Vector Formfactors in Hard Pion Chiral Perturbation Theory

Abstract

We use three-flavour hard pion Chiral Perturbation Theory (HPChPT) in both the heavy meson and a relativistic formulation to calculate the chiral logarithms $m^2\log (m^2/{\mu }^2)$ contributing to the formfactors of the $B_{(s)}\to \pi ,K,\eta$ and $D_{(s)}\to \pi ,K,\eta$ transitions at momentum transfer $q^2$ away from the endpoint $q_{\max }^2=(m_B-m_M{)}^2$. We compare our results with CLEO $D\to \pi$ and $D\to K$ data. We also calculate the Isgur-Wise function of the $B_{(s)}\to D_{(s)}$ semileptonic decay away from the endpoint and the chiral logarithms for the pion and kaon electromagnetic formfactor. In two-flavour HPChPT we calculate the chiral logarithms for the pion vector and the scalar formfactors at $s\gg m_{\pi }^2$. This allows us to test hard pion ChPT using the existing two-loop calculations for these quantities.

Comments: 24 pages