About the validity of complex mass scheme for the Δ resonance and higher energy region approaches

Abstract

It is a well known fact that when a resonance (R) is produced and decays, its unperturbed propagator will be singular at p2 mR = 2 when it appears in an s-type Feynman pole graph. Nevertheless this is not a problem, since i must be dressed by the successive re-interactions of the resonance with itself to all order-nucleon contributions. Recently, we have shown that within the one-loop approximation for the absorptive part it is possible to justify the use of the complex-mass description m → m-i⌈/2 over the unperturbed propagator, adopted in previous calculations to treat pionnucleon elastic and radiative scattering, and photo and weak pion production in the resonance region. Here we discuss the limits of the validity of this approximation, since in actual calculations we must go over this range. We show that, when the resonance energy is increased above p2 ∼1400 MeV, this approach becomes invalid and an alternative approximation should be considered. In addition, we discuss the usual energy dependent width approximation, present in several actual isobar models used to analyze the lastneutrino scattering experiments, and show that also it could be unappropriate.