$B\to D\ell {\nu }_{\ell }$ form factors beyond leading power and extraction of $|V_{cb}|$ and $R(D)$

Abstract

We investigate the subleading-power corrections to the exclusive $B\to D\ell {\nu }_{\ell }$ form factors at $\mathcal{O}({\alpha }_s^0)$ in the light-cone sum rules (LCSR) framework by including the two- and three-particle higher-twist contributions from the $B$-meson light-cone distribution amplitudes up to the twist-six accuracy, by taking into account the subleading terms in expanding the hard-collinear charm-quark propagator, and by evaluating the hadronic matrix element of the subleading effective current $\bar{q}{\gamma }_{\mu }i/D_{\perp }/(2m_b)h_v$. Employing further the available leading-power results for the semileptonic $B\to D$ form factors at the next-to-leading-logarithmic level and combining our improved LCSR predictions with the recent lattice determinations, we then carry out a comprehensive phenomenological analysis on the semi-leptonic $B\to D\ell {\nu }_{\ell }$ decay. We extract $|V_{cb}|=\left(40.2_{-0.5}^{+0.6}{|}_{\mathrm{th}}{}_{-1.4}^{+1.4}{|}_{\exp }\right)\times 10^{-3}$ ($|V_{cb}|=\left(40.9_{-0.5}^{+0.6}{|}_{\mathrm{th}}{}_{-1.0}^{+1.0}{|}_{\exp }\right)\times 10^{-3}$) using the BaBar (Belle) experimental data, and particularly obtain for the gold-plated ratio $R(D)=0.302\pm 0.003$.

arXiv comment28 pages plus appendices and references, 6 figures; v2: matches published version

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