image chiral perturbation theory for image decay amplitudes Original Research Article

We use one-loop image chiral perturbation theory (image ChPT) to study the behaviour of the form-factors for semileptonic image decays with the pion mass at image and at image, where q is the momentum transfer. At image, the final-state pion has an energy of approximately image (for image) and so is not soft, nevertheless it is possible to compute the chiral logarithms, i.e. the corrections of image. We envisage that our results at image will be useful in extrapolating lattice QCD results to physical masses. A consequence of the Callan–Treiman relation is that in the image chiral limit (image), the scalar form factor image at image is equal to image, the ratio of the kaon and pion leptonic decay constants in the chiral limit. Lattice results for the scalar form factor at image are obtained with excellent precision, but at the masses at which the simulations are performed the results are about 25% below image and are increasing only very slowly. We investigate the chiral behaviour of image and find large corrections which provide a semi-quantitative explanation of the difference between the lattice results and image. We stress the generality of the relation image in the image chiral limit, where image, D or B and briefly comment on the potential value of using this theorem in obtaining physical results from lattice simulations.