Δ++ contribution to the elastic and radiative π+p scattering

Elastic and radiative π+p scattering and properties of the Δ++ resonance

“…1(e-f) in Ref. [18]) are ignored. Furthermore, the finite width of the ∆ ++ which one expects to be important in the resonance region, are also ignored in Ref.…”

“…The experimental cross section can contain also non-resonant background contributions which can either, be parametrized in terms of a softly-varying function around the resonance (see for example [18,24]) or computed explicitly in a given dynamical model. In this paper we adopt the second approach.…”

“…[18], in the case of elastic and radiative π + p scattering, the Adependent Feynman rules involving the ∆ can be replaced by a set of A-independent vertices and propagators called reduced Feynman rules. The calculation of π + p scattering amplitudes using either set of rules, give rise to identical results [18]. The elastic scattering with the ∆ ++ intermediate state in the s-channel (see the first graph in Figure 1) is given by…”

“…The simplest solution to maintain gauge invariance in the radiative π + p scattering amplitude when finite width effects are incorporated, is to replace m 2 ∆ → m 2 ∆ − im ∆ Γ ∆ in all the Feynman rules involving the ∆ ++ resonance [18] (this is the so-called complex mass scheme). As it has been explained in the introduction, this prescription is well justified for the amplitudes involving intermediate Z 0 and W ± gauge boson [25,26] and the ρ ± meson resonances [22].…”

“…Since this limit may me questionable, let us point out that a Laurent expansion of the amplitude (with Dyson summation of the ∆ ++ self-energy corrections ) around the pole will give similar results to the complex mass scheme, with regular terms being absorbed into background contributions (see for example Refs. [18,20,25] and the discussion we present in the appendix).…”