Abstract
In the framework of the QCD light-cone sum rules (LCSRs) we present the
analysis of all \$B, B\_s\eta^(\prime)\$ and \$D, D\_s\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
\eta^(\prime)\$ and \$D, D\_s \eta^(\prime)\$ relevant for processes
like \$B \eta^(\prime) \nu\_\tau\$ or \$B\_s \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^+0.042\_-0.047\$, \$|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\$. Also phenomenological predictions for semileptonic
\$B, B\_s\eta^(\prime)\$ and \$D, D\_s\eta^(\prime)\$ decay modes are
given.
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