The $B\to \rho$ helicity form factors within the QCD light-cone sum rules

Abstract

We study the $B\to \rho$ helicity form factors (HFFs) by applying the light-cone sum rules up to twist-4 accuracy. The HFF has some advantages in comparison to the conventionally calculated transition form factors, such as the HFF parameterization can be achieved via diagonalizable unitarity relations and etc. At the large recoil point, only the $\rho$-meson longitudinal component contributes to the HFFs, and we have ${\mathcal{H}}_{\rho ,0}(0)=0.435_{-0.045}^{+0.055}$ and ${\mathcal{H}}_{\rho ,\{1,2\}}(0)\equiv 0$. We extrapolate the HFFs to physically allowable $q^2$-region and apply them to the $B\to \rho$ semileptonic decay. We observe that the $\rho$-meson longitudinal component dominates its differential decay width in low $q^2$-region, and its transverse component dominates the high $q^2$-region. Two ratios $R_{\mathrm{low}}$ and $R_{\mathrm{high}}$ are used to characterize those properties, and our LCSR calculation gives, $R_{\mathrm{low}}=0.967_{-0.284}^{+0.305}$ and $R_{\mathrm{high}}=0.219_{-0.070}^{+0.058}$, which agree with the BaBar measurements within errors.

arXiv comment11 pages, 7 figures, 8 tables

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• Investigation of the possible $D{\bar{D}}^{\ast }$/$B{\bar{B}}^{\ast }$ and $D{D}^{\ast }$/$\bar{B}{\bar{B}}^{\ast }$ molecule states
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• Branching fractions and polarizations of $D\to V(\omega ,\rho ,K^{\ast })\ell {\nu }_{\ell }$ within QCD LCSR
• $D\to P(\pi ,K)$ helicity form factors within light-cone sum rule approach
• $B_c\to J/\psi$ helicity form factors and the $B_c^{+}\to J/\psi +(P,V,{\ell }^{+}{\nu }_{\ell })$ decays
• Scrutinizing $B^0$-meson flavor changing neutral current decay into scalar $K_0^{\ast }(1430)$ meson with $b\to s{\ell }^{+}{\ell }^{-}(\nu \bar{\nu })$ transition
• $B_{(s)}\to S(a_0(1450),K_0^{\ast }(1430),f_0(1500))$ helicity form factors within QCD light-cone sum rules
• Branching fraction, $CP$ asymmetry, and polarization in $B\to \rho \rho$ decays with the modified perturbative QCD approach