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

TL;DR

This paper calculates the $B o ho$ helicity form factors using light-cone sum rules up to twist-4, providing insights into their behavior across the $q^2$ spectrum and implications for semileptonic decay analysis.

Contribution

It introduces a novel application of light-cone sum rules to compute $B o ho$ helicity form factors, highlighting their advantages and providing detailed $q^2$-dependent results.

Findings

Longitudinal component dominates at low $q^2$

Transverse component dominates at high $q^2$

Results agree with BaBar measurements within errors

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 $\mathcal{H}_{\rho,0}(0)=0.435^{+0.055}_{-0.045}$ 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 $R_{\rm low}$ and $R_{\rm high}$ are used to characterize those properties, and our LCSR calculation gives, $R_{\rm low}=0.967^{+0.305}_{-0.284}$ and $R_{\rm high}=0.219^{+0.058}_{-0.070}$, which agree with the BaBar measurements within errors.