Final state interactions in $D\to K\pi l\nu$ decay

Abstract

The semileptonic $D_{l4}$ decay including $D\to K\pi l\nu$ and $D\to \pi\pi l\nu$ have been extensively studied. In these references, the form factors and differential decay rate are explicitly stated. However, we would like to stress that in these papers the final state interactions are often overlooked, i.e. rescattering effect of the pseudoscalars produced by $D_{l4}$ decay may be very important, at least on the side of phase of form factors due to Watson's theorem. In this short paper, we will display this rescattering effect in the framework of heavy hadron chiral perturbation theory, it thus must be a very useful and indispensable supplement of the previous papers on $D_{l4}$ study.