Gauge boson masses in the 3D, SU(2) gauge-Higgs model

We investigate spectral properties of a fermion coupled with a massive gauge boson with a mass $m$ at finite temperature ($T$) in the perturbation theory. The massive gauge boson is introduced as a $U(1)$ gauge boson in the Stueckelberg formalism with a gauge parameter $\ensuremath{\alpha}$. We find that the fermion spectral function has a three-peak structure for $T\ensuremath{\sim}m$ irrespective of the choice of the gauge parameter, while it tends to have one faint peak at the origin and two peaks corresponding to the normal fermion and antiplasmino excitations familiar in QED in the hard thermal loop approximation for $T\ensuremath{\gg}m$. We show that our formalism successfully describe the fermion spectral function in the whole $T$ region with the correct high-$T$ limit except for the faint peak at the origin, although some care is needed for choice of the gauge parameter for $T\ensuremath{\gg}m$. We clarify that for $T\ensuremath{\sim}m$, the fermion pole is almost independent of the gauge parameter in the one-loop order, while for $T\ensuremath{\gg}m$, the one-loop analysis is valid only for $\ensuremath{\alpha}\ensuremath{\ll}1/g$ where $g$ is the fermion-boson coupling constant, implying that the one-loop analysis cannot be valid for large gauge parameters as in the unitary gauge.

The bound on the mass of the new gauge boson Z′ from the process μ→3 e

In this article, we present a detailed study of the masses of all gauge bosons, as well as explaining recent experimental data regarding the W-boson mass presented by the CDF collaboration and even possible changes that these data can bring to experimental measurements of the masses of Z-boson mass in the context of the Minimal Supersymmetric [Formula: see text] Model. We also intend to show a phenomenological analysis of possible mixtures of gauge bosons in this model. We will show that our numerical predictions for the masses of the physical gauge bosons are within the current experimental limits.

A unified electroweak theory is formulated using non-local field theory without including a Higgs particle. The W and Z gauge boson masses are induced from one-loop vacuum polarization graphs and the non-local weak scale is determined by the W boson mass and the Fermi constant to be Λw=424 GeV . The tree graphs for the gauge bosons are identical to those of the standard local electroweak theory, so any violation of locality occurs only at the quantum level for the finite loop graphs. The fermion masses are obtained from a four-Fermi interaction with a spontaneously broken vacuum based on the fermion condensate [Formula: see text]. The problem of severe fine tuning for the quark condensates in the standard local point field theory is avoided in our non-local field theory. The theory contains only the known particle spectrum of leptons, quarks, the anticipated top quark, the W and Z gauge bosons and the photon. The quark condensates could generate a spectrum of heavy vector bound states at an energy scale ~1−2 TeV .

A gauge theory involves two kinds of particles, those which carry ‘charge’ and those which ‘mediate’ interactions between currents by coupling directly to charge. In the former class are the fundamental fermions and nonabelian gauge bosons, whereas the latter consists solely of gauge bosons, both abelian and nonabelian. The physical nature of charge depends on the specific theory. Three such kinds of charge, called color, weak isospin, and weak hypercharge, appear in the Standard Model. The values of these charges are not predicted from the gauge symmetry, but must rather be determined experimentally for each particle. The strength of coupling between a gauge boson and a particle is determined by the particle's charge, e.g. the electron-photon coupling constant is –e, whereas the u -quark and photon couple with strength 2e/3. Because nonabelian gauge bosons are both charge carriers and mediators, they undergo self-interactions. These produce substantial nonlinearities and make the solution of nonabelian gauge theories a formidable mathematical problem. Gauge symmetry does not generally determine particle masses. A fermion mass term, although violating chiral symmetry, is consistent with gauge invariance. Although gauge-boson mass would seem to be at odds with the principle of gauge symmetry, the Weinberg-Salam model contains a dynamical procedure, the Higgs mechanism, for generating mass for both gauge bosons and fermions alike. Quantum Electrodynamics Historically, the first of the gauge field theories was electrodynamics. Its modern version, Quantum Electrodynamics (QED) , is the most thoroughly verified physical theory yet constructed.

Tuning effect in particle masses manifests itself in integer relations between lepton masses and parameters of the pion (its mass, the mass splitting and fπ). It involves parameters of constituent quark model and basic values of the Standard Model: masses of vector and scalar bosons, QED parameters and the top quark mass. The role of nuclear data is discussed.

The propagator of a gauge boson, like the massless photon or the massive vector bosons W± and Z of the electroweak theory, can be derived in two different ways, namely via Green’s functions (semi-classical approach) or via the vacuum expectation value of the time-ordered product of the field operators (field theoretical approach). Comparing the semi-classical with the field theoretical approach, the central tensorial object can be defined as the gauge boson projector, directly related to the completeness relation for the complete set of polarisation four-vectors. In this paper we explain the relation for this projector to different cases of the Rξ gauge and explain why the unitary gauge is the default gauge for massive gauge bosons.

The standard model and beyond

We propose a vector dark matter model from a hidden $\mathrm{SU}(2{)}_{\mathrm{D}}$ gauge symmetry at TeV scale. A scalar septuplet is introduced to break the $\mathrm{SU}(2{)}_{\mathrm{D}}$ symmetry spontaneously. The septuplet also plays the role of a portal between the standard model and the dark sector. We find that there are two different vacuum configurations corresponding to the sign of the quartic coupling ${\ensuremath{\lambda}}_{3}$, which yield different mass spectra for the gauge bosons. For a ${\ensuremath{\lambda}}_{3}<0$, the masses of gauge bosons are splitting, while for a ${\ensuremath{\lambda}}_{3}\ensuremath{\ge}0$, the masses are degenerate. We also study the RG evolutions of the couplings, and find that the perturbativity and vacuum stability can set a stringent bound on the parameter space. For the phenomenological aspect, we consider the experimental constraints including dark matter direct detection, indirect detection, relic density, and Higgs couplings measurements. We find that there are parameter space survivors from all the constraints, and they can be tested in future dark matter direct and indirect detection experiments.

A fully dynamical origin for the masses of weak gauge bosons and heavy quarks of the Standard Model is considered. Electroweak symmetry breaking and the gauge boson masses arise from new strong dynamics, which leads to the appearance of a composite scalar in the spectrum of excitations. In order to generate mass for the Standard Model fermions, we consider extended gauge dynamics, effectively represented by four fermion interactions at presently accessible energies. By systematically treating these interactions, we show that they lead to a large reduction of the mass of the scalar resonance. Therefore, interpreting the scalar as the recently observed 125 GeV state, implies that the mass originating solely from new strong dynamics can be much heavier, of the order of 1 TeV. The couplings of the scalar resonance with the Standard Model gauge bosons and fermions are evaluated, and found to be compatible with the current LHC results.

After a brief theoretical introduction of the warped extra-dimensional model with custodial protection the results of [1] are presented. In this work we analyze the impact of Kaluza-Klein (KK) gauge boson modes on ΔF = 2 observables, for the first time considering the full operator basis and including NLO renormalization group running. It is pointed out that the dominant contribution in the B-system does not come from the KK gluon, but that contributions from KK excitations of the weak gauge bosons are competitive. In a numerical analysis we assess the amount of fine-tuning necessary for obtaining realistic values for quark masses and mixings and at the same time realistic values for ϵk, the measure for CP violation in K meson mixing. We are able to show that a mass of the lightest KK gauge boson of 2-3 TeV, and hence in the reach of the LHC, is still possible for moderate fine-tuning. These results enable us to make predictions for not yet measured ΔF = 2 observables, such as Sψπ and A8SL, which can differ significantly from their SM values.

Extra neutral gauge bosons and Higgs bosons in an effective low-energy\n$SU(2)_L \\times SU(2)_I \\times U(1)_Y \\times U(1)_{Y^{\\prime}}$ model, which is\na subgroup of $E_6$, are studied. $SU(2)_I$ is a subgroup of $SU(3)_R$ and\ncommutes with the electric charge operator, so the three corresponding gauge\nbosons are neutral. Electroweak precision experiments are used to put\nconstraints on masses of the extra neutral gauge bosons and on the mixings\nbetween them and the ordinary Z boson, including constraints arising from a\nproposed measurment of the weak charge of the proton at Jefferson Lab. Bounds\non and relationships of masses of Higgs bosons in the supersymmetric version of\nthe model are also discussed.\n

An extension of the Standard Model to the local gauge group $SU(3)_c\otimes SU(3)_L\otimes U(1)_X$ which is a subgroup of the electroweak-strong unification group $E_6$ is analyzed. The mass scales, the gauge boson masses, and the masses for the spin 1/2 particles in the model are calculated. The mass differences between the up and down quark sectors, between the quarks and leptons, and between the charged and neutral leptons in one family are explained as a consequence of mixing of ordinary with exotic fermions implied by the model. By using experimental results we constrain the mixing angle between the two neutral currents and the mass of the additional neutral gauge boson to be $-0.0015 \leq \sin\theta \leq 0.0048$ and $600 GeV \leq M_{Z_2}$ at 95% CL. The existence of a Dirac neutrino for each family with a mass of the order of the electroweak mass scale is predicted.

Weak skyrmions from the hidden symmetry in the standard model

We have measure the correlation of microwave field and intensity versus polarization of the source and detector in a ensemble of randomly positioned alumina spheres. Unlike correlation functions in space, frequency, and time, for which the corresponding parameter may be unbounded and the field correlation function vanishes asymptotically with increasing parameter shift, the polarization variable is of finite range and the field correlation function vanishes when either the source or detector is rotated by 90 degrees. This facilitates an unambiguous experimental separation of the intensity correlation function into three components, with a form that is independent of the closeness to the localization threshold. The polarization correlation function depends upon the underlying field correlation function in a manner analogous to that found for the intensity correlation function with displacement [1]. The first component of the intensity correlation function is the product of the square of the field correlation function with shift of either source or detector and dominates intensity fluctuations. The field correlation function is simply the cosine of the angular shift of the polarization of the electromagnetic field. The second component is associated with long-range intensity correlation. It is proportional to the sum of the square of the field correlation function with respect to variation of the source and detector. The third component of the polarization correlation function gives rise to universal conductance fluctuations. It is the sum of a multiplicative and additive term involved in the short and long-range contributions to the correlation function and also includes a constant term, which is independent of polarization. Thus, the functional form of the intensity correlation function with polarization is remarkably simple. It is determined exclusively by the cosine of the angular shift of the polarization of the electric field at the source and detector.