B->eta(') Form Factors in QCD

Abstract

We calculate the semileptonic form factors $f_+^{B\to \eta}(q^2)$ and $f_+^{B\to \eta'}(q^2)$ from QCD sum rules on the light-cone (LCSRs), to NLO in QCD, and for small to moderate q^2, $0\leq q^2\leq 16 {\rm GeV}^2$. We include in particular the so-called singlet contribution, i.e.\ weak annihilation of the B meson with the emission of two gluons which, thanks to the U(1)$_{\rm A}$ anomaly, couple directly to $\etap$. This effect is included to leading-twist accuracy. This contribution has been neglected in previous calculations of the form factors from LCSRs. We find that the singlet contribution to $f_+^{B\to \eta'}$ can be up to 20%, while that to $f_+^{B\to \eta}$ is, as expected, much smaller and below 3%. We also suggest to measure the ratio ${\cal B}(B\to\eta' e \nu)/{\cal B}(B\to \eta e \nu)$ to better constrain the size of the singlet contribution.