Energy eigenvalues and 〈x²〉_n for the oscillators having potential energyV(x)=(ω²x²/2)+λ<x^2r>x^2s have been determined for various values ofλ, r, s andn using renormalized hypervirial-Padé scheme. In general, the results show an improvement over the findings of earlier workers. Variation of the evaluated quantities and of the renormalization parameter withλ, r, s andn has been discussed. In addition, this potential has been employed as an illustrative example of the applicability of alternative formalism of perturbation theory developed by Kim and Sukhatme (J. Phys.A25 647 (1992)).

We study the implication of triviality on Higgs sector in next to minimal supersymmetric model (NMSSM) using variational field theory. It is shown that the mass of the lightest Higgs boson in NMSSM has an upper bound ∼10M_W which is of the same order as that in the standard model.

We examine the sensitivity of $e \gamma$ colliders (based on $e^{+} e^{-}$ linear colliders of c.m. energy 500 GeV) to the anomalous couplings of the Higgs to 𝑊-boson via the process $e^{-} \gamma \rightarrow \nu WH$. This has the advantage over $e^{+} e^{-}$ collider in being able to dissociate $WWH$ vertex from $ZZH$. We are able to construct several dynamical variables which may be used to constrain the various couplings in the $WWH$ vertex.