$B\to D_0^{\ast }$ and $B_s\to D_{s0}^{\ast }$ form factors from QCD light-cone sum rules

Abstract

We present the first application of QCD light-cone sum rules (LCSRs) with $B_{(s)}$-meson distribution amplitudes to the $B_{(s)}\to D_{(s)0}^{\ast }$ form factors, where $D_{(s)0}^{\ast }$ is a charmed scalar meson. We consider two scenarios for the $D_0^{\ast }$ spectrum. In the first one, we follow the Particle Data Group and consider a single broad resonance $D_0^{\ast }(2300)$. In the second one, we assume the existence of two scalar resonances, $D_0^{\ast }(2105)$ and $D_0^{\ast }(2451)$, as follows from a recent theoretically motivated analysis of $B\to D\pi \pi$ decays. The $B\to D_0^{\ast }$ form factors are calculated in both scenarios, also taking into account the large total width of $D_0^{\ast }(2300)$. Furthermore, we calculate the $B_s\to D_{s0}^{\ast }$ form factors, considering in this case only the one-resonance scenario with $D_{s0}(2317)$. In this LCSRs calculation, the $c$-quark mass is kept finite and the $s$-quark mass is taken into account. We also include contributions of the two- and three-particle distribution amplitudes up to twist-four. Our predictions for semileptonic $B\to D_0^{\ast }\ell {\nu }_{\ell }$ and $B_s\to D_{s0}^{\ast }\ell {\nu }_{\ell }$ branching ratios are compared with the available data and HQET-based predictions. As a byproduct, we also obtain the $D_0^{\ast }$- and $D_{s0}^{\ast }$-meson decay constants and predict the lepton flavour universality ratios $R(D_0^{\ast })$ and $R(D_{s0}^{\ast })$.

Comments: 28 pages, 3 figures, table added, minor corrections