Up-down quark mass difference: Couplings of pions to nucleons or isobars and low-energy nucleon-nucleon scattering

Abstract

We investigate effects of the up-down quark mass difference on the couplings of pions to nucleons or isobars. The calculated $\ensuremath{\pi}\mathrm{NN}$ and $\ensuremath{\pi}\mathrm{N}\ensuremath{\Delta}$ couplings are used to derive the long-range one-pion-exchange potential and the intermediate-range attraction for the three different cases: p-p, n-p, and n-n. The resultant potentials are then used to determine numerically the low-energy scattering parameters, including both the scattering length $a$ and the effective range $r$. Our results indicate that a reasonable up-down quark mass difference such as 10 MeV yields a value for $|{a}_{\mathrm{pp}}|\ensuremath{-}|{a}_{\mathrm{nn}}|$ of about + 0.6 fm, which is sizable from the experimental point of view. Our results also suggest that the large observed value for $|{a}_{\mathrm{np}}|\ensuremath{-}|{a}_{\mathrm{nn}}|$ can be understood primarily as a manifestation of the pion mass difference.[NUCLEAR REACTIONS Application of quark models to nuclear physics; effects of the up-down quark mass difference on couplings of pions to nucleons or isobars; charge dependence and charge symmetry breaking in low energy nucleon-nucleon scattering.]