Hard Pion Chiral Perturbation Theory for $B\to\pi$ and $D\to\pi$ Formfactors

Abstract

We use one-loop Heavy Meson Chiral Perturbation Theory (HMCHPT) as well as a relativistic formulation to calculate the chiral logarithms $m^2_\pi\log{\left(m^2_\pi/\mu^2\right)}$ contributing to the formfactors of the semileptonic $B\rightarrow \pi$ decays at momentum transfer $q^2$ away from $q^2_\mathrm{max}=(m_B-m_\pi)^2$. We give arguments why this chiral behavior is reliable even in the energy regime with hard or fast pions. These results can be used to extrapolate the formfactors calculated on the lattice to lower light meson masses.