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

In the framework of the QCD light-cone sum rules (LCSRs) we present the analysis of all $B,B_s\to {\eta }^{(\mathrm{\prime })}$ and $D,D_s\to {\eta }^{(\mathrm{\prime })}$ form factors ($f^{+},f^0$ and $f^T$) by including $m_{{\eta }^{(\mathrm{\prime })}}^2$ 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 $B\to {\eta }^{(\mathrm{\prime })}\tau {\nu }_{\tau }$ 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: $f_{B\eta }^{+}(0)=0.168_{-0.047}^{+0.042}$, $|f^+{B_s\eta}(0)|= 0.212^{+0.015}{-0.013}$,$f^+{B\eta^\prime}(0)= 0.130^{+0.036}{-0.032}$,$f^+{B_s\eta^\prime}(0)= 0.252^{+0.023}{-0.020}$and$f^+{D\eta}(0)= 0.429^{+0.165}{-0.141}$,$|f^+{D_s\eta}(0)|= 0.495^{+0.030}{-0.029}$,$f^+{D\eta^\prime}(0)= 0.292^{+0.113}{-0.104}$,$f^+{D_s\eta^\prime}(0)= 0.558^{+0.047}{-0.045}$\mathrm{.}Alsophenomenologicalpredictionsforsemileptonic$B, B_{s}\to \eta^{(\prime)}$and$D, D_{s}\to \eta^{(\prime)}$ decay modes are given.