Form factors of B, Bs -> eta, eta' and D, Ds -> eta, eta' transitions from QCD light-cone sum rules

Abstract

In the framework of the QCD light-cone sum rules (LCSRs) we present the analysis of all $B,B_s\to {\eta }^{(\prime )}$ and $D,D_s\to {\eta }^{(\prime )}$ form factors ($f^{+},f^0$ and $f^T$) by including $m_{{\eta }^{(\prime )}}^2$ corrections in the leading (up to the twist-four) and next-to-leading order (up to the twist-three) in QCD, and two-gluon contributions to the form factors at the leading twist. The SU(3)-flavour breaking corrections and the axial anomaly contributions to the distribution amplitudes are also consistently taken into account. The complete results for the $f^0$ and $f^T$ form factors of $B,B_s\to {\eta }^{(\prime )}$ and $D,D_s\to {\eta }^{(\prime )}$ relevant for processes like $B\to {\eta }^{(\prime )}\tau {\nu }_{\tau }$ or $B_s\to {\eta }^{(\prime )}{l}^{+}{l}^{-}$ are given for the first time, as well as the two-gluon contribution to the tensor form factors. The values obtained for the $f^{+}$ form factors are as follows: $f_{B\eta }^{+}(0)=0.168_{-0.047}^{+0.042}$, $|f_{B_s\eta }^{+}(0)|=0.212_{-0.013}^{+0.015}$, $f_{B{\eta }^{\prime }}^{+}(0)=0.130_{-0.032}^{+0.036}$, $f_{B_s{\eta }^{\prime }}^{+}(0)=0.252_{-0.020}^{+0.023}$ and $f_{D\eta }^{+}(0)=0.429_{-0.141}^{+0.165}$, $|f_{D_s\eta }^{+}(0)|=0.495_{-0.029}^{+0.030}$, $f_{D{\eta }^{\prime }}^{+}(0)=0.292_{-0.104}^{+0.113}$, $f_{D_s{\eta }^{\prime }}^{+}(0)=0.558_{-0.045}^{+0.047}$. Also phenomenological predictions for semileptonic $B,B_s\to {\eta }^{(\prime )}$ and $D,D_s\to {\eta }^{(\prime )}$ decay modes are given.

Comments: 36 pages, 9 figures. Erroneously given uncertainties of the parameters alpha in Eq. (6.2) and (6.3) are corrected