Narrow Results

We show that the real parts of diagonal matrix elements of the exact effective Hamiltonian governing the time evolution in the subspace of states of neutral kaons and similar particles cannot be equal for t>t₀ (t₀ is the instant of creation of the pair K₀, ) when the total system under consideration is CPT invariant but CP noninvariant. The unusual consequence of this result is that, contrary to the properties of stable particles, the masses of the unstable particle, e.g. K₀, and its antiparticle, , need not be equal for t≫t₀ in the case of preserved CPT and violated CP symmetries.

The detection of a time variation of the angle between two distant sources would reveal an anisotropic expansion of the universe. We study this effect of cosmic parallax within the ellipsoidal universe model, namely a particular homogeneous anisotropic cosmological model of Bianchi type I, whose attractive feature is the potential to account for the observed lack of power of the large-scale cosmic microwave background anisotropy. The preferred direction in the sky, singled out by the axis of symmetry inherent to planar symmetry of ellipsoidal universe, could in principle be constrained by future cosmic parallax data. However, that will be a real possibility if and when the experimental accuracy will be enhanced at least by two orders of magnitude.

We calculate the cross-section of the near-threshold off-shell ZZZ and ZW⁺W^- production at the International Linear Collider taking into account their instability and the principal part of next-to-leading order corrections. The calculations are performed in the framework of the model of unstable particles with smeared mass-shell. We show that the contribution of the finite Z/W and H widths (their instability) is large in the Higgs resonance range (about -24% and -18% for ZZZ and ZW⁺W^-, respectively, at ) and should be taken into account in the Higgs boson studies at the future International Linear Collider.

In the Standard Model, the top quark decay width Γ_t is computed from the exclusive t → bW decay. We argue in favor of using the three body decays to compute Γ_t as a sum over these exclusive modes. As dictated by the S-matrix theory, these three body decays of the top quark involve only asymptotic states and incorporate the width of the W boson resonance in a natural way. The convolution formula commonly used to include the finite width effects is found to be valid, in the general case, when the intermediate resonance couples to a conserved current (limit of massless fermions in the case of W bosons). The relation Γ_t = Γ(t → bW) is recovered by taking the limit of massless fermions followed by the W boson narrow width approximation. Although both calculations of Γ_t are different at the formal level, their results would differ only by tiny effects induced by light fermion masses and higher-order radiative corrections.

Near-threshold production of neutral boson pairs is considered within the framework of the model of unstable particles with smeared mass. The results of calculations are in good agreement with LEP II data and Monte Carlo simulations. Suggested approach significantly simplifies calculations with respect to standard perturbative one.

The quantum field model of unstable particles with a smeared mass is suggested to describe the finite-width effects. Within the framework of this model, we derive the convolution formula for a width and factorized formula for a cross-section. The phenomenological consequences of the mass smearing is discussed in the various fields of particle physics.

Near-threshold production of charged boson pairs is considered within the framework of the model of unstable particles with smeared mass. The results of calculations are in good agreement with LEP II data and Monte Carlo simulations. Suggested approach significantly simplifies calculations with respect to standard perturbative one.

We construct an asymptotic expansion in powers of the coupling constant directly of the cross-section for pair production and decay of fundamental unstable particles. The resonant and kinematic singularities arising in the expansion we treat in the sense of distributions. This mode allows us to transform formally divergent integrals into absolutely convergent ones with keeping the asymptotic property of the expansion. The appropriate procedure is elaborated up to an arbitrary order of the expansion. The peculiarity of application of the procedure in the threshold region is analyzed. The scheme of the calculations within the NNLO approximation is explicitly discussed.

The effects of factorization are considered within the framework of the model of unstable particles with a smeared mass. It is shown that two-particle cross-section and three-particle decay width can be described by the universal factorized formulae for an unstable particles of an arbitrary spin in an intermediate state. The exact factorization is caused by the specific structure of the model unstable-particle propagators. This result is generalized to complicated scattering and decay-chain processes with unstable particles in intermediate states. We analyze applicability of the method and evaluate its accuracy.

The top quark pair production and decay are considered in the framework of the smeared-mass unstable particles model. The results for total and differential cross-sections in vicinity of threshold are in good agreement with the previous ones in the literature. The strategy of calculations of the higher order corrections in the framework of the model is discussed. Suggested approach significantly simplifies calculations compared to the standard perturbative one and can serve as a convenient tool for fast and precise preliminary analysis of processes involving intermediate timelike top quark exchanges in the near-threshold region.