B->eta(') Form Factors in QCD

TL;DR

This paper calculates B to eta and eta' semileptonic form factors using QCD sum rules, including the singlet contribution, revealing its significant impact on eta' form factors and proposing experimental ratios for better constraints.

Contribution

It introduces the first calculation of singlet contributions to B to eta and eta' form factors within QCD sum rules, highlighting their importance.

Findings

Singlet contribution to $f_+^{B o ext{eta}'}$ can be up to 20%.

Singlet contribution to $f_+^{B o ext{eta}}$ is below 3%.

Proposes measuring the ratio of branching fractions to constrain singlet effects.

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.