Isospin Violations in the Pion-Nucleon System

Abstract

We examine the effect of isospin-violating meson-nucleon coupling constants on low-energy pion-nucleon scattering. We compute the couplings in the context of a nonrelativistic quark model. The difference between the up and down constituent masses induces a coupling of the neutral pion to the proton that is slightly larger than the corresponding one for the neutron. This difference generates a large isospin-violating correction---proportional to the isospin-even contribution arising from the nucleon Born terms---to the charge-exchange (${\pi }^{-}p\to {\pi }^{0}n$) amplitude. In contrast to the isospin-conserving case, this correction is not cancelled by $\sigma$-meson exchange; in our model there is no isospin-violating $NN\sigma$ coupling at $q^2=0$. As a result, we find a violation of the triangle identity consistent with the one reported by Gibbs, Ai, and Kaufmann from a recent analysis of pion-nucleon data.

9 pages, no figures

References in corpus (5)

• The Momentum Dependence of the $\rho -\omega$ Mixing Amplitude in a Hadronic Model
• Constraints on the momentum dependence of rho-omega mixing
• The Off Shell $\rho$-$\omega$ Mixing in the QCD Sum Rules
• Charge-Symmetry Breaking, Rho-Omega Mixing and the Quark Propagator
• Charge symmetry breaking via rho-omega mixing from model quark-gluon dynamics

Cited by in corpus (7)

• S-wave pion nucleon scattering lengths from $\pi N$, pionic hydrogen and deuteron data
• Low-energy Pion-nucleon Scattering
• Hadronic Couplings Via QCD Sum Rules Using Three-Point Functions: Vacuum Susceptibilities
• Isospin Breaking in the Pion-Nucleon Coupling from QCD Sum Rules
• Systematic effects in the low-energy behavior of the current SAID solution for the pion-nucleon system
• The Okamoto-Nolen-Schiffer anomaly without rho-omega mixing
• Electromagnetic and Mass Difference Corrections in pion N Scattering