$q^2$-Dependence of Meson Mixing in Few-Body Charge Symmetry Breaking: $π^o-η$ Mixing to One Loop in Chiral Perturbation Theory

Kim Maltman

doi:10.1016/0370-2693(93)91213-7

paper

$q^{2}$ -Dependence of Meson Mixing in Few-Body Charge Symmetry Breaking: $π^{o} - η$ Mixing to One Loop in Chiral Perturbation Theory

arXiv:nucl-th/9211006 · doi:10.1016/0370-2693(93)91213-7

Abstract

It is pointed out that the meson mixing matrix elements usually considered responsible for the bulk of the observed few-body charge symmetry breaking are naturally $q^{2}$ -dependent in QCD. For $π^{o} - η$ mixing, using the usual representation of the pseudoscalar fields, the leading $q^{2}$ dependence can be explicitly calculated using chiral perturbation theory to one loop, the result being a significant decrease in the magnitude of the matrix element in going from timelike to spacelike values of $q^{2}$ . Since it is the latter range of $q^{2}$ which is relevant to NN scattering and the few-body bound state, this result calls into serious question the standard treatment of few-body charge symmetry breaking contributions associated with $π^{o} - η$ and $ρ - ω$ mixing.

14 pages

q2-Dependence of Meson Mixing in Few-Body Charge Symmetry Breaking: πo−η Mixing to One Loop in Chiral Perturbation Theory

Abstract

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$q^{2}$ -Dependence of Meson Mixing in Few-Body Charge Symmetry Breaking: $π^{o} - η$ Mixing to One Loop in Chiral Perturbation Theory