The sigma and rho in D and B decays

Abstract

We study the D^{+} -> sigma pi^{+}, D^{+} -> rho^0 pi^{+}, B^{-} -> sigma pi^{-}, B^{-} -> rho^0 pi^{-} and \bar{B}^0 -> rho^{\pm} pi^{\mp} decays in a valence quark triangle model, incorporating chiral symmetries. We find a good agreement with recent experimental data for D^{+} -> sigma pi^{+} and for D^{+} -> rho^0 pi^{+}. We point out that a "long-distance" contribution due to the axial vector a_1 meson pole, calculated by using chiral symmetry, can be relevant to explain D^{+}-> rho^0 \pi^{+} and for lowering the ratio R=Br(\bar{B}^0 -> rho^{\pm} pi^{\mp})/Br(B^{-} -> rho^0 pi^{-}) to be consistent with its phenomenological determination, within the large experimental uncertainity.