Masses Of Intermediate Bosons Research Articles

Hypersymmetry field rotation angle

The paper determines a limit energy under which hypersymmetry (HySy) is broken. According to gauge theories, interaction mediating spin-0 bosons must be massless. The theory of HySy predicted massive intermediate bosons. Hypersymmetry field rotation, described in this paper, justifies the mass of the HySy mediating boson. The mass of intermediate bosons must arise from dynamical spontaneous breaking of the group of HySy. HySy rotation is performed in the velocity-dependent D field. The derived rotation of the field is defined by the spontaneous symmetry breaking and precession of the velocity v around its third projection in the D field (that produced the mass of the field's bosons). The latter represents the real- and effective velocities of a boson-emitting particle in the direction towards a target particle. The mass of the discussed (fictitious) Goldstone bosons can be removed by the unitarity gauge condition through Higgs (BEH) mechanism. According to the simultaneous presence of a Standard Model (SM) interaction's symmetry group and the (beyond SM) HySy group, their bosons should be transformed together. Spontaneous breakdown of HySy may allow performing a transformation that does not influence the SM physical state of the investigated system. The paper describes a field transformation that eliminates the mass of the intermediate bosons, rotates the SM- and HySy bosons’ masses together while leaving the SM bosons intact. The result is an angle that characterises the HySy by a precession mechanism of the velocity that generates the field. In contrast to the known SM intermediate bosons, the HySy intermediate bosons have no fixed mass. The mass of the HySy intermediate bosons (that appear as quanta of a velocity-dependent gauge field D) depends on the relative velocity of the particles whose interaction they mediate. So, the derived precession angle is a function of that velocity.

Giving mass to the mediating boson of HyperSymmetry by a field transformation applying Higgs mechanism beyond the Standard Model

According to gauge theories, interaction mediating spin-0 bosons must be massless. Theory of hypersymmetry (HySy) predicted massive intermediate bosons. Hypersymmetry field rotation, to be described in this paper, gives mass to the HySy mediating boson. Hysy rotation is performed in the velocity dependent D field – a gauge field defined beyond the Standard Model (SM). Its angle is something similar to the weak mixing Weinberg angle that explains the surplus mass to the neutral weak vector boson; as well as it is similar to the fermion flavour mixing Cabibbo-Kobayashi-Maskawa angles that justify the mass change under weakly interacting quarks’ mixing, respectively. Mass of intermediate bosons must arise from dynamical spontaneous breaking of the group of HySy. The mass of the discussed (fictitious) Goldstone bosons can be removed by the unitarity gauge condition through the Higgs (BEH) mechanism. According to the simultaneous presence of a SM interaction’s symmetry group and the HySy group, their bosons should be transformed together. Spontaneous breakdown of HySy may allow to perform a transformation that does not influence the SM physical state of the investigated system. The paper describes a field transformation that eliminates the mass of the intermediate bosons by the application of the BEH mechanism, rotates the SM and HySy bosons’ masses together, while leaves the SM bosons intact. The result is an angle of precession inclination that characterises the HySy mechanism. In contrast to the known SM intermediate bosons, the HySy intermediate bosons have no fix mass. The mass of the HySy intermediate bosons (that appear as quanta of a velocity dependent gauge field D) depends on the relative velocity of the particles whose interaction they mediate, therefore the derived transformation angle is a function of that velocity.

Ultrahigh-Energy Neutrino-Nucleon Deep-Inelastic Scattering and the Froissart Bound

We present a simple formula for the total cross section σ(νN) of neutral- and charged-current deep-inelastic scattering of ultrahigh-energy neutrinos on isoscalar nuclear targets, which is proportional to the structure function F(2)(νN)(M(V)(2)/s,M(V)(2)), where M(V) is the intermediate-boson mass and s is the square of the center-of-mass energy. The coefficient in front of F(2)(νN)(x,Q(2)) depends on the asymptotic low-x behavior of F(2)(νN). It contains an additional lns term if F(2)(νN) scales with a power of ln(1/x). Hence, an asymptotic low-x behavior F(2)(νN)∝ln(2)(1/x), which is frequently assumed in the literature, already leads to a violation of the Froissart bound on σ(νN).

Unified spin gauge model and the top quark mass

Spin gauge models use a real Clifford algebraic structure Rp,q associated with a real manifold of dimension p + q to describe the fundamental interactions of elementary particles. This review provides a comparison between those models and the standard model, indicating their similarities and differences. By contrast with the standard model, the spin gauge model based on R3,8 generates intermediate boson mass terms without the need to use the Higgs-Kibble mechanism and produces a precise prediction for the mass of the top quark. The potential of this model to account for exactly three families of fermions is considered.

A precise determination of the electroweak mixing angle from semileptonic neutrino scattering

The cross-section ratio of neutral-current and charged-current semileptonic interactions of muon-neutrinos on isoscalar nuclei has been measured with the result:Rv=0.3093±0.0031 for hadronic energy larger than 4 GeV. From this ratio we determined the electroweak mixing angle sin2θW, wheremc is the charm-quark mass in GeV/c2. Comparison with direct measurements ofmw andmz determines the radiative shift of the intermediate boson mass Δr=0.077±0.025(exp.)±0.038(syst.), in agreement with the prediction. Assuming the validity of the electroweak standard theory we determined ϱ=0.990−0.013(mc−1.5)±0.009(exp.)±0.003(theor.).

Model for the dynamical generation of lepton, quark, and intermediate-boson masses.

In an SU(3${)}_{\mathrm{c}}$\ifmmode\times\else\texttimes\fi{}SU(2${)}_{\mathrm{L}}$\ifmmode\times\else\texttimes\fi{}U(1${)}_{\mathrm{Y}}$ gauge-invariant model without the Higgs sector the fermions are distinguished by different hypercharges of a new renormalizable interaction with an ``Abelian'' vector boson C of mass M. An interplay of all interactions which contribute to the fermion mass generation yields the fermion mass formulas ${\mathit{m}}_{\mathit{i}}$(l)=M exp [-\ensuremath{\pi}/3\ensuremath{\alpha}'(${\mathrm{\ensuremath{\mu}}}_{\mathit{i}}$)], ${\mathit{m}}_{\mathit{i}}$(u)=M exp{-\ensuremath{\pi}/[2${\mathrm{\ensuremath{\alpha}}}_{\mathit{s}}$(${\mathrm{\ensuremath{\mu}}}_{\mathit{i}}$)+2/3\ensuremath{\alpha}'(${\mathrm{\ensuremath{\mu}}}_{\mathit{i}}$)]}, and ${\mathit{m}}_{\mathit{i}}$(d)=M exp{-\ensuremath{\pi}/[2${\mathrm{\ensuremath{\alpha}}}_{\mathit{s}}$(${\mathrm{\ensuremath{\mu}}}_{\mathit{i}}$)-1/3\ensuremath{\alpha}'(${\mathrm{\ensuremath{\mu}}}_{\mathit{i}}$)]} for the charged leptons ${\mathit{l}}_{\mathit{i}}$, ${\mathit{u}}_{\mathit{i}}$, and ${\mathit{d}}_{\mathit{i}}$ quarks, respectively. Here \ensuremath{\alpha}' and ${\mathrm{\ensuremath{\alpha}}}_{\mathit{s}}$ are the running coupling strengths of the U(1${)}_{\mathrm{Y}}$ and SU(3${)}_{\mathrm{c}}$ gauge interactions, respectively, and ${\ensuremath{\mu}}_{i}$ are the physically preferred renormalization points determined by the C hypercharges. The intermediate-boson masses ${m}_{W}$ and ${m}_{Z}$ are expressed in terms of the fermion masses by sum rules.

Order αs corrections to intermediate boson masses

We present the order α s corrections to the masses of the Z and W bosons in the standard model. For the low mass quarks u, d, c and s the corrections are small and positive. Due to the Coulomb singularity which appears in the vector boson self-energy graph with one gluon exchange, we find a negative contribution from the t, b doublets.

Irreducible gauge theory of a consolidated Salam-Weinberg model

We derive the Salam-Weinberg model by gauging an internal simple supergroup SU( 2 1 ) . The theory uniquely assigns the correct SU(2) L ⊗ U(1) eigenvalues for all leptons, fixes θ W = 30°, generates the W ± σ, Z 0 σ and A σ together with the Higgs-Goldstone I L = 1 2 scalar multiplets as gauge fields, and imposes the standard spontaneous breakdown of SU(2) L ⊗ U(1). The masses of intermediate bosons and fermions are directly generated by SU( 2 1 ) universality, which also fixes the Higgs field coupling.

γ-W 0 mixing as an alternative to unified weak-electromagnetic gauge theories

A very simple model based on γ-W 0 mixing (but not on spontaneously broken gauge symmetry) is shown to reproduce all the quantitative predictions of the standard (Weinberg-Salam) model as far as low-energy phenomenology is concerned. The model predicts intermediate-boson mass relations weaker than Weinberg's. Weinberg's mass formulae, however, can be accommodated in our model provided the γ-W 0 mixing parameter and the coupling constants ( e and g) satisfy a special relation. This relation also guarantees asymptotic SU(2) × U(1), decent high-energy behavior in processes like v + v → W + + W − and the SU(2) × U(1) value for the W ± boson gyromagnetic ratio. Speculative attempts are made to understand the sign and magnitude of “sin 2 θ W”.

Electron, muon, proton, and strong gravity

Regarding the strong interaction as a manifestation of a strong gravity, the electron and the proton are identified as black holes in the strong gravitational field. The mass and classical radius of the electron are predicted to be $\frac{1}{2}\ensuremath{\alpha}{m}_{\ensuremath{\pi}}=0.51$ MeV and ${r}_{e}=\frac{2{e}^{2}}{2{m}_{p}{c}^{2}}=0.74$ cm, respectively. It is shown that the electron can be strongly interacting at energies above 240 GeV. The strong gravitational constant is predicted to be 3.9\ifmmode\times\else\texttimes\fi{} ${10}^{31}$ dyn ${\mathrm{cm}}^{2}$ ${\mathrm{g}}^{\ensuremath{-}2}$. The neutron-proton mass difference is partly explained. A neutral-pion-electron system bound by strong gravity is interpreted as the muon, and the muon-electron mass ratio is predicted to be $\frac{{m}_{\ensuremath{\mu}}}{{m}_{e}}=\frac{3}{2}(\frac{1}{\ensuremath{\alpha}})+\frac{(\frac{2}{\ensuremath{\alpha}}){m}_{e}}{{m}_{\ensuremath{\pi}}}=206.6$. It is suggested that the weak interaction might also be a manifestation of strong gravity and the intermediate-boson mass is of order 240 GeV.

Some Consequences of an SU(2) ⊗ U(1) Gauge Model

The experimental consequences of an SU(2) \ensuremath{\bigotimes} U(1) model in which the intermediate-boson mass ${m}_{W}$ is bounded below by 13 GeV are discussed. For the special choice of ${m}_{W}=18$ GeV neutral-current effects essentially disappear. The model includes a heavy neutral lepton of the muon type whose mass is bounded above and below by \ensuremath{\sim} 1.2 GeV and 390 MeV, respectively. The model is thus relatively more accessible to experimental tests than other gauge models. Other aspects of the model are discussed.

Lower Bound on the Intermediate-Boson Mass

Lower Bound on the Intermediate-Boson Mass

Comment on a Quark Model of the Weak Interaction

To improve the agreement with experiment a modification is made to a renormalizable SU(4)-symmetry model of the weak interaction. The quantum numbers of the new symmetry are electron and muon lepton numbers and first and second baryon numbers. A value for the intermediate boson mass is calculated assuming that the weak and electromagnetic interactions conspire to produce a finite lepton-mass renormalization.

Speculative Determination of the Intermediate-Boson Mass

It is shown that the algebra generated by the space integrals of the fourth components of the electromagnetic current and the weak-interaction current is that of an $\mathrm{SU}(2)\ensuremath{\bigotimes}\mathrm{U}(1)$ group. Let $\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}$ be the generator of this SU(2) group. By requiring the $|\ensuremath{\Delta}\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}|=1$ part of these current operators, including their respective coupling constants, to form a $\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}=1$ triplet, one finds that the semiweak coupling constant $g$ is related to the fine-structure constant $\ensuremath{\alpha}$ by ${(4\ensuremath{\pi})}^{\ensuremath{-}1}{g}^{2}=\frac{1}{8}\ensuremath{\alpha}$; therefore, in the absence of radiative corrections, the mass of the (hypothetical) spin-1, charged intermediate boson is 37.29 GeV.

Lepton Symmetry and Self-Mass

We consider the symmetry of leptonic weak and electromagnetic interactions unified in a model free of quadratic divergences. Explicit values for intermediate boson masses and coupling constants are obtained from the requirement of finite self-masses for leptons.

Nonleptonic Decays ofKMesons in Chiral Dynamics and the Proof of the ΔI=1/2 Rule

We construct weak interactions from the nonlinear chiral invariant Lagrangian, and dis­ cuss the nonleptonic decays of K mesons in the chiral vector meson model. Correction to this model due to the current-current interact jon and the K*- and KA-poles violates the AI=1/2 rule, but the violation is quite small and consistent with experiment. Moreover we assume the intermediate boson mass to be 12 Be V in the model to explain the K 1°-'>2rr: decay rate. 1 ) has derived an effective Lagrangian for soft-pion interac­ tion, which reproduces the results of current algebra in a simple way. On the basis of the (J model, he has employed an SU(2) chiral transformation. Schwinger2) has also derived an effective Lagrangian, and has introduced the vector and axial-vector mesons as gauge fields. The concept of chiral invariance plays ail important role in understanding the low energy phenomena. The purpose of this paper is to show that chiral invariance is also useful for the problem in weak interactions. Moreover we discuss the nonleptonic decays of K mesons, and prove the validity of the LJI = 1/2 rule on the basis of the chiral invariant Lagrangian. In§ 2 a generalization of the SU (2) chiral dynamics to SU (3) is formulated ll1 the quark model. S ) The vector and axial-vector mesons are introduced as gauge fields. The Lagrangian written by actual fields is invariant under the nonlinear chiral transformation. In § 3 the Lagrangian for the weak interaction is constructed from the Lagrangian for the strong interaction obtained in § 2. In § 4 the nonleptonic decays of K mesons and the LJI = 1/2 rule are discussed. It can be shown that the LJI = 1/2 rule holds, though at first sight the weak Lagrangian (17) seems to violate the 111=1/2 rule. In a previous paper 4 ) we considered the K-72n decay and proved the 111=1/2 rule for this process on the basis of the quark model. In this paper we consider the K1D decay by the self­ energy type diagram due to the vector mesons, the axial-vector mesons and the intermediate boson without introduction of quark. We find that this model (chiral vector meson model) also explains the 111=1/2 rule, and that the result of this model is the same as current algebra with a slight difference in coefficient. The contributions of the current-current interaction and the K* -pole and KA-pole;· 1402

Convergent Calculation of NonleptonicKDecay in the Intermediate-Boson Model

The nonleptonic decay amplitudes of the $K$ mesons are calculated using current algebra and the spectral-function sum rules. The result is convergent in the intermediate-boson model, but not for a direct current-current interaction. Comparison with the observed rate for ${{K}_{1}}^{0}$ decay shows that the intermediate-boson mass is about 8 BeV.

The μ → e + γ decay and the intermediate charged vector boson theory

The μ-e-γ vertex is calculated in the intermediate charged vector boson theory, as a function of the square of the four momentum of the photon. Consistency arguments show that the boson anomalous magnetic moment should be taken equal to zero. The result is then specialized to a real photon. The experimental branching ratio $$\varrho = (\mu \to e + \gamma )/(\mu \to e + v + \bar v) = 1.2 \pm 1.5$$ fixes the cut-off value at less than one fifth the intermediate boson mass. It is concluded that this theory does not reasonably account for the experimental data, no matter how massive the boson is assumed to be.