Model Of Unstable Particles Research Articles

Unstable states in quantum theory

Various approaches to the problem of describing unstable particles are reviewed. Fundamental problems that arise in quantum field description of these particles and the ways of their solution are considered. Among them, there is an approach related to the notion of the smeared (continuous) mass, which originates from the finite lifetime of unstable particles. The quantum field model of unstable particles with smeared mass, which is built upon two basic axiomatic elements, is considered in detail. The basic processes with unstable particles (decay and scattering) are considered within the framework of the model and the formalism for describing physical characteristics of those processes is developed. The model is successfully applied to describing the processes of pair and triple boson production at the linear collider, top quark pair production, and certain hadronic decays. Based on this model, the factorization method is developed, which allows a description of complicated and multistep scattering and decay processes with unstable particles to be considerably simplified.

FACTORIZATION EFFECTS IN A MODEL OF UNSTABLE PARTICLES

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.

Erratum to: “Factorization method in the model of unstable particles with a smeared mass”

Erratum to: “Factorization method in the model of unstable particles with a smeared mass”

ERRATA: "FINITE-WIDTH EFFECTS IN THE MODEL OF UNSTABLE PARTICLES WITH A SMEARED MASS"

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.

Factorization method in the model of unstable particles with a smeared mass

The method of factorization, based on the model of unstable particles with a smeared mass, is applied to the processes with an unstable particle in the intermediate state. It was shown, that in the framework of the method suggested, the decay rate and cross-section can be represented in the universal factorized form for an arbitrary set of particles. An exact factorization is caused by the specific structure of unstable particles propagators. We performed the phenomenological analysis of the factorization effect.

FINITE-WIDTH EFFECTS IN THE MODEL OF UNSTABLE PARTICLES WITH A SMEARED MASS

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.

The convolution formula for a decay rate

The convolution formula is derived within the framework of the decay-chain method for decay channels with three and four particles in a final state. To get this formula exactly for unstable particles of any type one must modify the propagators of vector and spinor fields. In this work we suggest proper modifications and get the convolution formula by direct calculations. It was noted that this approach naturally arises in the model of unstable particles with random mass.

The Markovian master equations for unstable particles

The theory of Markovian master equations is applied to a certain model of unstable particles. The exponential decay law is obtained in the weak coupling limit. The connection to the method of one-parameter contracting semigroups on a single particle Hilbert space is given.

Elastic partial-wave amplitude and poles of higher order

Starting from the usual formula for the elastic partial-wave scattering amplitude a new formal decomposition of the phase shift is given which leads to a new more general expression for energy-dependence exhibiting poles of higher order. This decomposition is in agreement with a multichannel decay model of unstable particles, which stands behind this approach.