On gauge theories of mass

The classical Einstein–Hilbert action in general relativity extends naturally to a blow-up (in the sense of algebraic geometry) of the usual space of pseudo-Riemannian metrics; this presents the metric tensor _gik$g_{ik}$ as a kind of Goldstone boson associated to the real scalar field defined by its determinant. This seems to be quite compatible with the Higgs mechanism in the standard model of particle physics.     

Proton-neutron mass difference in gauge theories of weak and electromagnetic interactions

The question of cancellation of logarithmic divergence appearing in the proton-neutron mass difference is studied in gauge theories of weak and electromagnetic interactions. In particular, we study the proton-neutron mass difference in three kinds of gauge models. It is found that the contribution from weak hadronic currents in two of the models cancels the logarithmic divergence arising from purely electromagnetic interaction, but as pointed out in the text these two models suffer from some other defects. In one of the models such a cancellation is not possible although the model is otherwise attractive. In this latter case, a mass renormalization counter term exists to absorb the infinity in the mass difference leaving the mass difference essentially a free parameter.     

On neutral currents in two-Z-boson gauge models

A systematic procedure is considered for the phenomenological analysis of neutral current interactions in an arbitrary two-Z-boson gauge model by means of a general neutral current effective Lagrangian. Expressions for two gauge boson masses and their mixing angle have been obtained directly through the effective Lagrangian parameters. A general classification of possible types of two-Z-boson gauge models is presented in accordance with the form of the effective Lagrangian.     

Neutrino mass and new light gauge boson in superstring models

The proposal that the neutrino owes the smallness of its mass to the spontaneous breaking of R parity in superstring models with an additional gauge boson coupled to the right-handed neutrino is analysed. The right-handed neutrino can not in general decouple from the low-energy theory in models with supersymmetry at the TeV scale and which possess the light Higgs doublets necessary for generating fermion masses. Experimental limits on neutrino mass then imply an upper limit on the new gauge boson mass m_Zr ⪅ 220 GeV.     

The estimation of the Z′ gauge boson mass in E 6 models

The aim of this study is to estimate the Z′ boson mass by using the calculations of the decay width of Z′(ϑ) boson. So, the decay width of the extra Z boson is calculated numerically in effective rank 5 models for different mixing angles ϑ of the model and for different mass values of the extra Z boson. The decay width of Z′ boson to the Standard Model (SM) fermions is found to be between 4.42 and 19.36 GeV and the full decay width of Z′ boson to all particles is found to be between 20.88 and 37.15 GeV. We calculated the full decay width at the angle ϑ ≊ 0 for Z′ and Z ₂ → Z′. The full decay width of Z′ boson is written in a single equation according to our calculations. By using these calculations and the previous works the mass of Z′ boson and the number of generations of the exotic particles are estimated. The article is published in the original.     

On the spectrum of excitations in some strong coupling gauge models

The spectrum of spinless excitations in (3+1)-dimensional ladder QED with additional four-fermion interaction and in (2+1)-dimensional QED is considered.     

On the π+−π0 mass difference

Theπ ⁺?π ⁰ mass difference is calculated from spectral function sum rules with finite widths ofρ and A₁ The deviation from the zero width approximation is found to be small.     

On the algebraic structure of self-dual gauge fields and sigma models

An extensive and detailed analysis of self-dual gauge fields, in particular with axial symmetry, is presented, culminating in a purely algebraic procedure to generate solutions. The method which is particularly suited for the construction of multimonopole solutions for a theory with arbitrary G, is also applicable to a wide class of non-linear sigma models.The relevant symmetries as well as the associated linear problems which underly the exact solubility of the problem, are constructed and discussed in detail.     

theK L-K S mass difference in left-right symmetric models and the right-handed Kobayashi-Maskawa matrix

Zeitschrift für Physik C Particles and Fields - K L-K S mass difference is computed in a left-right symmetric model with three generations of quarks. Under the assumption of...     

Fluxon solutions in non-abellian gauge models

The fundamental homotopic charges of the adjoint group in non-abelian gauge theories support fluxons, string-like non-peturbative degrees of freedom conjectured to be relevant to quark confinement and symmetry breaking. Fluxons as localized, static, sourceless solutions are constructed in pure SU(2) Yang-Mills theory and in the Georgi-Glashow model.     

Emergence of mass in the gauge sector of QCD

It is currently widely accepted that gluons, while massless at the level of the fundamental QCD Lagrangian, acquire an effective mass through the non-Abelian implementation of the classic Schwinger mechanism. The key dynamical ingredient that triggers the onset of this mechanism is the formation of composite massless poles inside the fundamental vertices of the theory. These poles enter the evolution equation of the gluon propagator and nontrivially affect the way the Slavnov-Taylor identities of the vertices are resolved, inducing a smoking-gun displacement in the corresponding Ward identities. In this article, we present a comprehensive review of the pivotal concepts associated with this dynamical scenario, emphasizing the synergy between functional methods and lattice simulations and highlighting recent advances that corroborate the action of the Schwinger mechanism in QCD.     

On the cancellation of hard anomalies in gauge field models: a regularization independent proof

In this paper we prove Bardeen's conjecture that the anomaly of the Adler-Bardeen-Bell-Jackiw-Schwinger type in gauge models are definitely absent if they are cancelled at the first order of the perturbation expansion. Our analysis develops within the regularization independent B.P.H.Z. renormalization scheme. We discuss the possible appearance of anomalies in an enlarged class of gauge models admitting soft violations of the Slavnov-Taylor identities which prescribe the gauge transformation properties of the Green functions. By a repeated use of the Callan-Symanzik equation we conclude that the lowest non vanishing contributions to the anomalies must necessarily correspond to the first order in the perturbation expansion, hence if they are cancelled at this order the theory will be definitely anomaly free.     

KL − KS mass difference and quark models

The matrix element $\text{〈}\text{K}\text{?}{}^0\text{|H}{}_{\mathrm{<mtext>W</mtext>}}\text{|}\text{K}{}^0\text{〉}$ is calculated in the quark MIT bag model and in several relativized versions of the quark harmonic-oscillator models for hadrons. The results of the MIT bag model depend strongly on the particular choice of parameters, while the results of the harmonic-oscillator model are relatively stable on the variation of model parameters. The harmonic-oscillator model which takes into account the c.m. motion (the RHO model) is in reasonably good agreement with the vacuum-saturation value.     

Curing fermion mass gauge variance in QED

The problem of the gauge dependence of the fermion mass in the Maxwell-Chern-Simons QED is revisited. Using Proca mass term as an intermediate infrared regulator we are demonstrating gauge-invariance of the fermion mass shell in QED in all orders of the perturbation theory.     

Confinement and mass gap in abelian gauge

First, we present a simple confining abelian pure gauge theory. Classically, its kinetic term is not positive definite, and it contains a simple UV regularized F⁴ interaction. This provokes the formation of a condensate such that, at the saddle point of the effective potential, the wave function normalization constant of the abelian gauge fields vanishes exactly. Then we study SU(2) pure Yang-Mills theory in an abelian gauge and introduce an auxiliary field for a BRST invariant condensate of dimension 2, which renders the charged sector massive. Under simple assumptions its effective low energy theory reduces to the confining abelian model discussed before, and the VEV of is seen to scale correctly with the renormalization point. Under these assumptions, the confinement condition Z _eff = 0 also holds for the massive charged sector, which suppresses the couplings of the charged fields to the abelian gauge bosons in the infrared regime. Received: 27 November 2002 / Published online: 14 April 2003 RID="a" ID="a" e-mail: Ulrich.Ellwanger@th.u-psud.fr RID="b" ID="b" e-mail: Nicolas.Wschebor@th.u-psud.fr ^* Unité Mixte de Recherche - CNRS - UMR 8627     

Rare decay modes of the K mesons and KL-KS mass difference in an asymptotically free gauge theory

Rare decay modes of the K mesons are calculated for the Weinberg-Salam model of weak and electromagnetic interactions, assuming that the strong interactions are described by an asymptotically free gauge theory.