Free boson representation ofq-vertex operators and their correlation functions

A bosonization scheme of theq-vertex operators of U_q(sl₂) for arbitrary level is obtained. They act as intertwiners among the highest weight modules constructed in a bosonic Fock space. An integral formula is proposed forN-point functions and explicit calculation for two-point function is presented.Partly supported by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture (No. 04245206)A Fellow of the Japan Society of the Promotion of Science for Japanese Junior Scientists. Partly supported by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture (No. 04-2297)     

Free boson representation ofU_q (\widehat{sl}_3 )

A representation of the quantum affine algebra of an arbitrary levelk is constructed in the Fock module of eight boson fields. This realization reduces the Wakimoto representation in theq 1 limit. The analogues of the screening currents are also obtained. They commute with the action of modulo total differences of some fields.On leave from Department of Physics, University of Tokyo, Tokyo 113, Japan.     

Vector boson decays of the Higgs boson

We derive the width of the Higgs boson into vector bosons. General formulas are derived both for the on–shell decay as well for the off–shell decays, and , where . For the off-shell decays the width of the decaying vector boson is properly included. The formulas are valid both for the Standard Model as well as for arbitrary extensions. As an example we study in detail the gauge-invariant effective Lagrangian models where we can have sizable enhancements over the Standard Model that could be observed at LEP. Received: 31 July 1998 / Revised version: 23 September 1998 / Published online: 6 November 1998     

Higgs boson production and weak boson structure

The influence of the QCD structure of the weak bosons on the Higgs boson production ine-p scattering is studied. The energy and Higgs boson mass dependence of the cross-section, following from the new contributions, is calculated. Work supported by the Polish State Committee for Scientifić Research (grant No. 2 P03B 081 09) and the Volkswagen-Stiftung     

Compact boson stars

We consider compact boson stars that arise for a V-shaped scalar field potential. They represent a one parameter family of solutions of the scaled Einstein–signum–Gordon equations. We analyze the physical properties of these solutions and determine their domain of existence. Along their physically relevant branch emerging from the compact Q-ball solution, their mass increases with increasing radius. Employing arguments from catastrophe theory we argue that this branch is stable, until the maximal value of the mass is reached. There the mass and size are on the order of magnitude of the Schwarzschild limit, and thus the spiraling respectively oscillating behaviour, well known for compact stars, sets in.     

Higgs boson cosmology

The discovery of the Standard Model Higgs boson opens up a range of speculative cosmological scenarios, from the formation of structure in the early universe immediately after the big bang, to relics from the electroweak phase transition one nanosecond after the big bang, on to the end of the present-day universe through vacuum decay. Higgs physics is wide ranging, and gives an impetus to go beyond the Standard Models of particle physics and cosmology to explore the physics of ultra-high energies and quantum gravity.     

Dyson-type boson mapping and SU(6) boson model

The Dyson-type boson mapping is applied to realistic cases to show that it is a very promising method for describing nuclear collective motion. Eigenvectors are obtained in the corresponding hermitian boson theory from the results of right- and left-hand-side eigenvalue problems in the Dyson boson theory. The numerical results are compared with those of the SU(6) boson model and exact quasiparticle shell-model calculations within the multi-phonon subspace.     

Higgs boson emission in very rare decays of an extra vector boson

We explore the phenomenological structure of E ₆-inspired grand unified group with the gauge group SU(3)_c×SU(2)_L×U(1)_Y×U(1), the emphasis being laid upon its implications for Higgs boson observation. In particular, we discuss the probability for the mass eigenstate Z ₂ to decay into a Higgs particle and a bound state composed of heavy quarks. Constraints on and relations between the Z ₂ and Higgs masses are presented.     

The equivalent vector boson approximation for intermediate mass Higgs boson production

We consider the equivalent vector boson approximation (EVBA) for the processqq→qqWW→qqH andqq→qqZZ→qqH. It is shown that the contributions σT and σL, of the transversely and longitudinally polarized vector bosonsV respectively, are comparable with each other for intermediate values ofm _H viz. 0.3 TeV to 0.6 TeV. σT can be as large as 1.5–2 times σL in this mass range. As a result the leading EVBA for σ=σL+σT overestimates the exact total cross-section by a factor, upto 2–3 even, at high energies. σT is negligible with respect to the leading contribution σL only form _H≧0.6 TeV, where EVBA is correct within 15–20%. Further the effect of the corrections to EVBA, which are naively of nonleading order, on these conclusions in the framework of the EVBA is discussed.     

The width of theZ boson

We present a detailed discussion of the electroweak radiative corrections to the partial decay widths of theZ boson into lepton and quark pairs (q≠t) and to the total width for 5 flavors. The results are only very weakly dependent on the Higgs mass. The top mass dependence leads to sizable variations ofΓ _z which have to be taken into account for precision experiments at thee ⁺ e ^? colliders LEP and SLC.     

Fermion to boson mapping

The enveloping algebra, D_n, of fermions is extended on the lattice to include the discrete space invariance. This extended algebra, denoted X, has the space symmetry as a factor: X/D_n = space group.     

On vector Goldstone boson

The possibility that higher dimensional field theories are broken spontaneously, through the usual Nambu-Goldstone mechanism, to 4-dimension is explored. As a consequence, vector Goldstone bosons can arise in this breaking of Lorentzian symmetry from higher dimension to 4-dimension. This can provide a simple mechanism for reduction to 4-dimension in theories with extra dimensions. Received: 3 January 2002 / Published online: 14 March 2003     

Electromagnetic properties of theZ boson

Direct (nonresonant) 3-body decays of charmed mesons are calculated in chiral perturbation theory. The magnitudes of the 20 and 84 representations of the effective chiralSU(4)×SU(4) Lagrangian are determined from the measured 2-bodyD→Kπ rate. For decay modes which do not contain nonspectator contributions, the agreement of theoretical predictions with the data is satisfactory. Nevertheless, the large discrepancy between theory and experiment for decays which can proceed through theW-exchange orW-annihilation might imply the importance of nonperturbative corrections to the nonspectator diagram and the existence of final-state interactions.     

Eigenstates of boson creation operator

We examine the existence of right-hand eigenstates (or eigenkets) of the boson creation operator a and determine their coordinate and their Bargmann representation. The eigenkets of the creation operator are ultrasingular and cannot be considered as a limiting case of normalizable states. Applications of these eigenstates as auxiliary states for purposes of representation of states by path integrals over coherent states are discussed. A completeness relation for coherent states on paths through the complex plane is derived and special examples of its application are considered. Received 9 March 2001 and Received in final form 13 June 2001