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

Abstract

The QCD light-cone sum rules (LCSR) provides an effective way for dealing with the heavy-to-light transition form factors (TFFs), whose non-perturbative dynamics are parameterized into the light-meson's light-cone distribution amplitudes (LCDAs) with various twist structures. By taking the chiral correlator 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, we observe that the twist-2 transverse DA ${\varphi }_{2;\rho }^{\perp }$ provides the dominant contribution, while the contributions from the remaining twist-3 and twist-4 terms are ${\delta }^2$-suppressed. Thus, our present improved LCSRs provides a good platform for testing the ${\varphi }_{2;\rho }^{\perp }$ behavior. For the purpose, we suggest a convenient WH-model for the $\rho$-meson leading-twist wavefunction, in which the parameter $B_{2;\rho }^{\perp }\sim a_2^{\perp }$ dominantly controls its longitudinal distribution. Typically, its DA ${\varphi }_{2;\rho }^{\perp }$ is CZ-like as $B_{2;\rho }^{\perp }\simeq -0.20$, which changes to be asymptotic-like as $B_{2;\rho }^{\perp }\simeq 0.00$. By varying $B_{2;\rho }^{\perp }\in [-0.20,0.20]$, we present a detailed comparison of the LCSR estimation for the $B\to \rho$ TFFs with those of pQCD and Lattice QCD predictions. Furthermore, by using the extrapolated TFFs, we estimate the CKM-matrix element $|V_{\mathrm{ub}}|$ with the help of two $B\to \rho$ semi-leptonic decays. The predicted value for $|V_{\mathrm{ub}}|$ increases with the increment of $B_{2;\rho }^{\perp }$, i.e. we have $\Vub=(2.91\pm0.19)\times 10^{-3}$ for $B_{2;\rho }^{\perp }=-0.20$ and $\Vub=(3.11\pm0.19)\times 10^{-3}$ for $B_{2;\rho }^{\perp }=0.00$. If using the BABAR prediction as a criteria, we observe that $B_{2;\rho }^{\perp }\in [-0.2,0.10]$, which indicates that the $\rho$-meson DA ${\varphi }_{2;\rho }^{\perp }$ prefers a single-peak behavior rather than a double-humped behavior.

arXiv comment14 pages, 3 figures and 12 tables. References updated and discussions improved. To be published in J. Phys. G

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