B → ρ transition form factors and the ρ-meson transverse leading-twist distribution amplitude

Abstract

The QCD light-cone sum rules (LCSR) provide an effective way for dealing with heavy-to-light transition form factors (TFFs), in which the non-perturbative dynamics are parameterized into the light-meson’s light-cone distribution amplitudes (LCDAs). By taking the chiral correlator as the starting point, we derive new LCSRs for TFFs up to twist-4 accuracy. In those LCSRs, the twist-2 transverse LCDA provides dominant contribution, while the twist-3 and twist-4 contributions are δ2-suppressed (). Thus, they provide good platforms for testing behavior. For the purpose, we suggest a WH-model for , in which a single parameter dominantly controls its longitudinal distribution. When setting , varies from the single-peak behavior to the double-humped behavior. We present a detailed comparison of the LCSR estimation for TFFs with those predicted by pQCD and lattice QCD calculations. The TFFs become smaller with the increment of and a larger is not allowed by lattice QCD predictions. By using the extrapolated TFFs, we further predict the Cabibbo–Kobayashi–Maskawa (CKM)-matrix element with the help of two semi-leptonic decays. The predicted increases with the increment of , i.e. we have for and for . If treating the BABAR prediction on as a criteria, we observe that should be within the region of [−0.20, +0.10], which indicates that the ρ-meson LCDA prefers a single-peak behavior rather than a double-humped behavior.