$B_{(s)}\to S(a_0(1450),K_0^{\ast }(1430),f_0(1500))$ helicity form factors within QCD light-cone sum rules

Abstract

In this paper, we investigate the helicity form factors (HFFs) of the $B_{(s)}$-meson decay into a scalar meson with a mass larger than 1~GeV, {\it i.e.,} $B\to a_0(1450)$, $B_{(s)}\to K_0^{\ast }(1430)$ and $B_s\to f_0(1500)$ by using light-cone sum rules approach. We take the standard currents for correlation functions. To enhance the precision of our calculations, we incorporate the next-to-leading order (NLO) corrections and retain the scalar meson twist-3 light-cone distribution amplitudes. Furthermore, we extend the HFFs to the entire physical $q^2$ region employing a simplified $z$-series expansion. At the point of $q^2=1\mathrm{Ge}{\mathrm{V}}^2$, all NLO contributions to the HFFs are negative, with the maximum contribution around $25\%$. Then, as applications of these HFFs, we analyze the differential decay widths, branching ratios, and lepton polarization asymmetries for the semi-leptonic $B_{(s)}\to S\ell \bar{\hat{I}}{½}_{\ell }$, FCNC $B_{(s)}\to S\ell \bar{\ell }$ and rare $B_{(s)}\to S\hat{I}½\bar{\hat{I}}½$ decays. Our results are consistent with existing studies within uncertainties. The current data still suffer from large uncertainties and need to be measured more precisely, which can lead to a better understanding of the fundamental properties of light scalar mesons.

26 pages, 7 figures, Matches published version