Direct Violation from Isospin Symmetry Breaking Effects for the Decay Process in PQCD

We investigate the direct violation for the decay process of (P,V refer to the pseudoscalar meson and vector meson, resp.) via isospin symmetry breaking effects from the mixing mechanism in PQCD factorization approach. Isospin symmetry breaking arises from the electroweak interaction and the u-d quark mass difference by the strong interaction, which are known to be tiny. However, we find that isospin symmetry breaking at the leading order shifts the violation due to the new strong phases.