperconductivity

We develop a notion of high-Tcsuperconductivity, which considers that phenomenon as a general property of close to half-filled bands of strongly correlated electrons confined to low-dimensional orbital lattices. Based on Andersons suggestion [1] we initially investigate the Cud electron system of the undoped mother substances of the high-Tc superconductors in the framework of the spin 1/2 Heisenberg model. We derive a new representation of the corresponding Hamiltonian in terms of triplet quasi-particles. The triplet representation leads to simple physical pictures for the ‘spin liquid’ state and to a hierarchy of nearly exact variational wave functions for the ground state of the linear chain. These wave functions are employed as vacuum states for doping with holes. Holes are shown to form a conduction band embedded in the Hubbard-Mott insulating phase of strongly correlated electrons. The chemical binding forces among these localized electrons entail a strong attractive pair potential acting between the mobile defects. The generality of the hole-hole attraction and its independence of a strict localization of the electrons in the Hubbard-Mott phase is demonstrated by nearly exact solutions of the Hubbard and Pariser-Parr-Pople models of small regular electron chains at various degrees of electron correlation. It is suggested that this exchange-driven attraction leads to an instability of the free hole gas towards Cooper pair formation.

Potentials in pure QCD on 32 4 lattices

A range of properties of pure SU (3) gauge theory are studied numerically on euclidean lattices of 32 4 points at β values of 6.29, 6.585 and 6.88. Potentials between static pairs of colour charges in the triplet, octet and sextet representations are calculated. The lowest energy (the A 1g) gluonic modes are considered for each of these plus the E u mode for the triplet case. In the calculations, the use of extended operators on the lattice is examined. The results are assessed for scaling but do not agree adequately with asymptotic behaviour based on the two-loop β-function.

Horizontal gauge interaction as the primary source of CP violation.

A model, in which the Kobayashi-Maskawa matrix is real and CP violation is mediated by a horizontal gauge interaction, is presented. Right-handed fermions are in triplet representations of an SU(2) horizontal group. The CP-violation parameter epsilon and K/sub L/-K/sub S/ mass difference are used to give a lower bound on the only (dominant) CP-violating phase, and also a bound on the horizontal gauge-boson mass (M/sub s//sub c//sub r//sub R/) range such that 66 TeVgreater than or equal to(g/sub L//g/sub R/)M/sub scrR/greater than or equal to5 TeV. epsilon' is found to be extremely small. Contributions to the theta parameter vanish at the tree and one-loop levels. It has an interesting value at the two-loop level. The branching ratio of K/sub L/..--> mu..e is predicted to be greater than 10/sup -10/ in the simplest version of the model. With present assumptions, the model does not permit CP violation to be observable in the B-meson systems, although rare lepton-number-nonconserving semileptonic B decays show interesting rates. The detection possibilities of the new gauge bosons at the Superconducting Super Collider are also explored. Directions for variations and extensions of the model are discussed.

Study of U(3) by embedding in O(6)

Two distinct sets of boson creation operators transforming, respectively, like the triplet and antitriplet irreducible representations of SU(3) are used, together with their corresponding annihilation operators, to realize generators and basis states of SU(3) ⊃ G where G is a proper continous subgroup of SU(3). The analysis involves the embedding of SU(3) into O(6), this being achieved through the concept of traceless bosons. The method allows other aspects of SU(3) to be studied also.

SU(3) ⊗ U(1) gauge theory of weak and electromagnetic interactions

We describe an SU(3) \ensuremath{\bigotimes} U(1) gauge theory of weak and electromagnetic interactions and study its experimental implications. In this theory all nonsinglet fermions are assigned to triplet representations of SU(3). The theory satisfactorily accounts for the trimuon events recently observed in neutrino reactions. Furthermore, the model naturally ensures quark-lepton and $e\ensuremath{-}\ensuremath{\mu}$ universality, absence of right-handed currents in $\ensuremath{\beta}$ and $\ensuremath{\mu}$ decay, and absence of $s\ensuremath{-}d$ neutral currents to order ${G}_{F}\ensuremath{\alpha}$. Various discrete symmetries play an important role in maintaining these properties. The model allows for $\ensuremath{\mu}$- and $e$-type lepton-number nonconservation at a naturally strongly suppressed level. The weak contributions to the anomalous magnetic moments of the electron and muon are calculated and shown to be in accord with experimental bounds. The predictions of the model for most neutral-current reactions are in good agreement with the data on these processes. Other features of the theory include the prediction of an absolutely stable massive neutral lepton, the absence of a sizable high-$y$ anomaly in antineutrino charged-current reactions, and the absence of large parity violation in heavy atoms.

A formulation of the Weinberg’s model of leptons based on the triplet representation

A formulation of the Weinberg’s model of leptons based on the triplet representation

Finite Transformations in Various Representations of SU(3)

A projection operator expansion is used to obtain the explicit forms of finite transformations in the triplet, octet, and decuplet representations of SU(3). The projection operators are obtained from the characteristic equations for the matrices in these representations. These characteristic equations are developed from known properties of the λi, Fi, and decuplet matrices; where multiple eigenvalues appear, it is shown that the relevant matrices also satisfy reduced equations in which no eigenvalue appears twice or more. General features of the method are discussed.