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

C. BARBERO; A. MARIANO

JOURNAL OF PHYSICS G. NUCLEAR PHYSICS

IOP Publishing

Año: 2015 vol. 42 p. 1051041 - 10510412

0305-4616

It is a well known fact that when a resonance (R) is produced and decays, itsunperturbed propagator will be singular at p^2= mRwhen it appears in an s-type Feynman pole graph. Nevertheless this is not a problem, since it mustbe dressed by the successive re-interactions of the resonance with itself to all orders through the non-pole T-matrix, which we include in this work for the self-energy one-loop pion-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 - iGamma /2 over theunperturbed propagator, adopted in previous calculations to treat pion?nucleonelastic and radiative scattering, and photo and weak pion production in theresonance 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 p^2 ~ 1400 MeV, thisapproach 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.