Finite width effects and gauge cancellations in W- and Z-boson production in the framework of modified perturbation theory

Abstract

The processes of production and subsequent decay of W-and Z-bosons in e + e − collisions are considered in a recently proposed modified perturbation theory (PT), based on a direct expansion of probabilities instead of amplitudes. In such an approach the non-integrable singularities in the phase space, which are intrinsic in the conventional PT, appear as singularities in the coupling constant (with subsequent compensation by the decay factors of unstable particles). In the present paper the systematic investigation of the modified PT is carried out. The results are compared with the results of the conventional approach, based on calculation of the amplitude with Dyson resummation. A solution to the problem of the loss of one-loop PT order in the resonance region is found. On the basis of this solution the proof of gauge cancellations in any order of the modified PT is given. A simple generalization of the fermion-loop scheme is proposed which provides a complete description of W-pair production in next-to-leading order approximation.

W-Pair Production in Modified Perturbation Theory

“…A modified perturbation theory (MPT) [8,9,10] is a probable candidate to become such an approach. Its main feature is the direct expansion of the probability instead of amplitude in powers of the coupling constant with the aid of distribution-theory methods.…”

Factorization in the model of unstable particles with continuous masses

“…It is essential that the effect of factorization does not depend on the form of the denominators P( ), but depends crucially on the tensor-spinor structure of the numerators in (10) and (11). The propagators (10) and (11) with a continuous mass parameter result in the exact factorization, while conventional field-theory expressions with a constant mass M lead to an approximate factorization in the narrow-width limit. We note that the factorization occurs in any model leading to the spectral representation (3) and (8) of the propagators.…”

“…For example, the following expressions are used instead of P (1) µν ( ): µν − µ ν /( − Γ/2) 2 [33], µν − µ ν /( 2 − Γ) [34], and P (1) µν ( ) ( 2 )+ µ ν / 2 ( 2 ) [54]. It should be emphasized that the structures (10) and (11) are not constrained by the choice of the gauge. The model under consideration is not a gauge one, because it describes effective unstable fields (see [41] for details).…”

“…For instance, double-pole approximation (DPA) [25][26][27]53], pinch-technique method [28,29], complex-mass scheme (CMS) [30,31], semi-analytical approximation [24], narrow-width approximation (NWA) [24,32], convolution method (CM) [33][34][35][36][37][38], etc. At the same time, alternative ways to deal with UPs were developed, such as effective theories of UP's [39,40], modified perturbation theory [10,21] and models with continuous mass spectrum [41,[55][56][57][58][59][60].…”

Twelve years of precision calculations for LEP. What s next?

“…Actually, it is a six-fermion process, however the cross-section σ(e + e − → tt) with tops on-mass-shell is an ingredient in various approaches like DPA [7], or the so-called Modified Perturbation Theory (MPT) [8].…”