Vector Formfactors in Hard Pion Chiral Perturbation Theory

TL;DR

This paper applies hard pion chiral perturbation theory to compute formfactors and chiral logarithms for heavy meson decays and electromagnetic form factors, comparing results with experimental data and testing theoretical predictions.

Contribution

It introduces calculations of chiral logarithms in heavy meson and electromagnetic form factors using both heavy and relativistic formulations of HPChPT, extending previous work.

Findings

Calculated chiral logarithms for B and D meson transitions.

Compared theoretical results with CLEO experimental data.

Tested hard pion ChPT predictions against two-loop calculations.

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 $B_{(s)}\rightarrow \pi,K,\eta$ and $D_{(s)}\rightarrow \pi,K,\eta$ transitions at momentum transfer $q^2$ away from the endpoint $q^2_\mathrm{max}=(m_B-m_M)^2$. We compare our results with CLEO $D\to\pi$ and $D\to K$ data. We also calculate the Isgur-Wise function of the $B_{(s)}\rightarrow D_{(s)}$ 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.