The $\rho$-meson longitudinal leading-twist distribution amplitude within QCD background field theory

Abstract

We revisit the $\rho$-meson longitudinal leading-twist distribution amplitude (DA) ${\varphi }_{2;\rho }^{\Vert }$ by using the QCD sum rules approach within the background field theory. To improve the accuracy of the sum rules for its moments $⟨{\xi }_{n;\rho }^{\Vert }⟩$, we include the next-to-leading order QCD correction to the perturbative part and keep all non-perturbative condensates up to dimension-six consistently within the background field theory. The first two moments read $⟨{\xi }_{2;\rho }^{\Vert }⟩{|}_{1\mathrm{GeV}}=0.241(28)$ and $⟨{\xi }_{4;\rho }^{\Vert }⟩{|}_{1\mathrm{GeV}}=0.109(10)$, indicating a double humped behavior for ${\varphi }_{2;\rho }^{\Vert }$ at small energy scale. As an application, we apply them to the $B\to \rho$ transition form factors within the QCD light-cone sum rules, which are key components for the decay width $\Gamma (B\to \rho \ell {\nu }_{\ell })$. To compare with the world-average of $\Gamma (B\to \rho \ell {\nu }_{\ell })$ issued by Particle Data Group, we predict $|V_{\mathrm{ub}}|=3.19_{-0.62}^{+0.65}$, which agrees with the BABAR and Omnès parameterization prediction within errors.

Comments: 10 pages, 5 figures. Revised version to be published in Phys.Rev.D