Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2007-06-25
JHEP 0708:025,2007
Physics
High Energy Physics
High Energy Physics - Phenomenology
21 pages; version to appear in JHEP
Scientific paper
10.1088/1126-6708/2007/08/025
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.
Ball Patricia
Jones Gareth Warren
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