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

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 B -> rho TFFs up to twist-4 accuracy. In those LCSRs, the twist-2 transverse LCDA phi(perpendicular to)(2;rho) provides dominant contribution, while the twist-3 and twist-4 contributions are delta(2)-suppressed (delta similar or equal to m(rho)/m(b)). Thus, they provide good platforms for testing phi(perpendicular to)(2;rho) behavior. For the purpose, we suggest a WH-model for phi(perpendicular to)(2;rho') in which a single parameter B phi(perpendicular to)(2;rho) similar to a(2)(perpendicular to) dominantly controls its longitudinal distribution. When setting B-2;rho(perpendicular to) is an element of[- 0.20, + 0.20], phi(perpendicular to)(2;rho) varies from the single-peak behavior to the double-humped behavior. We present a detailed comparison of the LCSR estimation for B -> rho TFFs with those predicted by pQCD and lattice QCD calculations. The TFFs become smaller with the increment of. B-2;rho(perpendicular to) and a larger B-2;rho(perpendicular to) is not allowed by lattice QCD predictions. By using the extrapolated TFFs, we further predict the Cabibbo-Kobayashi-Maskawa (CKM)-matrix element vertical bar V-ub vertical bar with the help of two B -> rho semi-leptonic decays. The predicted vertical bar V-ub vertical bar increases with the increment of B-2;rho(perpendicular to) i. e. we have vertical bar V-ub vertical bar = (2.91 +/- 0.19) x10(-3) for B-2;rho(perpendicular to) = -0.20 and vertical bar V-ub vertical bar = (3.11 +/- 0.19) x 10(-3) for B-2;rho(perpendicular to) = 0.00. If treating the BABAR prediction on vertical bar V-ub vertical bar as a criteria, we observe that. B-2;rho(perpendicular to) should be within the region of [-0.20, + 0.10], which indicates that the rho-meson LCDA prefers a single-peak behavior rather than a double-humped behavior.