Narrow Results

The phase transition associated with the standard electroweak model is very weakly first order. The weakness of the transition means that around the critical temperature the finite-temperature Higgs mass is much less than the critical temperature. This leads to infrared problems in the calculation of the parameters of the potential. Therefore, theories of electroweak baryogenesis, which depend on the details of the transition, must be calculated with care.

In this paper, we investigate the effect of a circularly polarized laser field on the inverse muon decay process $(e^{-}{\nu }_{\mu }\to {\nu }_e{\mu }^{-})$ in electroweak theory with the exchange of a boson vector $W^{-}$. Our method accounts for the dressing of incident electron and scattered muon by introducing the first-order laser-matter interaction of perturbation theory and using the relativistic Dirac–Volkov formalism. We have analyzed the behavior of the total cross-section (TCS) with charged-current as a function of the center-of-mass energy and the laser field parameters, such as the number of photons exchanged, the laser field strength and frequency. We have found that the circularly polarized laser field significantly affects the inverse muon decay process by reducing the TCS. We have also shown that the photonic energy transfer envelopes are perfectly symmetric with respect to the number of photons exchanged and rapidly drop when the indices of the Bessel functions are close to their arguments.

Electroweak data from the high energy electron–positron and proton–antiproton colliders are reviewed. On the whole the data is consistent with and supports the predictions of the electroweak theory. However, a crucial prediction of the theory remains to be verified: the existence of the Higgs boson and its light mass, less than 193 GeV, obtained from a fit to all the data within the electroweak framework. The lower limit on its mass from direct searches being 114 GeV, the mass of the Higgs is fixed within a narrow range which is expected to be explored at the Fermilab Tevatron experiments or later at the Large Hadron Collider at CERN.

According to the introduction of a minimal length to quantum field theory, which is directly related to a generalized uncertainty principle, the implementation of the gauge principle becomes much more intricated. It has been shown in another paper how gauge theories have to be extended in general, if there is assumed the existence of a minimal length. In this paper this generalization of the description of gauge theories is applied to the case of Yang–Mills theories with gauge group SU(N) to consider especially the application to the electroweak theory as it appears in the Standard Model. The modifications of the lepton-, Higgs- and gauge field sector of the extended Lagrangian of the electroweak theory maintaining local gauge invariance under SU(2)_L ⊗ U(1)_Y transformations are investigated. There appear additional interaction terms between the leptons or the Higgs particle respectively with the photon and the W- and Z-bosons as well as additional self-interaction terms of these gauge bosons themselves. It is remarkable that in the quark sector where the full gauge group of the Standard Model, SU(3)_c ⊗ SU(2)_L ⊗ U(1)_Y, has to be considered there arise coupling terms between the gluons und the W- and Z-bosons which means that the electroweak theory is not separated from quantum chromodynamics anymore.

In a previous paper, we showed theoretically that the total cross-section of the top-quark pair production by electron–positron annihilation is strongly reduced by the presence of a circularly polarized laser field. In this paper, we present the result for the case of a linearly polarized laser field. This time, the total cross-section is significantly enhanced by the laser field.

We put forward the hypothesis that the weak W boson be a compound of two 2-component Lorentz spinors. The resulting novel γWW vertex is no gauge field structure. Nevertheless, the Born amplitude of γγ→W_LW_L respects partial-wave unitarity. As in the Yang-Mills case, the amplitude consists of a direct term, a crossed term, and a sea-gull term, and no unobserved particles are to be involved to get the “good” high-energy behavior. This is due to an imaginary pseudoscalar γWW interaction term. Significant differences between angular distributions and total cross sections of the non-Abelian case and the case of the composite bosons are displayed. The unitarity constraint applied to the reaction γγ→W_TW_T leads to the prediction of the existence of a composite charged weak scalar Φ^±. It constitutes the spin 0 state of the constituents forming W^±. Furthermore, the existence of a second and heavy scalar-vector pair ω-X is predicted. These weak boson states are found to exclude the presence of a seagull graph. In the threshold region, the total cross section of γγ→WW in the compositeness case is smaller than in the non-Abelian case. In a broad intermediate energy region it can be larger. Upper unitarity mass-bounds are estimated. They suggest m_Φ≈m_w so that Φ^± might be discovered by forthcoming experiments. The structure of the γΦW, γXW and γωW transition vertices can be inferred without making recourse to unitarity. However, unitarity requires that the mass relation m_Φ/m_W=m_ω/m_X be valid.

In an Abelian chirally and gauge-invariant anomaly-free model we demonstrate that strong Yukawa couplings between massless fermion fields and a massive scalar carrying the axial charge generate dynamically vastly different fermion masses, and the gauge boson mass.