BHLS upgrade: spectra, muon HVP and the [ ] system.

The generic hidden local symmetry (HLS) model has recently given rise to its variant, defined by introducing symmetry breaking mostly in the vector meson sector; the central mechanism is a modification of the covariant derivative at the root of the HLS approach. However, the description of the dipion spectra, especially the Belle one, is not fully satisfactory, whereas the simultaneous dealing with its annihilation sector ( ) is optimum. We show that this issue is solved by means of an additional breaking term which also allows us to consistently include the mixing properties of the system within this extended ( ) scope.