Theory of the J=3/2, I=3/2 ΠN resonance

Abstract

We calculate the position W_R and width γ₃₃ of the J=3/2, I=3/2 P-wave ΠN resonance, using partial-wave dispersion relations. In the present calculation we treat as given the nucleon and ρ-meson masses and coupling constants, which determine the long-range part of the forces. The parameters, which characterize the distant part of the left-hand cut, are fixed by using the expressions for the (3/2, 3/2) P-wave ΠN state given by fixed energy dispersion relations, in a region where they are valid without subractions, in a way used by Balázs for the ΠΠ problem. We then impose the self-consistency demand that the position and width of the (3/2, 3/2) resonance used as input values in the crossed channel in the fixed-energy dispersion relation be the same as the calculated values of the position and width. The preliminary results of the calculation are W_R≈m+2.35 and γ₃₃≈0.14. The experimental values are W_R=m+2.17 and γ₃₃≈0.12, (where m is the nucleon mass and we use units in which ℏ=c=m_Π=1). These results constitute the first part of the intended selfconsistent calculation of the nucleon mass and (3/2, 3/2) resonance position, exploiting the "reciprocal bootstrap" mechanism discussed by Chew.