Form factors $f^{B\to \pi}_+(0)$ and $f^{D\to \pi}_+(0)$ in $QCD$ and determination of $|V_{ub}|$ and $|V_{cd}|$

TL;DR

This paper uses QCD light cone sum rules to calculate form factors for B and D meson decays to pions at zero momentum transfer, leading to improved estimates of CKM matrix elements |V_{ub}| and |V_{cd}|.

Contribution

It introduces a twist-5 level analysis with no twist-3 or -5 components, enhancing the convergence and accuracy of form factor calculations for semileptonic B and D decays.

Findings

Calculated $f^{B o \pi}_+(0)$ and $f^{D o \pi}_+(0)$ with uncertainties.

Estimated CKM matrix elements $|V_{ub}|$ and $|V_{cd}|$ from form factors.

Provided a numerical estimate for the decay constant $f_D$.

Abstract

We present a QCD study on $B, D\to\pi$ semileptonic transitions at zero momentum transfer and an estimate of magnitudes of the associated CKM matrix elements. Light cone sum rules (LCSRs) with chiral correlator are applied to calculate the form factors $f^{B\to \pi}_+(0)$ and $f^{D\to \pi}_+(0)$. We show that there is no twist-3 and-5 component involved in the light-cone expansions such that the resulting sum rules have a good convergence and offer an understanding of these form factors at twist-5 level. A detailed $\mathcal{O}(\alpha_s)$ computation is carried out in leading twist-2 approximation and the $\bar{MS}$ masses are employed for the underlying heavy quarks. With the updated inputs and experimental data, we have $f^{B\to \pi}_+(0)=0.28^{+0.05}_{-0.02}$ and $|V_{ub}|=(3.4^{+0.2}_{-0.6}\pm0.1\pm0.1)\times10^{-3}$; $f^{D\to \pi}_+(0)=0.62\pm0.03$ and $|V_{cd}|=0.244\pm0.005\pm0.003\pm0.008$. As a by-product, a numerical estimate for the decay constant $f_D$ is yielded as $f_{D}=190^{+12}_{-11}\mathrm{MeV}$.