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

TL;DR

This paper calculates the form factors for B, Bs, D, and Ds decays into eta and eta' mesons using QCD light-cone sum rules, including various corrections and contributions, providing new results for these transition form factors.

Contribution

It presents the first comprehensive calculation of all relevant form factors for B, Bs, D, and Ds to eta and eta' transitions with detailed QCD corrections and two-gluon contributions.

Findings

Provided numerical values for all relevant form factors at zero momentum transfer.

Included SU(3)-flavour breaking and axial anomaly effects in the calculations.

Made phenomenological predictions for semileptonic decay modes involving eta and eta'.

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: $f^+_{B\eta}(0)= 0.168^{+0.042}_{-0.047}$, $|f^+_{B_s\eta}(0)|= 0.212^{+0.015}_{-0.013}$, $f^+_{B\eta^\prime}(0)= 0.130^{+0.036}_{-0.032}$, $f^+_{B_s\eta^\prime}(0)= 0.252^{+0.023}_{-0.020}$ 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 $B, B_{s}\to \eta^{(\prime)}$ and $D, D_{s}\to \eta^{(\prime)}$ decay modes are given.