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

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 $\overline{MS}$ masses are employed for the underlying heavy quarks. With the updated inputs and experimental data, we have $f_{+}^{B\to \pi }(0)=0.28_{-0.02}^{+0.05}$ and $|V_{ub}|=(3.4_{-0.6}^{+0.2}\pm 0.1\pm 0.1)\times 10^{-3}$; $f_{+}^{D\to \pi }(0)=0.62\pm 0.03$ and $|V_{cd}|=0.244\pm 0.005\pm 0.003\pm 0.008$. As a by-product, a numerical estimate for the decay constant $f_D$ is yielded as $f_D=190_{-11}^{+12}\mathrm{MeV}$.

Comments: 23 pages, 4 figures, 3 tables, published in JHEP