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

Abstract We calculate π + – π 0 mass difference Δ m π 2 ≡ m π + 2 − m π 0 2 in the Hidden Local Symmetry (HLS) model, based on the Wilsonian matching and Wilsonian renormalization-group equations. Even without a 1 meson the result agrees well with the experiment in sharp contrast to the conventional approach where the a 1 meson plays a crucial role. For large N f QCD, there arises a large hierarchy between Δ m π 2 and the π decay constant F π 2 , Δ m π 2 / F π 2 ⪡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.