Renormalized hybrid loop-chain propagator and its effect for proton-antiproton elastic scattering in isospin space

The differential cross-section of pp-bar → pp-bar (proton-antiproton → proton-antiproton) elastic scattering with renormalized hybrid loop-chain propagators of the neutral pion π⁰ is 'strictly' calculated, bottomed on isospin-SU(2) invariant coupling model describing strong interaction between neutral/charged pions and nucleon-antinucleon; By comparison of differential cross-sections between cases of hybrid loop-chain propagator and tree propagator, we obtain crucial information of relevant radiative correction. The results achieved here would contribute to further studies on isospin-SU(2) invariant coupling model for strong interaction between pions and nucleon-antinucleon, and it also could be referential to theoretical or experimental researches on the proton-antiproton collision. (authors)