Nuclear central force in the chiral limit

Abstract

Chiral perturbation theory supplemented by the Omnes function is employed to study the strength of the isoscalar central nuclear interaction, ${G}_{S}$, in the chiral limit vs the physical case. A very large modification is seen, i.e., ${\ensuremath{\eta}}_{s}={G}_{S\phantom{\rule{0.3em}{0ex}}\text{chiral}}/{G}_{S\phantom{\rule{0.3em}{0ex}}\text{physical}}=1.37\ifmmode\pm\else\textpm\fi{}0.10$. This large effect is seen to arise dominantly at low energy from the extra contributions made by massless pions at energies near the physical threshold where the physical spectral function must vanish kinematically. The slope away from the chiral limit, ${d}_{S}$, is also calculated and is correspondingly large. I also explain why this large variation is to be expected.