π+–π0 mass difference in the Hidden Local Symmetry: a dynamical origin of little Higgs

We calculate π+–π0 mass difference Δmπ2≡mπ+2−mπ02 in the Hidden Local Symmetry (HLS) model, based on the Wilsonian matching and Wilsonian renormalization-group equations. Even without a1 meson the result agrees well with the experiment in sharp contrast to the conventional approach where the a1 meson plays a crucial role. For large Nf QCD, there arises a large hierarchy between Δmπ2 and the π decay constant Fπ2, Δmπ2/Fπ2⪡1, near the critical point where the chiral symmetry gets restored as the vector manifestation and the HLS model becomes a little Higgs model with two sites and two links, with the dynamically generated gauge coupling of the composite ρ becoming vanishingly small.