Resonant and nonresonantD+→K−π+l+νlsemileptonic decays

Abstract

We analyze the semileptonic decay ${D}^{+}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{l}^{+}{\ensuremath{\nu}}_{l}$ using an effective Lagrangian developed previously to describe the decays $\stackrel{\ensuremath{\rightarrow}}{D}\mathrm{Pl}{\ensuremath{\nu}}_{l}$ and $\stackrel{\ensuremath{\rightarrow}}{D}\mathrm{Vl}{\ensuremath{\nu}}_{l}.$ Light vector mesons are included in the model which combines the heavy quark effective Lagrangian and chiral perturbation theory approach. The nonresonant and resonant contributions are compared. With no new parameters the model correctly reproduces the measured ratio ${\ensuremath{\Gamma}}_{\mathrm{nres}}/{\ensuremath{\Gamma}}_{\mathrm{nres}\mathrm{}+\mathrm{}\mathrm{res}}.$ We also present useful nonresonant decay distributions. Finally, a similar model, but with a modified current which satisfies the soft pion theorems at the expense of introducing another parameter, is analyzed and the results of the models are compared.