B->eta(') Form Factors in QCD

Abstract

We calculate the semileptonic form factors $f_{+}^{B\to \eta }(q^2)$ and $f_{+}^{B\to {\eta }^{\prime }}(q^2)$ from QCD sum rules on the light-cone (LCSRs), to NLO in QCD, and for small to moderate q^2, $0\le q^2\le 16{\mathrm{GeV}}^2$. 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)${}_{\mathrm{A}}$ anomaly, couple directly to $\text{etap}$. 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 $f_{+}^{B\to {\eta }^{\prime }}$ 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 $\mathcal{B}(B\to {\eta }^{\prime }e\nu )/\mathcal{B}(B\to \eta e\nu )$ to better constrain the size of the singlet contribution.

Comments: 21 pages; version to appear in JHEP