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

TL;DR

This paper calculates chiral logarithms for $B o\pi$ and $D o\pi$ formfactors using Heavy Meson Chiral Perturbation Theory, providing a method to improve lattice QCD extrapolations at higher pion energies.

Contribution

It introduces a reliable approach to compute chiral logarithms for hard pions in semileptonic heavy meson decays, extending chiral perturbation theory applicability.

Findings

Calculated chiral logarithms for $B o\pi$ formfactors at various momentum transfers.

Argued the validity of chiral behavior in the hard pion energy regime.

Provided a framework for lattice QCD formfactor extrapolation.

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.