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The QCD light-cone sum rules (LCSR) provides an effective way for dealingwith the heavy-to-light transition form factors (TFFs), whose non-perturbativedynamics are parameterized into the light-meson's light-cone distributionamplitudes (LCDAs) with various twist structures. By taking the chiralcorrelator as the starting point, we calculate the LCSRs for the $B\to\rho$TFFs up to twist-4 accuracy. As for the TFFs at the large recoil region, weobserve that the twist-2 transverse DA $\phi_{2;\rho}^\bot$ provides thedominant contribution, while the contributions from the remaining twist-3 andtwist-4 terms are $\delta^2$-suppressed. Thus, our present improved LCSRsprovides a good platform for testing the $\phi_{2;\rho}^\bot$ behavior. For thepurpose, we suggest a convenient WH-model for the $\rho$-meson leading-twistwavefunction, in which the parameter $B_{2;\rho}^\bot\sim a^\bot_2$ dominantlycontrols its longitudinal distribution. Typically, its DA $\phi_{2;\rho}^\bot$is CZ-like as $B_{2;\rho}^\bot\simeq-0.20$, which changes to be asymptotic-likeas $B_{2;\rho}^\bot\simeq0.00$. By varying $B_{2;\rho}^\bot\in[-0.20,0.20]$, wepresent a detailed comparison of the LCSR estimation for the $B\to\rho$ TFFswith those of pQCD and Lattice QCD predictions. Furthermore, by using theextrapolated TFFs, we estimate the CKM-matrix element $|V_{\rm ub}|$ with thehelp of two $B\to\rho$ semi-leptonic decays. The predicted value for $|V_{\rmub}|$ increases with the increment of $B_{2;\rho}^\bot$, i.e. we have$\Vub=(2.91\pm0.19)\times 10^{-3}$ for $B_{2;\rho}^\bot=-0.20$ and$\Vub=(3.11\pm0.19)\times 10^{-3}$ for $B_{2;\rho}^\bot=0.00$. If using theBABAR prediction as a criteria, we observe that$B^{\perp}_{2;\rho}\in[-0.2,0.10]$, which indicates that the $\rho$-meson DA$\phi_{2;\rho}^\bot$ prefers a single-peak behavior rather than a double-humpedbehavior.

$B\to \rho$ transition form factors within the QCD light-cone sum rules and the $\rho$-meson leading-twist distribution amplitude