The Ratio $\mathcal{R}(D)$ and the $D$-meson Distribution Amplitude

TL;DR

This paper calculates the $B o D$ transition form factors and predicts the ratio $ (D)$ using improved D-meson distribution amplitudes, highlighting the significance of twist-3 contributions and their impact on theoretical predictions.

Contribution

The paper develops a new model for twist-3 DAs of the D-meson based on QCD sum rules, enhancing the accuracy of $ (D)$ predictions compared to previous models.

Findings

Predicted $ (D) = 0.320^{+0.018}_{-0.021}$, close to experimental data.

Twist-3 contributions are sizable across the entire $q^2$ region.

Improved DAs lead to more precise form factor calculations.

Abstract

In this paper, we calculate the $B\to D$ transition form factors (TFFs) within the light-cone sum rules (LCSR) and predict the ratio $\mathcal{R}(D)$. More accurate $D$-meson distribution amplitudes (DAs) are essential to get a more accurate theoretical prediction. We construct a new model for the twist-3 DAs $\phi^p_{3;D}$ and $\phi^\sigma_{3;D}$ based on the QCD sum rules under the background field theory for their moments as we have done for constructing the leading-twist DA $\phi_{2;D}$. As an application, we observe that the twist-3 contributions are sizable in whole $q^2$-region. Taking the twist-2 and twist-3 DAs into consideration, we obtain $f^{B\to D}_{+,0}(0) = 0.659^{+0.029}_{-0.032}$. As a combination of the Lattice QCD and the QCD LCSR predictions on the TFFs $f^{B\to D}_{+,0}(q^2)$, we predict $\mathcal{R}(D) = 0.320^{+0.018}_{-0.021}$, which improves is about $1.5\sigma$ deviation from the HFAG average of the Belle and BABAR data. At present the data are still of large errors, and we need further accurate measurements of the experiment to confirm whether there is signal of new physics from the ratio $\mathcal{R}(D)$.