A spontaneously broken quintet Baryon model for strong interactions

A gauge type model of quantum field theory for strong interactions based on a quinted of observed fields, namely the proton, neutron, , _c and _b baryon fields is proposed. Gauging the resulting global symmetry groupK= SU(3)×¹ U(1)ײ U(1)׳ U(1) for matter fields, one obtains boson-fermion field theory with eleven gauge bosons. The analysis of admissible Higgs sector indicates that the Higgs multiple consists of one adjoint and two fundamental representationsSU(3) and three scalar representations of¹ U(1),² U(1) and³ U(1). The structure of the Higgs sector implies that the original symmetry group extends to the groupK×U(2). Breaking spontaneously the obtained field theory, one converts gauge bosons into the eleven massive vector bosons which can be identified with the observed , K^*, ¯K^*, , , J/ and Y vector mesons. The surviving global symmetry is isomorphic with the symmetry groupSU(2)× ⁰ U(1)× ×¹ U(1)ײ U(1)׳ U(1) corresponding to the isospin, strangeness, baryon number, charm and beauty conservation observed in strong interactions. The surviving Higgs scalars have the same quantum numbers as , K, ¯K, , S, , , and _b mesons. The model gives a newSU(3) classification scheme for baryons without charm and beauty in terms of triplets, sextets and 15-plets. These multiplets can be identified with the observed baryons; the scheme also includes the observed Z₀ and Z₁ baryons (the experimental evidence of which is, nevertheless, still weak). The model predicts the existence and the specific quantum numbers of new mesons and baryons with charm and beauty, and provides a very simple framework for the dibaryon analysis. Since all final physical fields are massive, this model is free from infrared divergences.Invited talk presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.     

Dimensional reduction of the Abelian Higgs Carroll-Field-Jackiw model

Taking as a starting point a Lorentz non-invariant abelian Higgs model defined in 1 + 3 dimensions, we carry out its dimensional reduction to D = 1 + 2, obtaining a new planar model composed by a Maxwell-Chern-Simons-Proca gauge sector, a massive scalar sector, and a mixing term (involving the fixed background ) that imposes the Lorentz violation to the reduced model. The propagators of the scalar and massive gauge field are evaluated and the corresponding dispersion relations determined. Based on the poles of the propagators, a causality and unitarity analysis is carried out at tree level. We then show that the model is totally causal, stable and unitary.Received: 2 July 2004, Revised: 21 September 2004, Published online: 1 December 2004     

Axial-vector symmetry breaking and the mass generation of the singlet pseudoscalar meson

The Fabri-Picasso formulation of the spontancous breaking of theSU _A (3) symmetry is applied to theU _A (1) symmetry. It is argued that the notion of the spontaneous breaking of theU _A (1) symmetry is different from that of theSU _A (3) symmetry. In contrast to the octet sector, absence of the massless Goldstone mode amounts to the existence of an exotic vacuum-like degenerated state.     

Spontaneous symmetry breaking with quaternionic scalar fields and electron-muon mass ratio

We investigate the problem of using quaternionic scalar fields as Higg's mesons in theories of spontaneously broken symmetries. We are led to the symplecticSp(1,Q) U(1) as a possible gauge group for a unified theory of electromagnetic and weak interactions. The features of this model are worked out and compared with those of Weinberg'sSU(2) U(1) model.     

Quantum mechanics of Klein-Gordon fields I: Hilbert Space, localized states, and chiral symmetry

We derive an explicit manifestly covariant expression for the most general positive-definite and Lorentz-invariant inner product on the space of solutions of the Klein-Gordon equation. This expression involves a one-parameter family of conserved current densities , with a ∈ (−1, 1), that are analogous to the chiral current density for spin half fields. The conservation of is related to a global gauge symmetry of the Klein-Gordon fields whose gauge group is U (1) for rational a and the multiplicative group of positive real numbers for irrational a. We show that the associated gauge symmetry is responsible for the conservation of the total probability of the localization of the field in space. This provides a simple resolution of the paradoxical situation resulting from the fact that the probability current density for free scalar fields is neither covariant nor conserved. Furthermore, we discuss the implications of our approach for free real scalar fields offering a direct proof of the uniqueness of the relativistically invariant positive-definite inner product on the space of real Klein-Gordon fields. We also explore an extension of our results to scalar fields minimally coupled to an electromagnetic field.     

Maximal atmospheric neutrino mixing in an <Emphasis Type="Italic">SU</Emphasis>(5) model

We show that maximal atmospheric and large solar neutrino mixing can be implemented in SU(5) gauge theories, by making use of the U(1) _F symmetry associated with a suitably defined family number F, together with a Z₂ symmetry which does not commute with F. U(1) _F is softly broken by the mass terms of the right-handed neutrino singlets, which are responsible for the seesaw mechanism; in additio n, U(1) _F is also spontaneously broken at the electroweak scale. In our scenario, lepton mixing stems exclusively from the right-handed-neutrino Majorana mass matrix, whereas the CKM matrix originates solely in the up-type-quark sector. We show that, despite the non-supersymmetric character of our model, unification of the gauge couplings can be achieved at a scale 10¹⁶ GeV < m _U < 10¹⁹ GeV; indeed, we have found a particula r solution to this problem which yields results almost identical to the ones of the minimal supersymmetric standard model. Received: 29 November 2002 / Published online: 3 March 2003 RID="a" ID="a" e-mail: walter.grimus@univie.ac.at RID="b" ID="b" e-mail: balio@cfif.ist.utl.pt     

Geometric quantization and internal symmetry

As a part of an attempt to geometrize physics, internal symmetries in the covariant classification of matter by itsT type are considered in relation to phase transformations generated by complex and quaternionic structures on space-time. The Rainich theory of electromagnetism and neutrinos is compared with the theory ofU(1) ×SO(1, 3) torsional gauge fields, and extended to the quaternionic case. It is shown by the Kostant technique of geometric quantization that complex and quaternionic phase transformations for an Einstein space are associated with one-dimensional and three-dimensional harmonic oscillators.     

Dirac leptogenesis and anomalous <Emphasis Type="Italic">U</Emphasis>(1)

We consider Dirac leptogenesis in supersymmetric theories where the supersymmetry breaking is transmitted to the observable sector by an anomalous U(1) symmetry. This kind of supersymmetry breaking is known to provide a solution to the problem and avoid large CP-violation effects. The asymmetries generated by the decays of heavy leptons do not suffer from wash-out due to the equilibration of left- and right-handed neutrinos thanks to the extreme smallness of the neutrino masses. The model ties up the smallness of the neutrino masses and the out-of-equilibrium nature of the heavy lepton decays with no tension with the overproduction of gravitinos.Received: 23 October 2003, Revised: 31 August 2004, Published online: 20 October 2004     

Field-theory approach to the disintegration of bound systems on the basis of a local gauge nature of an electromagnetic field

An approach is developed that makes it possible to take into account the structure of bound (nonlocal) matter fields in photodisintegration processes with allowance for the requirements of the fundamental principles of covariance and gauge invariance. The approach is based on employing the local U(1) gauge nature of an electromagnetic field, whose vector potential is identified with a connection that performs a parallel transportation of matter-field operators in a fiber space with an interior charge symmetry along “minimum” trajectories.     

Mini little Higgs and dark matter

We construct a little Higgs model with the most minimal extension of the standard model gauge group by an extra U(1)$U(1)$ gauge symmetry. For specific charge assignments of scalars, an approximate U(3)$U(3)$ global symmetry appears in the cutoff-squared scalar mass terms generated from gauge bosons at one-loop level. Hence, the Higgs boson, identified as a pseudo-Goldstone boson of the broken global symmetry, has its mass radiatively protected up to scales of 5–10 TeV. In this model, a Z₂$Z_2$ symmetry, ensuring the two U(1)$U(1)$ gauge groups to be identical, also makes the extra massive neutral gauge boson stable and a viable dark matter candidate with a promising prospect of direct detection.     

Lightest U-parity particle (LUP) dark matter

We suggest a U(1)^′$U{(1)}^{\prime }$ gauge symmetry as an alternative to the usual R  -parity of supersymmetric standard models, showing that it can also work as a common source of stabilities of proton and dark matter in addition to other attractive features. The residual discrete symmetries of a single U(1)^′$U{(1)}^{\prime }$ can provide stabilities to both the MSSM sector (proton) and the hidden sector (new dark matter candidate, LUP). The LUP can expand the viability of many models such as R-parity violating models and gauge mediation models regarding dark matter issue.     

Light-Front Hamiltonian and BRST Formulations of a Two-Dimensional Abelian Higgs Model in the Broken Symmetry Phase

The light-front Hamiltonian and BRST formulations of an abelian Higgs model involving the electromagnetic vector gauge field are investigated in one space, one time dimension in the broken symmetry phase, where the phase (x, t) of the complex matter field (x, t) carries the charge degree of freedom of the complex matter field and is, in fact, akin to the Goldstone boson.     

Gauge and Space-Time Symmetry Unification

Unification ideas suggest an integral treatment of fermion and boson spin andgauge-group degrees of freedom. Hence, a generalized quantum field equation,based on Dirac's, is proposed and investigated which contains gauge and flavorsymmetries, determines vector gauge field and fermion solution representations,and fixes their mode of interaction. The simplest extension of the theory with a6-dimensional Clifford algebra has an SU(2) _L × U(1) symmetry, which isassociated with the isospin and the hypercharge, their vector carriers, two-flavorcharged and chargeless leptons, and scalar particles. A mass term producesbreaking of the symmetry to an electromagnetic U(1), and a Weinberg's angle_W with sin ²(_W) = 0.25. A more realistic 8D extension gives coupling constantsof the respective groups g = 1/2 .707 and g = 1/6 .408, with thesame _W.     

QED with vector and axial vector types of interaction and dynamical generation of particle masses

We consider a model of electrodynamics with two types of interaction, the vector \((e\bar \psi (\gamma ^\mu A_\mu )\psi )\) and axial vector \((e_A \bar \psi (\gamma ^\mu \gamma ^5 B_\mu )\psi )\) interactions, i.e., with two types of vector gauge fields, which corresponds to the local nature of the complete massless-fermion symmetry group U(1) ? U _A (1). We present a phenomenological model with spontaneous symmetry breaking through which the fermion and the axial vector field B_μ acquire masses. Based on an approximate solution of the Dyson equation for the fermion mass operator, we demonstrate the phenomenon of dynamical chiral symmetry breaking when the field B_μ has mass. We show the possibility of eliminating the axial anomalies in the model under consideration when introducing other types of fermions (quarks) within the standard-model fermion generations. We consider the polarization operator for the field B_μ and the procedure for removing divergences when calculating it. We demonstrate the emergence of a mass pole in the propagator of the particles that correspond to the field B_03BC when chiral symmetry is broken and consider the problems of regularizing closed fermion loops with axial vector vertices in connection with chiral symmetry breaking.     

A six-dimensional gauge-Higgs unification model based on E6 gauge symmetry

We construct a six-dimensional gauge-Higgs unification model with the enlarged gauge group of E₆ on S²/Z₂$S^2/Z_2$ orbifold compactification. The standard model particle contents and gauge symmetry are obtained by utilizing a monopole background field and imposing appropriate parity conditions on the orbifold. In particular, a realistic Higgs potential suitable for breaking the electroweak gauge symmetry is obtained without introducing extra matter or assuming an additional symmetry relation between the SU(2) isometry transformation on the S²$S^2$ and the gauge symmetry. The Higgs boson is a KK mode associated with the extra-dimensional components of gauge field. We also compute the KK masses of all fields at tree level.     

Hierarchy of symmetry breakings and neutral currents in anSU(6) grand unification model

In anSU(6) grand unification model with eight quarks and eight leptons belonging to 15-plet and singlet representations, the symmetry is spontaneously broken by the sequenceSU(6)SU(3) ^c ×SU(2)×U(1)×U(1)SU(3) ^c ×U(1). Fror two cases of symmetry breakings the effective weak neutral current coupling constants are compared with experiment. For theSU(3) ^c ×SU(2)×U(1)×U(1)×SU(3) ^c ×U(1) symmetry breaking, the coupling constants reproduce the Weinberg-Salam model with a small correction term. Agreement with the experimental mean values is improved with the correction term. Parity violation in atomic physics is also discussed.     

Spontaneous Symmetry Breaking and Higgs' Mechanism in the Nonsymmetric Jordan-Thiry Theory

In the paper we construct the nonsymmetric Jordan-Thiry theory unifying Moffat's theory of gravitation, the Yang-Mills' field, the Higgs' fields and scalar forces in a geometric manner. We discuss spontaneous symmetry breaking, the Higgs' mechanism and mass generation in the theory. The scalar field Ψ (as in classical Jordan-Thiry theory) is connected to the effective gravitational constant. This field is massive and has Yukawa-type behavior. We discuss the relation between R₊ invariance and U(1)_F from G. U. T. within Einstein λ-transformation, and fermion number conservation. In this way we connect W _μ-field from nonsymmetric theory of gravitation with a gauge field A from G. U. T. We derive the equation of motion for a test particle from conservation laws in the hydrodynamic limit.     

Massless phases and symmetry restoration in abelian gauge theories and spin systems

We give a new, elementary proof for the existence of a deconfining transition to a massless (QED) phase in the four-dimensionalU(1) lattice gauge theory and of an intermediate QED phase, accompanied by dynamical restoration of localU(1) invariance, in the four dimensional _N models, withN large. Our methods can also be used to prove the existence of a phase transition in theXY model in three or more dimensions, in three- and four-dimensional abelian Higgs models, and in more general models admitting some local, abelian gauge invariance.Work supported in part by the NSF under grant DMR 81-00417